Global Thinkers: Physics and Chemistry 4. Secondary (sample)

SECONDARY EDUCATION

J.M. Vílchez

A.M.ª Morales

G. Villalobos

P. Tonda

L. Garrido

Chemist4 ry and Physics sample

Scientific activity

The scientific method and a hypothesis

1. Scientific research

2. Physical quantities and units

3. Measuring physical quantities. Errors

4. Analysing experimental data

Guidelines Problem solving Research project

Recreational science Thought experiments

Practical work Can you talk about ‘the density’ of modelling clay? Understand

1 The atom and the periodic table

The complexity of an atom

1. Discreteness of matter

2. Discoveries that allowed the idea of the atom to evolve

3. The first atomic models

4. Atomic spectra and the Bohr model

5. Quantum model of the atom

6. The periodic table of the chemical elements

7. Atomic masses

Guidelines Problem solving

ICT Atomic models

Recreational science The petites Curie

Practical work Cathode rays and Discharge tubes

2 Chemical bonds and intermolecular forces

Chemical bonds

1. The chemical bond

2. Ionic bonds

3. Covalent bonds

4. Intermolecular forces

5. Metallic bonds

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3 Compounds of carbon

Convenient carbon

1. The carbon atom

2. Allotropes of carbon

3. Formulas and molecular models

4. Hydrocarbons

5. Compounds of carbon with oxygen and nitrogen

6. Molecules of special interest

ICT ICT helps you consolidate knowledge Recreational science

polystyrene

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4 Chemical reactions: foundations

When the miracle became science

1. Chemical changes

2. Reaction rate

3. Amount of substance

4. Stoichiometric calculations

5. Energy in chemical reactions

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6. Industrial, biomedical and technological applications Guidelines Problem solving

ICT Simulating chemical reactions

Recreational science The oxidation reaction of iron

Practical work Factors that affect the reaction rate

5 Some important chemical reactions

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6. Summary of the properties of chemical compounds

Guidelines Problem solving

ICT Spreadsheets and web resources

Recreational science Types of substances

Practical work Determining the type of bonds

Understand

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One chemical reaction, two approaches, and the birth of modern chemistry

1. Acids and bases

2. Combustion reactions

3. Importance of combustion reactions

4. Oxidation reactions

5. Importance of oxidation reactions

6. Synthesis reactions

Guidelines Problem solving

ICT Graphs

Recreational science Home-made PH indicators

Practical work Identifying CO2 in combustion

Understand, reflect and test your skills

9 Forces in fluids. Pressure

Roman cisterns: evidence of an understanding of pressure

1. Pressure

6 Kinematics

1.

2.

3.

4.

5.

6.

7 Newton’s laws of motion

3.

4.

8 Forces in the universe

168 The universe; the great unknown

1. Historical evolution of the study of the universe

2. Gravitational forces

3. Applications of the universal law of gravity

4. Artificial satellites in orbit

Guidelines Problem solving

ICT Stellarium

Recreational science Simulation of Einstein’s theory of gravity

Practical work Finding celestialobjects Understand, reflect and test your skills

2. Hydrostatic law

3. Archimedes’ principle

4. Pascal’s law

5. Atmospheric pressure

6. Meteorological concepts

Guidelines Problem solving

ICT Online interactive application

Recreational

10 Mechanical energy and work

A modern concept of energy

1. Energy

2. Work

3. Power

4. Kinetic energy

5. Potential energy

6. Conservation of mechanical energy

7. Energy transport via mechanical waves

Guidelines Problem solving

ICT Working with spreadsheets

Recreational science The sun as a renewable energy source

Practical work The sun as a renewable energy source

11 Thermal energy and heat

Heat: an invisible substance or an energy transfer?

1. Thermal energy. Temperature

2. Thermal equilibrium. Heat and heat transfer

3. Effects of heat

4. Heat engines

5. Energy loss

6. Energy and society

Guidelines Problem solving

ICT Geogebra

Recreational science Building a spectroscope

Practical work Water’s latent heat of fusion

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SCIENTIFIC ACTIVITY

THE SCIENTIFIC METHOD AND A HYPOTHESIS

In 1821, following several failed experiments, Thomas J. Seebeck discovered a fascinating connection between heat and electricity when he welded a copper and a bismuth wire together in a loop. He noticed that when one of the metals was heated at a high temperature, while the other was kept at a lower temperature, a magnetic field was formed. Although at the time Seebeck did not realise that there was an electrical current involved, shortly afterwards Danish physicist Hans Christian Ørsted, who was involved in investigations to prove the connection between electricity and magnetism, noticed a small voltage due to the temperature gradient generated. This effect was eventually called the ‘thermoelectric effect” or ‘Seebeck effect’ in honour of the person who discovered it.

This brief glance at history shows us the importance of collaboration in scientific research and the mistakes that

can be made either during the research process or when interpreting findings. Are you surprised by these insights into scientific research? What else would you add?

READING AND LISTENING

1 In the text, what vocabulary is used to describe the process of scientific discovery? What is the overall impression that it gives you about the scientific process?

2 The conclusion states that the anecdote shows the:

• importance of collaboration

• the possibility for making mistakes

What parts of the text support these conclusions?

3 Although the scientific method is consistent, humans still make mistakes. Why does this happen?

LANGUAGE BANK SPEAKING

4 In 2010, a European company developed a prototype of waterproof boots, called Power Wellies, that generate electrical energy using the thermoelectric effect. Search the Internet for information on this prototype and its potential applications.

a) Discuss how these boots generate electricity with a classmate.

b) Could the same effect be applied to a different object? What would you choose and why?

This technology could have applications in agriculture. Animal’s heat could generate electricity to use on the farm.

What about other types of clothing? Maybe your coat could generate electrical energy to warm itself up.

WRITING

5 The prototype of waterproof boots discussed above and thermal power plants both use heat to generate electrical energy. Write a report discussing thermoelectric technology in relation to SDG targets 3.9, 13.3 and 13.a. Make sure to include the following points:

• Positives of thermoelectric technology

• Negatives of thermoelectric technology

• How thermoelectric technology relates to the SDG

• A conclusion in which you say whether the overall impact is positive or negative

CHALLENGES THAT LEAVE AN IMPRINT

LEARNING SEQUENCE

GAME 1. TYPE A. THE SCIENTIFIC METHOD

1.1 Propose a hypothesis related to a scientific or pseudoscientific piece of news that can be resolved through a simple investigation on the Internet.

1.2 Design the physical card that will contain the hypothesis and where the players will enter the result (if it is correct, they will mark value 1; if incorrect, value 0), and contains the address of the website where they should consult the news item.

GAME 2. TYPE B. MAGNITUDES AND MEASURES

2.1 Think of an activity in which you have to measure a physical quantity with a measuring instrument.

2.2 Players must calculate the relative error that is made and express the complete result in scientific notation. The exponent of the power of 10 will be the digit sought.

2.3 Design the card with the clues for the players, write on it the measured result and leave it next to the measuring instrument.

CREATE AN EQUATION

The escape room cannot be solved until the first three units have been finished, but now the keys that help solve the enigma will be determined:

3.1 The digits 1 and 0 obtained in the type A games of the three units of the book will make a binary number that corresponds to the first two numbers of the padlock combination.

3.2 The equation that will give the last two digits of the combination will come out.

SAFETY STANDARD SHEETS

For more each type B game, a card will be designed with the essential safety regulations to be able to carry it out. Players will find those tokens next to each of the microgames.

+ for more guidelines, go to anayaeducacion.es

SCIENTIFIC RESEARCH

Correlation and causation

Correlation is the relationship between two variables and causation means one causes the other. They must not be confused, because although two variables are related, it does not imply causation between them. For instance, rain and lightning are related. It is more likely that there is lightning when it rains, but rain is not the cause of lightning or vice versa. There is a correlation between these two variables, but no causation.

Causation is one of the postulates of science. The scientific method often seeks to establish cause-effect relations. That is why experiments use controlled variables, which you will learn about later on.

1.1 The scientific method

Sometimes you will hear it said that ‘science is defined by its method’. But what is science, and what is its method?

The first part of the question is not easy to answer, and it may not even be the right question as ‘science’ refers to many scientific disciplines with different characteristics. Despite that, they all generate reliable knowledge that enables us to better understand our surroundings and, just as importantly, to act on them. We will return to these questions later.

The answer to the second part of the question is not simple, either. The methods of generating scientific knowledge can vary and differ in complexity. The scientific method, a term that includes all these methods, does not consist of a series of steps to follow rigorously in the right order until you discover the laws of science. Instead, it is a system of requirements to ensure the reliability of the final conclusions.

Today, the convention is that the scientific method has steps, some of which require large doses of creativity. A simplified outline of the method appears in the figure below.

The process arises from the necessity of answering a question or explaining a fact which is not easily explained with existing theoretical knowledge.

To answer a question, you produce a hypothesis and test it by running experiments. lf the experiments confirm the hypothesis, the hypothesis advances. Otherwise, you must produce a new hypothesis and start the whole process again

A problem or question arises when an observation of reality does not match previously existing scientific knowledge. Hypotheses are possible explanations of the problem (conjectures).

To test whether a hypothesis answers the question, scientists often run experiments, though it is not always possible or necessary.

Experiments produce data that, once analysed, allow evidence-based conclusions to be drawn that can confirm or contradict the hypothesis. In the first instance, the hypothesis could be considered a law or part of a scientific theory.

Sometimes, if it is difficult to test a hypothesis, scientists test consequences that can be deduced from the hypothesis That is why we sometimes refer to the hypothetico-deductive method.

1.2 Hypotheses, laws and theories

Hypotheses, laws and theories are terms with different meanings.

As we have seen, hypotheses In other words, they are possible explanations for problems that need to be solved. It is important to note that for a hypothesis to be scientific, it must be testable against reality

When a hypothesis is confirmed and accepted by the scientific community, which may not occur immediately, it becomes part of scientific knowledge.

It may do so as a scientific law, which describes patterns of the phenomena studied; or as part of a scientific theory, a system of hypotheses and rules by which we explain such patterns.

In summary, laws describe and theories explain. They can never change from one to the other, because they are different types of knowledge.

In this section, the meanings of hypothesis, law and theory in scientific terminology have been shown. These terms have other everyday meanings, so be aware of using them correctly depending on the context.

An example of laws and theories

In previous years you have studied some fundamental laws of chemistry, in particular the law of conservation of mass and the law of definite proportions.

The first, stated by A. Lavoisier in 1785, states that mass is neither created nor destroyed in a chemical reaction.

The second, stated by J. L. Proust ten years later, states that when two or more elements combine to form a compound, they always do it in the same proportion.

Both are empirical laws, emerging from experiments that describe the behaviour of matter in chemical reactions, without any apparent connection.

The first to explain them was J. Dalton, in 1808, when he described his atomic theory. Dalton’s atomic theory, apart from explaining these laws and including them in the theory, served as a guide for subsequent research.

In fact, when Dalton established his law of multiple proportions, he did it guided by his atomic theory, which he already had in mind

Atomic theory is a clear example of how the scientific community does not immediately accept scientific knowledge. Although Dalton published it in 1808, there are books by prestigious authors at the end of that century that do not mention the atom.

1 Explain in your own words how scientific knowledge arises and evolves.

2 In the following passage, identify the steps of the scientific method (adapted from the book Great Ideas of Science, by Isaac Asimov):

"At the end of the 18TH CENTURY people thought that heat was a weightless fluid called caloric and that warmer bodies had more of it. At the time, B. Thompson, who worked in a cannon factory, wondered why both the metal and the drill bit warmed up when he drilled metal. The hypothesis at the time was that by breaking the metal, the caloric escaped. But Thompson was not content with that and tried drilling the metal with a dull bit. He found that, despite not breaking the metal, both parts still heated up. This made him see that the caloric was not escaping from broken metal, and that maybe the heat did not come from the metal, which started out cold. Finally, he concluded that heat was not a fluid, but a type of motion.’

3 Why is Galileo Galilei considered the father of modern science? Look for information and justify the reliability of your sources.

4 Why do we talk about the law of conservation of mass instead of the theory of conservation of mass? And why do we talk about Dalton's atomic theory and not Dalton's atomic law?

5 Logic wheel. Old books refer to Avogadro’s hypothesis and more modern ones refer to Avogadro’s law. What do you think the reason is?

6 Analyse the different meanings of the term 'theory' in the Oxford English Dictionary. Which is the closest to the definition in this book? With which other word could it be confused?

7 In many television series, to solve a problem, the characters say they have ‘a theory'. Are they using the word the correct way, from a scientific terminology viewpoint? What word might be better? Explain your answer.

8 Name a physical theory and a physical law, different to those discussed on these pages, and explain why they are what they are. lf you need to, review some of the material studied in previous years.

9 Summarise in a couple of sentences the text on Dalton’s atomic theory, explaining the main ideas in relation to the content of these pages.

Focus on English

When we write a hypothesis in English, we normally write it using either the first conditional or the second conditional We use the first conditional when it is a hypothesis that is very likely to be true. For example, if the temperature drops, the water will turn into ice. We use the second conditional when we are less sure that something is true. For example, if technology advanced sufficiently, we would travel to Mars.

1.3 Scientific knowledge

A few centuries ago the evolution of scientific knowledge was attributable to individuals. Nowadays, it emerges from a collective activity in which many men and women dedicate their effort in multidisciplinary teams.

Scientific knowledge, characterised by its method, is reliable knowledge since it meets the following conditions:

• It can be tested against reality

For knowledge to be considered scientific, it must be able to be tested against reality. In other words, we must be able to test whether what is being explained happens in nature. And with good reason, as one of the principal objectives of science is to explain the world around us. The previous requirement implies another characteristic of scientific knowledge: the experiments from which it arises must be reproducible. In other words, it must be possible to repeat the experiment as many times as necessary and the results must agree each time.

• It is evidence-based

The final conclusions must be based on evidence collected from experiments. Scientific knowledge cannot be based on beliefs or ideologies because then it would not be testable. Testing against reality, reproducibility and the use of evidence to draw conclusions are characteristics that enable us to distinguish between scientific knowledge and other types of knowledge.

Problem solved

1 On a website you can read the following text. Is it scientific knowledge?

'The law of attraction is the belief that thoughts influence a person's life, and that like energy can attract like energy, Advocates of this law believe that a person's thoughts lead to emotions, beliefs and consequences. The process is called harmonic vibrations of the law of attraction.

Some followers of this belief claim that the law of attraction is a universal law because it applies to everybody without exception, and people cannot choose whether to apply it or not'.

Adapted and translated from the Wikipedia search "The law of attraction".

Although the text uses scientific terms such as law, energy and vibrations), its content does not qualify as scientific knowledge.

The text lacks scientific characteristics. Even if you could argue that it is somehow testable or based on evidence (someone else’s evidence, with a large degree of subjectivity), this knowledge is not reproducible since the same results will not always occur.

Furthermore, the last paragraph asserts that the ‘law’ is a belief (something considered true without first-hand knowledge or without evidence). The claims made are not experimentally verifiable.

Many of the messages you receive in your daily life contain scientific terminology to give them authority. But, as you have seen, that is not enough to make them scientific.

1.4 Experimentation

Experimentation characterises scientific knowledge. That said, it is not always possible to use experiments. In an experiment we reproduce a phenomenon and control the variables. To do so, we keep all the quantities in the phenomenon constant except for one. Then we test how changing that quantity affects the result. While measuring the data is an activity that is part of experimentation, it is not an experiment. For example, astronomy is a discipline in which experimentation is impossible. Therefore, we must be content with analysing measurements of electromagnetic radiation from space. There are also occasions when, given the difficulty of designing an experiment, we resort to thought experiments. These involve using our imagination and existing scientific knowledge to draw conclusions consistent with what we already know

The box on the right shows an adapted excerpt from Galileo's Dialogues, written in 1632, in which Salviati (representing Galileo) explains the law of inertia to Simplicius using a thought experiment.

Thought experiment for the law of inertia

SALVIATI Hitherto you have explained to me the accidents of a body on two different planes. On a declining plane, the body moves spontaneously, accelerating continually. On a plane sloping upwards, the motion would be continually decreasing and retarding until it disappears. Now tell me, what would befall the same body upon a surface that had neither acclivity nor declivity?

SIMPLICIUS. There being no declivity, there can be no natural inclination to motion; and there being no acclivity, there can be no resistance to being moved; therefore, I think it ought naturally stand still.

SALVIATI. So I think, provided one did lay it down gently; but if it had an impetus directing it towards any part, what would follow?

SIMPLICIUS. That it should move towards that part.

SALVIATI. But with what sort of motion?

SIMPLICIUS. I see no cause for acceleration or retardation.

SALVIATI. How long therefore would you have the body move?

SIMPLICIUS. As long as that surface, neither inclined nor declined, shall last.

SALVIATI. Therefore if such a space were interminate, the motion upon it would be perpetual?

SIMPLICIUS. I think so, if the body is of a durable matter.

10 A magnetic necklace factory uses the following advertising message:

Electromagnetic energy has beneficial properties for the body and a new product brings all these properties together: magnetic necklaces. These necklaces are an innovative combination of three of the latest technologies: magnetic technology, which uses tiny magnets that, activated by the Earth’s magnetic field, stimulate the metabolism; long wave infrared technology, which reflects negative energy by a gradual warming effect; and natural anion technology, which releases the type of ions found in forests and lakes, bringing you the same relaxing sensation felt there.

Extract the scientific terminology. Is it scientific knowledge? Why/why not?

11 Of the scientific terms in the previous exercise, which use scientific concepts inappropriately? Explain your reasoning.

12 In the laboratory, you put ice in a beaker and warm it with a bunsen burner At regular time intervals you measure the temperature until all the water has evaporated and you plot the data on a temperature time graph. When you leave the laboratory could you say that you had conducted an experiment? Why/why not?

13 Search for information on 'Newton's orbital cannon'. What was Newton trying to explain with this cannon? Is it a thought experiment? Why/why not?

14 1-2-4. Explain in your own words what is meant by a 'control variable'.

15 Read Galileo's thought experiment on the law of inertia again. Explain what the conclusion of the experiment is.

16 In astronomy we can only observe and measure (we cannot reproduce a star in the laboratory). That said, we can produce hypotheses to explain what we observe. Summarise in a few sentences what observations produced the hypotheses of ‘dark matter’ and ‘dark energy'.

Understand, think, investigate…

Draw and explain

Using the billiard ball model with different levels of abstraction, draw a vessel containing water vapour.

1.5 Scientific models

Reality, the object of scientific study, is very complex. The movement of a leaf falling from a tree or the behaviour of gas in a container are examples of phenomena that are difficult to explain with both accuracy and precision. In such cases, science relies on scientific models.

A scientific model is an abstract, simplified representation of reality and is used to obtain a preliminary approach in the study of phenomena. Thus in the previous examples, to locate a leaf during its fall we use a material point system and for the behaviour of a gas, the ideal gas model (box below).

Furthermore, depending on the study, models may have different levels of abstraction, as you can see in the following figures.

Scientific models: some examples

Material point

To study an object’s trajectory, it is possible to ignore its shape and assume that all its mass is concentrated at a point at the centre of mass. This is called a point object or point particle, as shown in figure I. lf the object is homogeneous, the centre of mass is at the geometric centre.

This model would not be valid to describe an object’s rotation, but it is for finding its location.

Ideal gas

To study the behaviour of a gaseous system, we assume that its constituent particles only interact with the walls of their containers.

That is not what really happens, since the particles also interact with each other. However, even while ignoring those interactions, it is possible to obtain an approximate explanation of the behaviour of the gas.

To represent the particles in a gas, we use a billiard ball model, which has different levels of abstraction.

• First level of abstraction

lf each ball in figure II represents an air particle, these may be either nitrogen or oxygen (molecules) or any of the minor components (atoms or molecules).

• Second level of abstraction

To distinguish them, we use models such as that in figure III, in which each ball represents an atom rather than a molecule.

Atomic models

Although they are not used in ideal gas models, at another level of abstraction, we can represent atoms as more complex models. In these we distinguish between the nucleus and the electron layer, or the parts of the nucleus. You studied some of these in previous years and will study others this year

I.

Translational motion is studied by assuming that an object’s mass is concentrated at its centre of mass

II.

In this model, each ball, regardless of whether they are atoms or molecules, represents a particle of gas.

In this case, in which we can see the structure of each air particle, each ball represents an atom.

1.6 Science, technology and society

So far, we have only discussed scientific knowledge, but we should not forget that science, technology and society have always been connected

Science and technology have always gone hand in hand and developed together. At times, scientific research has had to wait until the right technology has become available (better measuring instruments, for example), which was made possible thanks to scientific research (for example, researching the material components necessary to build said instruments).

Society can influence the type of research done, depending on its demands or needs. What is more, research projects can require large amounts of funding, which in turn can require the participation of several countries.

lt is difficult to discuss scientific knowledge without also discussing technological development and social interests. The study of these together is known as Science, Technology and Society STS studies.

As a result, when we analyse scientific knowledge we must also take into account technological development and society at the time.

Understand, think, investigate…

17 Write around What model appears in the following figure? What does each ball represent? Apart from models, with what other previous sections could they be related? Justify your answer.

Basic research

At the end of a lecture in which M. Faraday had demonstrated his experiments with electromagnetic induction, somebody asked him “What good it is?”, to which he replied: “What good is a newborn baby?”

We tend to believe that scientific research, a priori, must have some intended use. Yet this is not the case, because scientists often conduct basic research without immediate practical, economic or social goals, with the sole objective of gaining more knowledge about our environment.

This does not mean that the results of this research is useless, especially with the right technological development. For example, Faraday’s electromagnetic induction made it possible for us to have electricity in our homes today.

18 Draw the atomic models of Thomson and Rutherford What are the similarities and differences? Which is closer to reality? How do we know this? ls it a true representation?

19 In many books you will find images similar to the one below to represent the solar system. Is it a model? Why/ why not? With what you know from previous years, what criticisms of it could you make?

20 When the possible discovery of the Higgs boson was published in 2012, some asked what it was good for: Find out and respond to these people.

Michael Faraday, during one of his demonstrations.

PHYSICAL QUANTITIES AND UNITS

2.1 Scalar and vector quantities

Remember that in past years we learned that:

• A physical quantity is any property of a material that can be quantified in an objective manner

• The unit of a physical quantity is whatever arbitrary quantity has been adopted as standard.

There are physical quantities that are described by a number followed by a unit. So if someone told you a film lasted 98 minutes or that they had bought 250 grams of popcorn, you would understand perfectly. These quantities, such as time and mass, a called scalar quantities.

Scalar quantities are defined by a numeric value followed and a corresponding unit.

But there are other quantities that contain more information. If someone asked you to throw an object at 2 km/h, would you know what to do? Upon reflection, you’d easily reach the conclusion that you need more information, specifically the direction in which to throw the object.

Force diagram

Using the point mass model, draw a body on which three forces are acting: one horizontal, one in the opposite direction and double in magnitude, and another perpendicular to both and half the first in magnitude.

Someone could tell you, for example, to throw the object upwards (direction) and at 2 km/h (magnitude). These quantities, such as velocity, are called vector quantities.

Vector quantities are defined by a direction and magnitude.

Vector quantities, such as velocity, acceleration or force, are represented by arrows with an orientation called vectors (see below).

Magnitude

To specify that a quantity is a vector, we put a small arrow above the symbol of the quantity (for example, v would be the velocity vector). A vector in bars () v ;; , or the quantity symbol on its own (v) refers to the magnitude of the vector.

To define a vector quantity, you must provide the following information:

• Base point. This is the point where the vector acts. For example, the centre of mass of an object.

• Direction. This is the line along which a vector acts and its orientation in space. For example, a horizontal line moving to the right.

• Magnitude. This is proportional to the length of the vector and is expressed with a numeric value followed by the matching unit. For example, 2 km/h.

In English, ‘direction’ as it applies to motion contains two kinds of information: the axis of movement and which way along the axis the movement occurs.

Graphic representation of vector quantities. Vectors

2.2 Vector operations

To add, for example, two values of time, all you need to do is to add their numeric values, convert them to the same unit of measurement and give the result in the same unit.

So if you watch a 98-minute film, take 10 minutes to say goodbye to your friends and 15 minutes to get home, you will get home 123 minutes after the start of the film. Likewise, to multiply a scalar magnitude, all you need to do is to multiply it by the number in question (so if you watch the film twice, you will have been watching it for 196 minutes).

However, to calculate mathematical operations with vector quantities, you must take into account the direction, as you can see in ‘Problem solved 2’.

The supplement to this book demonstrates how to perform some operations with vectors (the ones you’ll need this year). Consult it when you need to obtain vector calculations.

Do not forget that to add or subtract quantities, whether they are scalar or vector, you must always express them in the same units. Otherwise, the result will be incorrect.

To do that, we recommend that when you substitute data in an equation, don’t just write the numeric values: include the units. You will then avoid making errors (for example, you cannot add metres to millimetres without converting them to the same unit).

Understand, think, investigate…

21 Below is a list of some quantities with which you will work this year For each one, decide whether it is a scalar quantity or vector quantity and explain the reasons for your choice: mass, time, length, force, velocity, acceleration, pressure, energy, work, and heat

22 Choose one of the vector quantities from the previous exercise and draw the vector that represents it, applying it to a point object. Describe the elements of the vector and explain what a point object is.

23 The cruising speed of an airplane in calm air is 600 km/h What would happen if it flew in a 10 km/h tailwind? And with a headwind? Draw, in both cases, the velocity vectors of the airplane and the air.

Problem solved

2 Two forces act on an object, one 40 N northward and the other 20 N eastward. What is the sum of both forces?

You should not think that the answer is 60 N, because the forces are vector quantities. That is why, in addition to their magnitudes, we provide their axes and directions.

First, we draw the vectors and the vector sum or result, R (see supplement if you need it):

In this case, in which the forces are perpendicular, it’s possible to calculate the magnitude of the vector sum, R, by using the Pythagorean theorem:

But this is just the magnitude. You must also indicate that the resulting force is pointed towards the northeast, more to the north than the east, as you can see in the force diagram.

24 Let the vectors A and B represent any physical magnitude (‘u’ is their unit):

25 Draw AB + and 2 · A – 3 · B and calculate its magnitude.

26 Decompose the vector AB + from the previous exercise on two perpendicular axes, one vertical and the other horizontal, and in the same coordinate system but rotated 30° anti-clockwise (consult the supplement).

In 1960 the 11th General Conference on Weights and Measurements approved the International System of Units (SI). The definitions of the base units have changed over the years. They are currently defined based on universal constants in physics and chemistry.

2.3 Fundamental and derived quantities. SI units

We can measure many properties of phenomena or systems and they all have an associated physical quantity. Of these, the scientific community has selected a set of properties from which all the rest may be derived. They are called fundamental quantities.

A fundamental quantity is that which, by convention, does do not depend on another.

Moreover, the scientific community has also decided on an International System of Units (SI) to use when communicating results at an international level. The fundamental quantities and their SI units are in the left-hand box below.

From these fundamental quantities you can express all the rest, which are called derived quantities.

Derived quantities are expressed in terms of fundamental quantities.

Some derived quantities are shown in the right-hand box below. Pay attention to their relationship with the fundamental quantities and the SI units, since you will need them throughout the year.

The set of units for international use, the international system of units (SI), emerged from the XI General Conference of Weights and Measures in 1960.

From the unit of a derived quantity, you can work out how it is related to fundamental quantities. For example, the SI unit for density is kg/m3, that is, the mass unit divided by the volume unit, which will make you think that the density is defined as the mass contained in a unit of volume.

2.4 Multiples and submultiples

When the numeric value of a quantity is very large or very small we tend to use multiples or submultiples of SI units. To do so, we use prefixes that indicate the value by which we are multiplying or dividing the unit. Consult the most common in the supplement and check it when necessary. These prefixes themselves have no physical meaning on their own. 'Kilo' means a thousand and only refers to a quantity when it is accompanied by a unit. For example, a kilosecond is equal to a thousand seconds (1 ks = 1000 s), and a kilogram is a thousand grams (1 kg = 1000 g).

2.5 Dimensional equations

In addition to SI units and multiples and submultiples of this number there are other units for expressing quantities. To refer to them together we say that the time quantity has a dimension of time and it is expressed as [t] = T, where the letter 'T' is equivalent to a unit of 'time'. The fundamental quantities do not depend on others, and their units are also independent. In the table to the right we include the units for these quantities.

The units of derived quantities are expressed in terms of fundamental units, which is how we obtain their dimensional equations. For example, the dimensional equation of density is:

==

Furthermore, all physical equations must have dimensional homogeneity, which means that the dimensional equation of both sides must be the same. The following ‘Problem solved’ gives an example so that you can understand the utility of dimensional analysis.

Problem solved

3 You are in an exam and you must calculate the potential energy of an object. You cannot remember if the correct equation is EP = m · g · h, or EP = m · g · h2 . Work it out using a dimensional analysis.

You can obtain the unit of energy (J) by multiplying the unit of force by that of length (see the table on the previous page). You can obtain the unit of force (N) by multiplying the unit of mass by the unit of acceleration. Thus:

The second part of the correct equation must have units of energy. Let’s see which one does:

[m] · [g] · [h] = M · (L · T–2) · L = M · L2 · T–2

[m] · [g] · [h2] = M · (L · T–2) · L2 = M · L3 · T–2

The correct equation, therefore, is the first (EP =  m ·  g ·  h), since it meets the condition of homogeneity (the dimensional equation on both sides is the same).

27 The mass of an object is 750 g. Express it in kilogram and in milligram.

28 We all contribute. For the scalar quantities of mass, length, time and temperature, propose two units that are not in the lnternational System (SI) nor multiples or submultiples of SI units. In each case, relate them to SI units.

29 Work out the dimensions of the derived quantities on the previous page and indicate two possible units for each.

30 Verify the homogeneity of the equation of the distance covered by a particle under uniform acceleration given by the following formula:

MEASURING PHYSICAL QUANTITIES. ERRORS

• Measuring is a process to find the quantity of something relative to its unit.

• Measuring instruments have qualities. One of these is sensitivity, or the minimum variation in quantity that it can detect. This is related to the smallest subdivision of its scale.

• Every measurement is affected by errors. Random errors are accidental and unpredictable. Systematic errors are caused by the measuring equipment or misuse.

3.1 Absolute error

Measuring instruments

Once you have studied the following section, write the measurements taken with the following instruments:

When taking a measurement, we cannot be sure if the value we obtain is the real value of the quantity we are measuring. As well as random and systematic errors, measurements can be incorrect due to limits on an instrument’s sensitivity. This is because variations smaller than the instrument’s sensitivity will not be registered by the instrument

Therefore, the value obtained by the measurement differs from the real value. The difference between these values is the absolute error.

Absolute error, εa, is the absolute value of the difference between the measured value and the real value

The absolute error is an estimate, as you never know the real value.

3.2 Relative error

Absolute error does not provide information about the quality of the measurement. lt is not the same to commit a 1 cm error when measuring, for example, the length of a page, as when measuring a bus.

To estimate the quality of the measurement we use relative error.

Relative error, εr , is the coefficient of the absolute error and the real value of the measured quantity.

The lower the relative error the higher the quality of the measurement.

Problems solved

4 Using a tape measure, the length of a rope is measured as 79.6 cm. lf the rope is really 80 cm, calculate the absolute and relative errors in the measurement.

If 'lm' is the measured value and 'l' the real value:

5 lf using the tape measure from the previous exercise we measure a length of 100 cm with the same absolute error, what value would we obtain? Which measurement is the most precise?

The tape measure will show 0.4 cm (εa) less than the real length, or 99.6 cm.

Relative error is dimensionless, and to express it in % we multiply it by 100.

Since this is measured with a smaller relative error, it has higher precision.

3.3 Error in a single measurement

When you take a single measurement, you trust that the equipment is in a good condition and you assume that the given value is correct. However, all measurements have an inevitable uncertainty associated with them. The absolute error associated with a measurement is equal to the sensitivity of the instrument used.

For example, you measure the height and width of an A4 sheet using a ruler marked with millimetres. The height is 297 mm and the width is 210 mm. In both cases the absolute error is 1 mm. The lengths are expressed:

lheight = 297 ± 1 mm

lwidth = 210 ± 1 mm

This means that the height can be between 296 mm and 298 mm, and the width between 209 mm and 211 mm. When using an instrument with a graduated scale, you are subject to two easily avoidable errors: zero error and parallax error. They are discussed in the following box.

Understand, think, investigate…

31 Round table. lndicate the precision of the common measuring instruments with which these measurements may have been made:

a) l = 71 cm.

b) m = 24.5 g.

c) t = 2.35 s.

d) l = 35.7 cm.

e) m = 1 235 g.

f) t = 23.7 s.

32 Write the previous measurements with their absolute errors.

33 Which measurement is more accurate, the height or the width of the A4 sheet?

Zero and parallax errors

Zero error

Occurs with uncalibrated instruments that show a value even when not measuring anything. It is solved by calibrating the instrument.

Parallax error

Occurs when the person taking the measurement is positioned incorrectly. lt is solved by paying attention to the correct way of taking the measurement.

The dynamometer is calibrated with the screw on top until it reads 0 at rest.

To take a measurement with a graduated scale, the mark in question should be at eye-level.

3.4 Minimising errors

To minimise errors, we take multiple measurements. In this way the errors balance each other out.

The measurement value is the arithmetic mean of the individual measurements. If to measure X we need N measurements (X

XN ), the value of the measurement is:

To estimate the error associated with a measurement, we first calculate the statistical dispersion, which is defined as:

At this point, the absolute error of a given measurement (εaX ) is the largest value between the statistical dispersion and the instrumental precision.

Finally, the measurement is expressed as:

The procedure described here applies to direct measurements, in other words, those obtained using measuring instruments.

Indirect measurements are those obtained by calculation using values from direct measurements. In future years, you will study the techniques used to estimate the errors of indirect measurements.

Problem solved

6 Using a stopwatch with an instrumental error of one centisecond (cs), we measure the time it takes an object to fall to the ground from a known height. We repeat this experiment four times and get the following results:

t1 = 3.47 s ; t2 = 3.89 s ; t3 = 3.53 s ; t4 = 3.65 s

Write these measurements and the value of the final measurement, indicating the errors.

The direct measurements are affected by an absolute error equal to the instrumental error of the stopwatch:

To estimate the error, we calculate the statistical dispersion:

The value of the measurement is the arithmetic mean of the measurements:

As you can see, in this case the statistical dispersion is larger than the instrumental error of the stopwatch, so we take it as the absolute error of the measurement. Thus:

= 3.635 ± 0.092870878 s

But, this is not the correct way to express the measurement because it must be rounded up or down, as explained in the next section.

3.5 Correctly expressing a measurement

Although calculators give results to many decimal places, it does not make sense to use them all.

For example, in ‘Problem solved 6’, the calculator provides a time value to three decimal places (ms). However, the stopwatch used cannot measure this because it only measures to 1 cs. The same occurs with the absolute error if you express it to nine decimal places (ns). As a rule of thumb, when you record the result of a measurement, always remember that:

The absolute error can only have one significant digit, and the numeric value of the measurement must be rounded to the place of that digit.

In the following box we explain what significant digits are and review the rules for rounding off. After studying it,

you’ll easily understand that the final result of ‘Problem solved 6’ is expressed as:

t › 3.64 ± 0.09 s

Which means that the measured time is between 3.55 s and 3.73 s, with a relative error equal to:

εr = 0.025

The relative error of this measurement is 2.5 %..

Rounding off rules and the correct use of graduated scales

Rounding off rules

To round off, remember that:

• lf the first digit to discard is less than 5, do not change the digit before it. For example:

0.542 ≃ 0.5 ; 13.27 ≃ 10

• If the first digit to discard is greater than 5, or 5 followed by any digit other than zero, round up the preceding digit. Thus:

0.552 ≃ 0.6 ; 16.27 ≃ 20

• lf the first digit to discard is a 5 followed by a zero and the previous digit is odd, round up the preceding digit, but if it is even, leave it unchanged. For example:

0.550 ≃ 0.6 ; 0.650 ≃ 0.6

In solution 6 an error occurs, rounded to the first digit other than zero, which is 0.09 s. Therefore, the time value also needs to be rounded to one hundredth of a second, giving t ≃ 3.64 s. Note how, when rounding, the '=' sign is not used, and instead '≃', which denotes rounding.

Understand, think, investigate…

34 Round off to the hundredth place:

a) 3.124.

b) 15.357.

c) 9.5850.

d) 0.2350.

35 Correct any incorrect measurements:

a) t = 1.236 ± 0.15 g.

b) m= 15.4 ± 0.1 g.

c) l = 3.98 ± 0.1 cm.

Correct use of graduated scales

When a graduated instrument is used, the measurement reading might lie between two of the markings. In these cases, no matter how close to the higher marking it is, the lower one is always used, because this is as far as the measurement goes, since the instrument is not sensitive enough to read any further:

In the case of an ammeter, the reading is (0.78 ± 0.02) A.

36 The following measurements are made using a digital scale with a precision of 1 cg:

m1 = 12.00 g ; m2 = 11.89 g ; m3 = 11.94 g ; m4 = 12.07 g

Write the result of the measurement.

Remember you must calculate the arithmetic mean and the statistical dispersion and compare it with the scale’s precision; finally, you must round off and correctly write the measurement.

ANALYSING EXPERIMENTAL DATA

To analyse experimental data we use graphical representations from which we extract physical laws that relate to quantities.

4.1 Graphical representations

The data from an experiment are normally organised in tables, from which pairs of data points can be represented in a Cartesian coordinate system. The abscissa represents the independent variable (the one we control) and the ordinates, the dependent variable (the one we are studying).

Graphical representations are a way of expressing physical laws through graphs.

From the graph we establish the relationship between variables, which in our case are physical quantities. The most common relationships in physics are direct or indirect proportionality and quadratic relationships.

4.2 Physical equations

Far from being mathematical formulae, these equations indicate relationships between quantities that are involved in a phenomenon.

Velocity graph

Draw a graph to show the velocity of an object that moves at a constant speed for five seconds.

Physical equations are a mathematical way of expressing the physical laws.

Graphs and physics equations are a common part of the common language of science. In ‘Problem solved 7’ there is an example of how to extract a physical law by analysing experimental data.

Relationships between quantities

Direct proportionality

A quantity, M2, is directly proportional to another, M1, if, when you multiply M1 by a number, you also multiply M2 by that number. i.e.:

Mk M 21 =

Direct quadratic

A quantity, M2, has a direct quadratic relationship with M1, if, when you multiply M1 by a number, M2 it is multiplied by the square. So:

Mk M 21 2 =

Indirect proportionality

A quantity, M2, is inversely proportional to another, M1, if, when M1 grows in multiplies of a number, M2 it is divided by that same number. In that case:

M M k 2 1 =

Linear relationship

This is when a straight line does not pass through the origin of the coordinate system. The equation is:

M2 = k1 + k2 · M1

If k1 increases, the line

Problem solved

7 To study the relationship between the height of a falling object and the time it takes to hit the floor, we drop an object from five different heights(εa = 0.01 m). For each height, we take three measurements of the time(εa = 0.01 s). The following table shows the results. Based on the data, state the physical law that relates the two quantities.

Note how, in every case, the precision of the stopwatch is greater than the statistical dispersion. So we take that as the absolute error of the measurements, which are expressed thus:

Before you start, note that the instrument used to measure the height is precise to 1 cm (εa = 0.01 m), and the stopwatch is precise to 1 cs (εa = 0,01 s), hence those are the absolute errors of the measurements.

First we calculate the arithmetic mean and the statistical dispersion of the measured duration of each fall (as in ‘Problem solved 6’, but with N = 3). We get the following values:

The graphical representation of these data, with height on the ordinate and time on the abscissa, is:

From the graph we can work out that the height from which an object falls and the time it takes to fall have a direct quadratic relationship. This is represented by the following physical equation, where k is a constant:

As you have seen, a physical law can be expressed verbally (a statement), mathematically (a physics equation) and graphically (a graph).

Understand, think, investigate…

37 Preparing for the task. The physical law in ‘Problem solved 7’ can also be expressed in the following terms: ‘height is directly proportional to time squared’. lf so, graphing the height as a function of time squared should produce a straight line. Check it for yourself.

38 Here are three measurements of the displacement of a spring (εa = 0.1 cm) when hung with different weights. From the data, derive the physical law.

39 What physical law can you derive from the following graph? Express it in words and mathematically.

GUIDELINES PROBLEM SOLVING

EXAMPLE

Calculate the deformation of a spring with spring constant 50 N/m when you hang a 200 g weight on it.

SOLUTION

UNDERSTAND THE PROBLEM AND EXTRACT DATA

Try to ensure you understand the problem statement before you begin solving the problem.

• Read the problem statement without rushing and look up the meaning of any words you do not know.

• Extract the data it asks for and the data it provides. ldentify which physical quantities it refers to and write them down using their symbols and SI units.

DRAW A DIAGRAM OF THE SITUATION

Physics problems tend to refer to situations in our surroundings that are easy to draw:

• Using models, such as the material point object draw a diagram of the situation described in the problem statement.

• In your drawing, include both the scalar and vector quantities involved in the phenomenon.

IDENTIFY THE PHYSICAL LAWS THAT APPLY

This is the most creative part of the process because you must identify physical laws that you will use to solve the problem. Remember that physical laws express relationships between quantities:

• Analyse the data in the problem statement and decide if it is a problem of motion, forces, gravity, energy, etc.

• Check the relevant physical laws and decide which to use. We will provide guidance throughout the book.

OBTAIN A RESULT AND CHECK IT

• With the physical equations of the laws, carry out mathematical operations until you have an equation for the relationship between the quantities in the problem statement.

• Put the data in the equation and calculate the final result.

• Check whether the value is possible and if it is expressed correctly.

• Recall that a spring constant of 50 N/m means that the spring will stretch to 1 m with a 50 N weight.

• The problem statement provides and asks for these data:

– Spring constant: k = 50 N/m.

– Mass of the object: m = 200 g = 0,2 kg.

– Deformation of the spring: x = ?.

This problem is about forces, specifically the deformations produced by them.

We can therefore solve it using Hooke’s Law, which states that the magnitude of the force applied to an elastic system is directly proportional to the deformation. Mathematically: F = k · x

In this case, the force applied is the weight (P) of the object: P = m · g

The equation that relates the quantities is: 88 x k mg FP kx mg = $ ==

• Putting in the data gives this result: 50 N/m 02 kg 981m/s x 2 =  = 0.03924 m

• Since a ruler’s accuracy is usually 1 mm (0.001 m), we round to the third decimal place: x = 0.039 m = 3,9 cm

A reaction of 62 g of white phosphorus (P4) and 213 g of chlorine (Cl2) forms 275 g of phosphorus trichloride (PCl3). Explain what would happen if we combined 170.50 g of white phosphorus with 600.00 g of chlorine.

SOLUTION

UNDERSTAND THE PROBLEM STATEMENT AND IDENTIFY THE SUBSTANCES

Read the problem statement twice, to ensure that you understand the situation:

• After the first reading, look up the definitions of words you don’t know and which seem relevant.

• The second time you read it, extract the data and identify what you are being asked to find. Remember that it is important to express quantities with their symbol and try to use subscripts for the different substances.

MAKE AN OUTLINE OF THE SITUATION

In chemistry problems we tend to use models to represent substances and the changes that occur, like this:

• If it is a problem to do with the structure of the material, we use models for atoms and bonds.

• lf it is a chemical reaction problem we write the chemical equation.

IDENTIFY THE RELEVANT LAWS

No matter what type of problem we are solving, we must rely on different laws or quantitative definitions. We remind you to review the relevant theory before trying to solve a problem. This problem is one of chemical changes, in particular the gravimetric laws.

OBTAIN A RESULT AND CHECK IT

• Do the necessary calculations in your problemsolving strategy and remember to use consistent units for the quantities of the reactants.

• Analyse the result and discuss it if necessary.

• The problem statement discusses the production of a new substance so it is about a chemical change.

• Note that the statement does not ask for a particular calculation. lt asks you to explain what will happen with a different amount of reactants.

• Observed reaction:

– Reactants: mP4 = 62 g ; mCl2 = 213 g.

– Products: mPCl3 = 275 g.

• Proposed reaction:

– Reactants: m’P4 = 170.50 g ; m’Cl2 = 600.00 g.

In this case, it is useful to write the chemical change in simplified form, collecting the masses of the substances beneath each one in a table:

Recall that the law of definite proportions states that the masses of substances in a reaction always maintain the same proportion. We must also keep in mind that the law of conservation of mass also applies to every chemical change.

• Write the data in terms of a proportion:

• Calculate the mass of chlorine that reacts:

• We conclude that there will be extra chlorine: 600.00 g – 585.75 g = 14.25 g of Cl2 does not react The reaction will also produce:

g + 170.50 g = 756.25 g of PCl3

SCIENCE WORKSHOP

Research project

General Considerations

All scientific research begins with the need to answer a problem or explain an observed phenomena. It concludes with communicating the results and conclusions. But the final conclusions can be reached in a variety of ways and that is why it is important to plan ahead which to use.

To guide us in the process, we should begin with the design of a research proposal.

A research proposal is a document that describes in detail all the aspects that, a priori, may guarantee the success of the research.

In the following box we show the sections that should be included in all research proposals.

Research proposal

Title page

You should try to make this as attractive as possible. lt should contain the title of the project, the names of the researchers, the institution to which they are affiliated and the date.

Contents

A table of contents, including page numbers, and showing the structure of the project.

Problem statement

Describe the problem to be researched. lf it is a complex problem, it may help to divide it into smaller research problems that will guide the process. Theoretical framework

lt is important to fit the problem into available scientific knowledge, which will enable you to decide what scientific laws and theories to use.

Objectives

You should state the objectives as clearly as possible. lf they are complex, you may define secondary or intermediate objectives that, once achieved, contribute to the main ones.

When writing these, you should use verbs in the infinitive.

Hypothesis

You must produce possible answers to the problem or research question. These hypotheses must be testable against reality.

Methods

You should describe in detail the method you will follow to check your hypothesis, including the necessary equipment. lt is important that you ensure reproducibility.

Funding

lf the project requires funding, you will have to describe how you will spend what you are requesting.

Bibliography

You should include a list in alphabetical order of all the sources consulted.

Scientific report

Once you complete your research, you must present the results you obtained and the conclusions you drew from them. To do that, you should write a scientific report.

A scientific report is a document that contains the specifications of a research project and its results and conclusions.

The scientific report has the same sections as a research proposal, except for funding, which is justified separately. In addition, a scientific report contains results and conclusions (you can consult the sections in the box on the right) and a bibliography.

Finally, it is important that you know how to format bibliographical references. The box below indicates how to do so.

• Title page

• Contents

Scientific report

• Statement of the problem

• Theoretical framework

• Objectives

• Hypothesis

• Method

• Results

Shown using verbal and mathematical language and graphically.

• Conclusions

Did you verify the hypothesis? Did you meet the objectives?

• Limitations

Define, if necessary, the scope of your conclusions.

• Future steps

New lines of research that could emerge from yours.

• Bibliography

Writing bibliographies

A bibliography is a set of data that you must provide so that others can find the sources of your information. There are different styles for reference bibliographies, but all should meet the standards of the lnternational Organization for Standardization (ISO).

According to these, the data and format of a bibliographical reference depend on whether it is:

• A book: Surname, lnitial. (year). Title. Location of publication: publisher.

Example: Asimov, l. (1969). Great Ideas of Science. Bastan: Houghton Mifflin.

• An article: Surname, lnitial (year). Title. Journal name, year, volume (number), first page - last page.

Example: Welsh, W. and Doyle, L. (2014). Worlds with Two Suns. Scientific American, 2013, 309, 40-47.

• Web: Author or entity. Title. <URL> [Consulted: date].

Example: NASA. NASA’s Curiosity Mars Rover Heads Toward Active Dunes. http://www.jpl.nasa.gov/news/ news.php?feature=4772 [Consulted: 28 November 2015].

Although it is not in the bibliographical entry, books have another piece of reference information: their lnternational Standard Book Number (ISBN), a number that identifies each published book.

For periodicals such as magazines or journals, it is useful to know the lnternational Standard Serial Number (ISSN), an eight-digit number that identifies each publication.

An Earth without iron and Mars 2031

There are two proposed research projects on anayaeducacion.es: ‘An Earth without iron’ and ‘Mars 2031’.

You will find two documents that describe the method and the activities you can carry out once you have acquired the knowledge in each unit.

Chemistry project: An Earth without iron

Physics project: Mars 2031

SCIENCE WORKSHOP Research project

An Earth without iron

How to do the project

You should do this project throughout the course; as you learn the chemical concepts we teach, you will be able to solve the proposed activities. Here are the units in the book relevant to each activity:

• The atom: questions 1 and 2.

• Chemical bonds: question 3.

• Carbon chemistry: questions 5 and 7.

• Chemical reactions I: question 4.

• Chemical reactions II: 6 and 8.

Iron is a chemical element which we can find all around us. Its abundance in the Earth’s crust is around 5 %. Humans have known about iron for thousands of years and its use has shaped history. In fact, the era in which there were many remarkable advances in human quality of life is called the iron age. It is a very important element because it is used in diverse areas of life, from manufacturing tools, instruments and weapons to construction.

Furthermore, iron is one of the trace elements; that is, it forms part of our body, and its role is vital. What would happen if this element did not exist, or if there was a shortage of iron on our planet?

Throughout this research project you will discover the importance of iron in different settings. Once finished you will write a report in which you discuss the relevance of iron for our planet and its inhabitants, then present the most relevant information from each stage, or the stage that you found most interesting.

Remember to address each issue using the scientific method to test your hypotheses. If you must search for information, remember to always cite the source that you use (if it is a web page, include its URL).

Role of iron in the Earth

The Earth’s core is composed partly of molten iron, and there the abundance is much greater than 5 %.

What is the role of iron in the core? We start from a hypothesis based on our experience: the interaction of iron with magnets. If magnets attract iron it must be because it has magnetic properties. We might think, therefore, that the presence of iron is directly related to the existence of Earth’s magnetic field.

The iron in our planet

1. Search for information about the behaviour of paramagnetic, ferromagnetic, and diamagnetic materials and the Curie temperature or Curie point. From this research, answer the following question: “Is the Earth’s magnetic field caused exclusively by the presence of iron in the core of our planet?”.

2.  The what if... What would happen if the Earth’s core were not formed in part by iron? We have already seen the behaviour of a ferromagnetic material. Write the electron configuration of iron and compare it with that of a group 2 metal. Is it possible for unpaired electrons to exist in group 2? Would it have ferromagnetic behaviour?

Iron as a raw material

In the Iron Age, the use of this metal to manufacture tools and weapons was a very important technological advance, making some civilizations invincible. Its mechanical properties were improved through the development of various metallurgical techniques, such as adding carbon to make steel. Steel is still used a lot today.

Iron around us

3. Identify the type of substance iron is and its main mechanical properties. How do those properties change with the addition of carbon to iron in steel?

4.  Effect and reach. One of the most common problems with iron (Fe) objects is corrosion due to the formation of rust (Fe2O3). This corrosion is more frequent in coastal areas or in areas where acid rain is more frequent. Why?

Iron in living things

Iron is present in virtually all living organisms and is essential for their metabolism. It is called a trace element, since, although it is essential to living things, it is only necessary in very small amounts.

Iron in us

5. Iron is responsible for the colour of our blood, since it is present in the heme group. Can a heme group transport oxygen alone, or is a protein also necessary?

6.  Let’s check. Some years ago researchers developed a hypothesis that humans might reduce the greenhouse effect by fertilizing the ocean with iron. Search for information about this hypothesis and check its validity, analysing the environmental advantages and risks.

Other uses: iron and fuel

In addition to everything discussed so far, iron also has many other applications in industry. In this final section, we will examine its use as an additive in fuels.

More applications of iron

7.  Step diagram. There is a type of fuel called ‘unleaded petrol’. Does the petrol initially obtained from oil contain lead? Why do you think that petrol stations advertise that their petrol does not contain lead?

8. One of the substances that have replaced the lead compounds in petrol is ferrocene. Why? How does ferrocene affect petrol’s octane?

SCIENCE WORKSHOP Research project

Mars 2031

How to do the project

You should do this project throughout the course; as you learn new physics concepts you will be able to solve the proposed activities. Here are the units in the book relevant to each activity:

• Kinematics: question 2.

• Dynamics: question 4.

• Gravity: questions 1 and 3.

• Fluids: question 10.

• Mechanical energy: questions 8 and 9.

• Thermal energy: questions 5, 6, and 7.

The planet on which we live will not always have good conditions for our subsistence. Throughout the history of Earth there have been at least five mass extinctions... and something like that could happen again. We cannot rule out the possibility that the Earth, either for natural or artificial causes, could become inhabitable.

If human beings, as a species, are to survive we will need to expand and establish colonies on other planets. Scientific knowledge and technological advances offer us the opportunity to try and survive. We would go from being inhabitants of the Earth to being citizens of the universe.

We do not yet have sufficient scientific and technological knowledge; we must go one step at a time. Surely, a first step will be to establish a colony on Mars. So we propose that with the knowledge you gain during this course, you start designing a plan for human beings to begin colonizing Mars in 2031.

As you expand your knowledge of physics, you will be responding to the necessary questions for this project to be successfully put into action. Therefore, at the end of each unit we will refer you back to these pages to solve the relevant problems.

You must approach each question using the scientific method. You may check your hypothesis on the Internet. If you do, make sure the sources are reliable and note the source of the information you have used. When you finish, gather your findings in a scientific report and prepare a presentation to share them.

Preparation: before launch

There are two important issues to consider for planning the launch:

• The ship must be launched into space with enough velocity to overcome the gravitational pull. This is known as the ‘escape velocity’ and is about 40 000 km/h for the Earth. Without it, the ship would fall back to the planet.

• In addition, the Earth and Mars are not always at the same distance. A question to be considered, then, is the ideal time to launch, so that the ship travels the minimum possible distance. But keep in mind that the planets will move in their orbits after launch.

Plan the launch

1. Decide whether it would be appropriate to establish a launch pad on the Moon.

2.  RQAS. Should we launch the spaceship when Earth and Mars are closest together? Before answering, search for information on ‘launch windows’.

Note that in this picture, as throughout the book, distances and sizes are not to scale.

Launch: traveling to Mars

At a typical speed of 4.5 km/s, it would take about 200 Earth days to reach Mars orbit. We must think about the welfare of the crew during that time.

Moreover, almost all the propulsive energy is consumed during the launch. However, we also need to reserve some to adjust the trajectory and, also, to prevent damage when landing on the surface Mars.

During the voyage

3. Will the astronauts move like they do on Earth? What could be tried to help them experience something similar to Earth’s gravity? What health problems could the crew suffer?

4.  Circle of viewpoints. With regard to energy storage, would it be necessary to keep the engines burning throughout the trip? Once in space how would you control the trajectory of the ship? How could you place the ship on the surface of Mars without damaging it?

Arrival and establishment

On the surface of Mars

5. We need energy to run electronics, produce oxygen, heat our dwellings, etc. What energy sources will we have? Are they renewable energy or non-renewable energy sources?

6. Suits and modules will have to protect the expedition members from external threats. What are these threats? How could they be protected against those threats?

7. When they arrive on Mars, the crew must establish a food supply, so that settlers can be self-sufficient. What is your food production plan?

8. To prepare the camp base, we will have to move heavy objects. Given that inertia is an intrinsic property of matter and that weight depends on the gravitational attraction, how will our handling of heavy objects differ on Mars?

9. Given the less dense atmosphere of Mars, sound will travel at a different speed than in the Earth’s atmosphere. How will this affect the pitch of sounds relative to how we hear them on Earth?

10. Eventually we may want to make the surface of Mars habitable for human beings. Would it be possible to modify the atmosphere of Mars to make it similar to the Earth’s?

Once on the surface of Mars, the crew must work against the clock. Since the supplies and provisions are finite they will eventually run out.

The most urgent tasks are assembling energy, oxygen, and food production modules. All this must be done in a very unfamiliar environment, where gravity is about one third that of Earth. Also, the Martian atmosphere, with 95 % CO2, has a more than 150-fold lower pressure than Earth, with the average temperature being about –45 °C. Then, on top of everything else, there is no magnetic field to protect the crew from high-energy solar radiation that reaches the surface.

SCIENCE WORKSHOP

Recreational science

Thought experiments

In order to test hypotheses against reality, experiments are often designed under controlled conditions to study the dependence between physical quantities. However, sometimes this is not possible. In such cases, one can resort to “thought experiments”. A well-known though experiment is one in which Galileo Galilei, in the 17th century, in a dialogue between Salviati and Simplicius, tries to prove that Aristotle was wrong when he said that heavy objects fall faster than light ones.

SALVIATI: Aristotle says: “An iron ball of one hundred pounds falling from a height of one hundred cubits reaches the ground before a onepound ball has fallen a single cubit”.

I think both will arrive at the same time; if you do the experiment yourself you will see that, whether they fall from a height of 50 or 100 cubits, both will touch the ground at the same time…

But even without conducting the experiment, it can be clearly proved that it is not true that, assuming they are both the same material, a heavier object falls faster than a lighter one by a simple and conclusive demonstration... If we had two objects whose natural speeds were unequal and we put them together, it is obvious that, in a certain sense, the faster one would be slowed down by the slower one and the slower one would be accelerated by the faster one. Do you agree?

SIMPLICIO: I think it would indeed be like this.

SALVIATI: But if this is true, and if it is also true that a big stone falls with a speed of, say, 8 units and a small stone falls with a speed of 4 units, then if we tie them together, so that they fall together, they must move with a speed of less than 8 units.

But, on the other hand, the two stones together will result in a larger stone than the first one and should therefore fall at a speed greater than 8 u.

SIMPLICIO: I am very confused.

Experiment

Work proposal

Galileo, using Aristotle’s hypothesis (heavy objects fall faster than light ones) reaches an absurd conclusion, which invalidates it and leaves his hypothesis standing (all objects, large or small, fall with the same speed). Many scientists, such as Newton, Maxwell and Einstein, have defended some of their hypotheses in this way. Today, theoretical physicists use logical-mathematical developments to advance knowledge, although it is experiments that confirm their conclusions.

Organise the class into small groups of three or four people. Each group should prepare a poster about a thought experiment, stating the hypothesis being defended and the conclusions reached. Once the posters have been made, they can be displayed and shared.

Representation of Galileo’s thought experiment.

Practical work

Can you talk about ‘the density’ of modelling clay?

Guidelines for taking measurements

• Avoid zero error on the scale.

• Keep in mind parallax error when using the ruler and the measuring cylinder.

• Measure all the quantities (length of the modelling clay and the mass and volume of the piece of modelling clay) three times (with their errors) and write the final result of each measurement in the correct format.

• Write the measurements in a data table. There is an example on the right.

Proposed problem

There are different brands and colours of modelling clay. Do they all have the same density? Search for information on how modelling clay is made and make a hypothesis.

Our proposal

To calculate the density of an object you must divide its mass by its volume.

In small groups, measure the density of modelling clay using two methods:

• Divide the mass on the label by the volume. Calculate the volume by measuring the width, height and thickness of the modelling clay.

• Take a piece of modelling clay and divide its mass by its volume.

Your proposal

Before reading our proposal, write your own and, if possible, check whether it enables you to answer the problem statement.

Equipment you will need

• Bars of modelling clay from different manufacturers and of different colours (one per group) • Ruler • Scale • Measuring cylinder

With these guidelines, measure the density of the modelling clay and answer the initial problem. Afterwards, do the activities proposed at the end of the section.

Manufacturers tend to indicate the mass of their modelling clay. Use that data for the first method.

Understand, think, search…

1 Write a brief scientific report on the practical work, ensuring it has the sections described in this unit.

2 Did you confirm your hypothesis? Why or why not?

3 Do the densities measured via the two methods match? lf not, why?

4  Numbered heads. How could you minimise the errors of the individual measurements?

lt is very useful to organise data in tables, since you can see them all at a glance. This is an example of a table to use for the second method.

5 Are the quantities in the exercise fundamental or derived? Were the measurements direct or indirect?

6 Can you say that you participated in a scientific experiment? Why or why not?

7 Given the density you calculated, do you think the modelling clay would float in water?

8 Search on the Internet for ‘floating modelling clay’ and return to the previous question.

CHALLENGES THAT LEAVE AN IMPRINT

UNDERSTAND

1 Using the material point systems, represent a swimmers velocity when crossing a river perpendicular to the river’s current, which we assume is constant across the entire width of the river.

2 On the material point system model you have drawn, indicate the point at which the swimmer will each land after crossing the river.

3 Fill in the blanks in the systemic concept map below.

Remember that you have the solutions to the numeric problems at anayaeducacion.es.

Scientific research

1  Shared interpretation. In the following text, identify the steps of the scientific method.

In Ancient Greece, King Hiero commissioned a gold crown, but he wondered whether the goldsmith had substituted the gold for copper or silver. He asked Archimedes to check.

Archimedes didn’t know what to do. If the goldsmith had used metals lighter than gold in the crown, then that crown would take up more volume, but Archimedes didn’t know how to measure volume.

One day he took a bath and watched how the water moved around him. In that moment, he realised that the volume of an object is equal to that of the water it displaces. He leapt out, naked, shouting, ‘Eureka!’.

He put the crown in a body of water and measured the volume of the displaced water. He did the same with a pure gold ingot of the same weight and… the king ordered the goldsmith to be executed.

2 Review the scientific method, and describe an everyday situation in which you think you use it.

3 What is a hypothesis, a scientific law and a scientific theory? Can one type turn into another type?

4 The law of conservation of energy states that in an isolated system, energy is conserved. Why do we call it a ‘law’ and not a ‘theory’?

5 Look up information about your horoscope and decide whether it is scientific knowledge.

6 What does ‘to experiment’ mean? Does using a measuring instrument mean you are experimenting?

7 Search for information about resource depletion and analyse how science, technology and society (STS) interact in relation to this problem.

Physical quantities

8 Describe an everyday situation with which you can show that forces are vector quantities.

9 Describe the following vectors.

Measuring physical quantities

14 A 50 g weight measured on an old scale measures m = 53.3 g. What relative error does it have?

15 The following measurements have been written incorrectly. Correct them: a)  t = 3.45 ± 0,01 s. b) V = 123 ± 2.5 mL. c) l = 3.46 ± 0.1 cm.

16 We take three measurements of the mass of an object (ea = 0.1 g): m1 = 45.8 g, m2 = 45.6 g; m3 = 46.1 g. What is the final result of the measurements?

10 Two people push an object with forces of the same magnitude, F = 90 N. Draw the resultant force, F R 8 , and calculate its magnitude, if the forces act...

a) ... in the same direction.

b) ... in parallel but opposite directions.

c) ... perpendicular to each other.

11 Explain the type of quantity each value represents and write them in scientific notation and SI units:

a) 18 Gm; b) 11.6 µs; c) 54 cg; d) 9.56 MN (consult this book ‘s supplement if necessary).

12 Check that the Earth’s gravity has the same dimensions expressed in m/s2 and in N/kg.

13 The equation of ideal gases is: p · V = n · R · T where p is pressure; V, volume; n, the amount of substance, and T, temperature. Determine the dimensional equation of the gas constant, R. Check the dimensional homogenity of the general hydrostatic equation: p = p · g · h (p: pressure; d: density; g: gravitational constant; h: depth).

Analysis of experimental data

17 Three measurements are taken of the electric current in a light bulb at three different voltages. Work out the physical law that relates these quantities and express it a) verbally b) mathematically c) graphically.

18 Pressure is directly proportional to the force applied and inversely proportional to the surface area on which the force is applied. Express this definition in mathematical language and graphically.

19 What type of motion does each of the following graphs represent?

Science and technology: What are the people who do scientific research like?

Draw a scientist and include some of the material and resources with which you think they work. There are many studies showing that when people make these drawings they tend to draw bald or white-haired men with glasses, lab coats, surrounded by measuring instruments and glass beakers.

This is known as the ‘stereotypical scientist’ and it is far from the truth. People who do science, both men and women, are normal people who do normal things, and they do not always work with measuring instruments. One of the hypotheses for why this incorrect image is so widespread is that scientists often appear that way in television advertisements, films and cartoons. So whenever you get a ‘scientific message’, whether it is verbal or visual, you should ask yourself whether it really matches reality.

• Search the Internet for ‘women scientists’. Choose three and explain why they are interesting.

• Discuss whether your drawings represent stereotypical scientists.

• Think of someone you know who conducts scientific research and compare them with the stereotypical scientist.

THE ATOM AND THE PERIODIC TABLE 1

THE COMPLEXITY OF AN ATOM

Before starting this unit, think about the fact that the diameter of an atom, approximately 0.1 nanometres (10–10 m), is ten thousand times smaller than that of Staphylococcus aureus (a type of bacterium responsible for several skin infections). For this reason, finding out the structure of the atom represented a considerable challenge for the scientific communities of the 19th and 20th Centuries.

At the start of the 19th Century, John Dalton claimed in one of his atomic hypotheses that “matter is formed of indivisible atoms”. Later, J.J. Thomson discovered the electron 1897; E. Rutherford discovered the proton in 1919; J. Chadwick discovered the neutron in 1932; and in 1964, M. Gell-Mann and G. Zweig discovered quarks! Quarks which are even smaller than the others, combine with each other to form subatomic particles such as protons and neutrons.

This brief step-back in history shows that knowledge is constantly evolving and every discovery starts with a question, which is triggered by curiosity. So what are electrons made of, if they consist of a particle? At the moment this question remains unanswered.

READING AND LISTENING

1 Look for information about the Atoms for Peace program: how many times it has been held, where, which countries participated, the main topics covered, the conclusions drawn, etc. Share your findings with the rest of the class.

2 What are main applications of nuclear energy?

CHALLENGES THAT LEAVE AN IMPRINT

LANGUAGE BANK

SPEAKING

3 On August 2nd, 1939, Albert Einstein sent a letter to the president of the United States F.D. Roosevelt. In this letter, he alerted him to recent developments in the field of nuclear energy. He expressed his concern about three main points for the president to consider. Read the letter, which you can find easily on the Internet. Discuss in pairs which are the three main points that Einstein emphasises. Now, think about some technological developments of our time. Talk about what you think will happen as a consequence of these developments.

We are going to have environmental problems if we don’t develop cleaner technology. Prosthetics will improve because of developments in robotics.

WRITING

4 In 1953 the president of the United States, Eisenhower, presented the “Atoms for Peace” program to the United Nations. It aimed to promote various peaceful nuclear projects and generate agricultural, industrial, medical, transport, and energy development. With similar objectives, in May 2018 the international symposium

“Atoms for Peace and Europe: Nuclear Energy Networks in Europe and around the Globe” was held in Spain. Find information on the Internet on the various applications of nuclear energy. Relate your finding to how nuclear energy can help reach targets 2.1, 3.4, 9.1 and 16.4 of the SDGs. Write a paragraph summarising your research.

LEARNING SEQUENCE

HOW MUCH DO YOU KNOW ABOUT CHEMISTRY?

1.1 In groups, write a list of chemistry concepts you already know and add any others that occur to you. Share them with the other groups and between you draw a tree diagram with ‘Matter’ as the root node.

CREATE DATA CARDS

2.1 Subatomic particles Look for information about the atomic models that have existed over the years and how they have evolved: experiments that led to these models, the people involved, where and when in history, etc.

2.2 The gravimetric laws. From the information that you can read at anayaeducacion.es, perform two laboratory practical experiments to test the law of conservation of mass and the law of definite proportions.

2.3 The periodic table How many previous versions of the modern periodic table are there? Look for the least known ones and explain why they were rejected.

2.4 Radioactivity. Radioactivity has many different uses, from medicine to nuclear weapons, and is even present in the home, for example in toothpaste and hair creams. Look for old adverts about products containing radioactive elements and explain how they could affect the population in the short and long term.

OTHER HISTORICAL CONSIDERATIONS

The escape room cannot be solved until the first three units have been finished, but now the keys that help solve the enigma will be determined:

3.1 Why has it been so difficult to arrive at the current atomic model? And at the current periodic table? Are modern laboratories the same as laboratories from hundreds of years ago? Based on these questions, comment on

+ for more guidelines, go to anayaeducacion.es

DISCRETENESS OF MATTER

1.1 Gravimetric laws

The two main goals of science have been to understand the ultimate components of matter and explain their nature. This unit will look at how the idea of matter has evolved, starting with one of its main characteristics: matter is discrete.

We must first note that what we understand as discrete matter is far removed from our everyday experience of it. We are surrounded by matter. We are ourselves matter. We perceive it as a continuum (everything is matter, where one collection of matter ends another begins) and we can explain many aspects of our surrounding world with our view of matter as continuous. We need to come up with another idea of matter, though, to explain a multitude of facts. Accordingly:

• In 1789, A. Lavoisier publishes Traité élémentaire de chimie (Elementary Treatise on Chemistry) which lays the foundations for chemistry developments in the 19th century. In his book, he establishes an empirical law by taking precise measurements of mass, which proved that mass does not change in a chemical reaction.

In 1661, Robert Boyle published The Sceptical Chymist, in which he explains the difference between an element and a compound. An element is any substance that cannot be broken down into simpler ones whereas a compound can be broken down into elements.

• In 1799, J. L. Proust states that all chemical compounds are formed by elements in a definite proportion.

• In 1803, J. Dalton builds on Proust’s theory by stating that two chemical elements can be combined in different proportions, resulting in different compounds.

These three statements are known as the gravimetric laws. Dalton’s atomic law explains these three laws, as you will see below.

Supporting arguments using data tables

Law of conservation of mass and law of definite proportions

In each of the experiments in the first table, the measured mass of iron and of oxygen are shown, both as simple substances, which are combined and result in an iron oxide, which is a compound. The leftover (excess) mass is not shown for one of the substances involved in forming the compound, which would be present in the second and fourth experiments (shaded rows). You can calculate this excess mass easily.

Law of multiple proportions

The second table shows the results of measuring masses of carbon and oxygen present in two types of different compounds, A and B. Note that the 'mass of carbon/mass of oxygen' ratio is different in each compound. You can also see that there is a simple number ratio between the masses of carbon (54.0 g and 27.0 g) that are combined with the same mass of oxygen (71.9 g): (54.0 / 27.0 = 2).

1.2 Atomic theory

In 1808, J. Dalton published the first part of A New System of Chemical Philosophy in which he explains the gravimetric laws based on the atomic theory. This can be summed up in four ideas:

1. Matter is formed by atoms, which are indivisible particles.

2. All atoms of a given element are identical in mass and properties, and the atoms of one element differ from the atoms of all other elements.

3. Compounds are formed by atoms of different chemical elements. Atoms of different elements combine in fixed, simple whole number ratios to form chemical compounds.

4. During a chemical reaction atoms rearrange, and the atoms of the reactants regroup to form new chemical substances (the products). The main idea behind Dalton’s atomic theory is that matter is discrete and is formed by atoms with a specific mass. Although this idea has been expanded on over the centuries, it is still considered the most powerful theory in modern science.

Dalton’s atomic symbols

Symbols of the chemical elements and of some combinations (compounds) in Dalton’s original text. Number 1 refers to hydrogen, 3 to carbon, and 4 to oxygen.

Interpretation of the gravimetric laws according to Dalton’s hypothesis

In a chemical reaction, mass stays the same because the atoms rearrange; it is neither created nor destroyed. Since matter is discrete, the masses will stay in the same proportion during the chemical reaction. The following examples explain this fact using the postulates of Dalton’s theory.

For the reaction between iron and oxygen, four iron atoms bond with two oxygen atoms, but a bit of iron does not bond with a bit of oxygen. That is why there is no leftover atom of any element in the first reaction but there is a leftover iron atom in the second reaction.

In the case of carbon and oxygen, Dalton was right when he stated that one of the compounds, carbon monoxide, was a binary compound, and the other, carbon dioxide, a ternary compound. The fact that there is a simple whole number ratio between the two amounts of oxygen that are combined with the same mass of carbon (in this case 2) shows that the compound is formed by a given number of atoms in each element.

1 Logic wheel. Using the tables on the previous page and the pictures on this one, how many times greater is the mass of an iron atom than an oxygen atom? If you had not had the information underneath the images, could you have answered the above question?

2 Dalton found the correct composition of carbon monoxide and carbon dioxide, but not for another abundant substance. Which substance was that? Use the picture in the margin on this page. What error did he make when he described it?

DISCOVERIES THAT ALLOWED THE IDEA OF THE ATOM TO EVOLVE

In the late 19th century and early 20th century, more knowledge was gained about phenomena such as electricity and radioactivity, which furthered the development of the atomic models.

2.1 Electricity and chemical elements

Electrical phenomena were known from the 5th century BC onwards. Thalus from Miletus noticed that when amber was rubbed it became electrically charged (elektron in Greek, hence the name of this phenomenon). This is the phenomenon of static electricity. An organised flow of electrical charges is an electric current, like in lightening, which B. Franklin proved in 1792.

The first battery to produce continuous electricity was invented by A. Volta. In 1801, he demonstrated how a pile of zinc and copper disks and paper soaked in saltwater could generate an electric current. From this discovery, and subsequent ones, elements could be isolated by applying electrolytic methods. In the 19th century, H. Davy used electrolysis to isolate potassium, sodium, strontium, magnesium and calcium. Years later, M. Faraday introduced the term ‘ion’ for the entities that carry the electric current through a melted compound or a solution (in Greek ‘ion’ means to go). However, he did not know what those ions consisted of. Thomson came up with the answer with the discovery of the electron, which we will cover later on.

Remember that atoms have the same number of protons as electrons, making them neutral. If an atom gains or loses electrons, ions are formed, which have a net charge of something other than zero.

If an atom loses electrons a cation is formed, which can have a +1, +2 or +3 charge. Likewise, the charge of an anion is –1, –2 or –3 if the atom gains one, two or three electrons, respectively.

When a solution undergoes electrolysis, the cations travel towards the cathode, which contains an excess negative charge. Anions, on the other hand, move towards the anode, giving it a negative charge. This flow of charges completes the electric circuit.

2.2 Radioactivity

The discovery of the phenomenon of radioactivity is credited to both H. Bequerel and the Curies. In 1896, the former noticed that uranium salts emit radiation, and two years later, the Curies discovered that this was a new phenomenon. This led to new lines of research, and E. Rutherford, working with F. Soddy, discovered that radioactivity is due to the spontaneous disintegration of atoms with a large mass. These days we know that there are certain radioactive isotopes that disintegrate spontaneously, called radioisotopes, and they can be produced artificially for a specific purpose. As we will see later on, the atom nucleus was discovered through experiments with radioactive emissions.

2.3 Quanta of light and the photoelectric

In the year 1900, M. Planck suggested a new concept in physics: quanta. These are the minimum amount of energy involved in an interaction.

Five years later, A. Einstein applied this idea to light, and was able to explain the photoelectric effect. N. Bohr later used the idea of quanta of light in his atomic model which in turn explained another phenomenon: atomic spectra.

To conclude, science advanced dramatically during the first part of the 20th century and gave rise to the ‘Atomic Age’. This had significant benefits for society, but also negative impacts, for example, the invention of atomic weapons. Photoelectric effect

Tritium H 1 3 _ i

Atoms are represented by their atomic number Z, and their mass number, A, X Z A . Atoms of the same chemical element have the same atomic number, and if they have different mass numbers they are called isotopes. The picture shows the isotopes of hydrogen.

Understand, think, search...

3 When calculating the mass of an atom, the number of electrons is usually ignored since their contribution is negligible. Look up the mass of subatomic particles and explain why the mass of the electrons can be ignored.

4 Based on the symbols for the following chemical substances, specify the number of protons, neutrons and electrons for each of them:

Be,BeU 4 9 4 10 2 92 238 +

5 Look for information about the photoelectric effect. Why was it such an important discovery? What are its applications? Share your findings with the rest of the class.

Proton Neutron Electron

When a metal surface is illuminated with monochromatic light it could give two different effects:

Einstein explained that quanta of light with sufficient energy (high frequency) ejected the electrons from the metal surface producing an electric current.

THE FIRST ATOMIC MODELS

In this section we will review the first atomic models and the discovery of the main subatomic particles.

3.1 Thomson’s atomic model

In 1897, J.J. Thomson discovered the electron and concluded that electrons were part of the atom. This was the first evidence that showed that atoms were more complex than what Dalton had proposed.

Years before, W. Crookes had experimented with electrical discharge tubes. These are glass tubes with two metal discs, called electrodes, in which he created a vacuum. When he applied a large voltage to the electrodes, the anode lit up: they were cathode rays. So:

• Crookes observed that a shadow appeared on the anode when he placed something in the beam of cathode rays. He deduced that the cathode rays emerged from the cathode and travelled towards the anode.

• He put tiny turbines inside his tubes and observed that they started to move. Cathode rays are formed by particles.

• Thomson modified the tubes to include two parallel plates, one positively charged and the other negatively charged. He observed that the beam deviated* towards the one with a positive charge: so cathode rays have negative charge.

Thomson then proposed his model for the atom in 1904.

Focus on English

Deviate: to change direction.

Crookes tube

According to Thomson, an atom is a positively charged sphere with electrons in it. The electrons may enter or leave the atom, creating ions.

Experimental evidence that led to Thomson’s model

Thomson’s atomic model

Electrons distribute themselves uniformly

Cathode rays are particles.

Thomson tube

Cathode rays have a negative charge.

Atomic models include a certain degree of speculation. We may not say whether they are true or false, so much as how well they explain observed phenomena.

■ The magnitude of the electron charge

Thirty years passed between the discovery of the electron and working out its charge. In 1910, R. A. Millikan measured the electron charge. He obtained a value of –1.6 · 10–19 C.

3.2 Rutherford’s atomic model

In 1911, E. Rutherford and his colleagues Geiger and Mardsen proposed a new atomic model: the nuclear model. It was based on experiments in which they bombarded gold with alpha particles (which have a positive charge).

The Rutherford model describes the atom as a mostly empty space containing a nucleus of positive charge which contains almost all the atom’s mass, orbited by electrons, which have negative charge.

The description of the atom’s shell of electrons orbiting the nucleus does not come from experiments; it is the speculative part of the theory.

■ The discovery of the proton

In 1919, Rutherford discovered that he could convert one element into another by bombarding it with high-energy alpha particles. This process did not only result in a new element. In addition, a particle with a charge of +1, that shared characteristics with the hydrogen nucleus, was obtained. This particle was a proton.

He had transmuted one element into another by changing the number of protons in the nucleus.

Understand, think, search...

6 Associative analysis. Explain the relationship between the Crookes and Thomson experiments and the electron’s properties.

7 According to Thomson’s model, what is the smallest electrical charge that can be isolated?

8 Which of the following phenomena does Thomson’s atomic model explain?

a) The formation of ions.

b) The existence of isotopes.

c) Nuclear reactions.

Rutherford’s atomic model

Rutherford’s experiment

Rutherford bombarded a thin sheet of gold with alpha particles, observing different behaviours.

Analysis of a impact on the screen

There is a large empty

The atom is mostly empty. The postitively-charged nucleus is at the centre and the negatively-charged electrons are in orbit around it.

From these results, Rutherford deduced a new atomic model that included a new subatomic particle: the proton.

9 Logic wheel. Explain the speculative part of Thomson’s atomic model.

10 Search for information about the Millikan oil drop experiment and write a simple report explaining it. Include relevant diagrams.

11 According to Rutherford, the atomic nucleus is a tiny place containing all the positively charged protons. Comparing the masses of protons with those of the nucleus, researchers postulated that there was another particle, the neutron. Chadwick discovered it in 1932. Working with a group, answer this question: Why do you think that protons in the nucleus do not repel each other?

A few ricochet

ATOMIC SPECTRA AND THE BOHR MODEL

4.1 Inconsistencies in the Rutherford model

The Rutherford model had two inconsistencies: according to classical electromagnetism, the electron could not just travel in any orbit. As the electron is a charged particle it emits energy as it rotates. This implies that, as it lost energy, it would move closer and closer to the nucleus until the electron would finally crash into it.

The second problem was that it could not explain the phenomena of atomic spectra. Atomic spectra is when incandescent light, passed through a prism, splits up (decomposes).

■ Types of spectra

Incandescent: emitting light as a result of being heated.

White light from an incandescent light sources decomposes into colours as it passes through a glass prism. These colours are the light spectrum passing through the prism (refracted light). Each band of colour has an associated range of energy and the spectrum is a continuous spectrum, with no clear separation between colours.

If instead of white light, we pass light from a sufficiently hot source through a prism we see that only some lines appear. This is a line spectrum.

4.2 The Bohr atomic model

In 1913, Niels Bohr, a colleague of Rutherford’s, improved Rutherford’s model by introducing the idea of the quantisation of energy According to Rutherford, the orbit of an electron could be at any distance from the nucleus, with more energy the further away it was. But Bohr added two hypotheses to this model:

• The electron orbits around the nucleus in an orbit with a fixed radius where it neither gains nor loses energy: stationary orbits.

• An electron may move from a lower-energy orbit to a higher-energy one by absorbing a fixed amount of energy; it may reverse the move by emitting the same amount of energy.

The first hypothesis solves the problem of incompatibility with electromagnetism and the second explains atomic spectra.

The spectrum of white light is continuous. Note that there is no detectable separation between the colours in the image.

Hydrogen line spectrum

y HdrogenH

1

4.3 Atomic spectra and the Bohr model: their relationship

The Bohr atomic model uses the idea that the energy of electrons in the atom is discrete, that is, not continuous.

The quantisation of electron energy levels in the shell of the atom is a fundamental property of electrons.

Bohr managed to quantify the electron energy levels as a function of the atom’s atomic number and an integer parameter, n; whose value is always a natural number (1, 2, 3…), that specifies the orbital number. This way we may directly relate the energy of a level with its matching value of n.

If an electron is not in the lowest possible energy level, we say the atom is in an excited energy state. If not, and all the electrons in an atom are at their lowest possible energy levels, we say the atom is in its ground energy state.

Explain your answer

1-2-4. Why do the steps in the drawing have different heights? How many jumps between steps does the staircase have?

Explanation of hydrogen’s spectrum

The four lines in hydrogen’s spectrum correspond to the electron’s jumps from its possible excited states down to the n = 2 energy level:

Jump from n = 6 to n = 2 8 E6

Jump from n = 5 to n = 2 8 E5

Jump from n = 4 to n = 2 8 E4

Jump from n = 3 to n = 2 8 E3

Electron jumps from energy levels above n = 1 are in the ultraviolet band, which is invisible to the human eye.

An

analogy for electron energies

Imagine the potential energy of an object on a staircase as similar to the energy of an electron.

Not every value is possible: only those that match the height of each step.

If an electron rises it is because it has absorbed the energy difference and when it falls it emits the energy as radiation, which is what we see in atomic spectra.

Understand, think, search...

12 What does it mean to call an orbit stationary?

13 Explain what experimental evidence led to each atomic model.

14 Explain why atomic spectra are lines and not continuous.

15 Could hydrogen have more spectral lines with different energy values? If so, to what energy jumps would they belong?

16 CAF. Indicate if this statement is true or false and explain why: For an electron to move from n = 2 to the n = 3 state it must absorb energy.

QUANTUM MODEL OF THE ATOM

Bohr’s atomic model had limitations: it could only produce precise calculations of the energy levels of hydrogen or ions with one electron. The quantum model of the atom overcomes that limitation by introducing the concept of the atomic orbital.

5.1 Atomic orbitals

Focus on English

A model is a representation of something, usually on a smaller scale: ‘a model train’. It is also a standard to be imitated: ‘she was my model for good behaviour’. Today, a model is usually associated with a person whose profession is posing for artists or photographers or employed to wear clothing or pose with a product.

Bohr’s atomic model visualises the electron’s movement as orbiting around the nucleus. But according to W. Heisenberg’s uncertainty principle, it is impossible to know the exact trajectory of a subatomic particle, such as an electron. At best, we may be able to work out the probability of where the subatomic particle is. We moved from talking about an orbit to orbitals.

An atomic orbital is an area where the probability of finding an electron is very high. A maximum of two electrons can be in an orbital.

Atomic orbitals are referred to by a letter. The simplest are: s, p, d and f. Not all energy levels have the same orbitals. Each layer of electrons, that is, each energy level, may contain a different number of electrons. So each level corresponds to different orbitals (see table below).

Atomic orbitals s and p; levels and sub-levels of s, p, d and f S and p orbitals

• Since they are regions in space, atomic orbitals have different geometric shapes. The simplest is a sphere, the shape of s orbitals.

• There are three types of p orbitals, each oriented in a different direction, X, Y or Z. They have lobes.

• There are five types of d orbitals at each energy level, starting at the third.

• There are f orbitals starting at the fourth energy level. There are seven types.

Energy-orbital relationships

• Each electron orbital has 2 electrons. The s orbitals only accept 2 electrons; the p orbitals accept 6 electrons; the d orbitals accept 10 and the f orbitals accept 14.

• As a general rule we may say that the number of electrons in each type of orbital is twice the number of orbitals at each level.

5.2 Electron configuration

The number of electrons in the highest, or outermost, energy level determines an atom’s chemical properties. Predicting the chemical properties of atoms of different elements using the number of electrons is very important. It gives us information, for example, about the type of bonds they will form, as we will see in the following unit. To do so, we need to know the electron configuration.

The electron configuration is the way the electrons are distributed in the shell of an atom.

Before writing the electron configuration we need to know the rules that govern how electrons fill atomic orbitals.

■ Rules for filling orbitals

• Atomic orbitals fill from least to most energy. We need to know the order of the orbitals in terms of energy, as shown in the figure. Note that the 3d orbitals have higher energy than the 4s orbitals, so they will fill only after the 4s orbital fills.

• As orbitals with the same energy level fill up, the next ones begin filling. In the figure, each arrow represents an electron. See how there are two arrows, or electrons, for each full orbital. In the example in the figure, the orbitals are filled up to the 5p level, which begins filling when the 4d level is full.

• Electrons occupy the maximum number of orbitals at any given energy level. This is known as Hund’s rule of maximum multiplicity. As we see in the figure, four electrons occupy three 5p orbitals, rather than remaining grouped in just two orbitals.

■ Writing electron configurations

• We write the element’s symbol in square brackets when we are referring to its electron configuration.

• We designate the orbitals of each level as follows:

– The s orbital in the first energy level: 1s.

– The s orbital in the second energy level: 2s.

– The p orbitals in the second energy level: 2p.

• We use superscript to specify the number of electrons in each type of orbital. For example:

– 2 s1: there is one electron in the s orbital in the second energy level.

– 3 p5: there are 5 electrons in the p orbitals in the third energy level.

So the electron configuration of oxygen, with 8 electrons, is like this:

[O] = 1 s2 2 s2 2 p4

Note that the p orbitals of the second level are not full.

The arrows in the figure represent the two electrons in each orbital. To distinguish them, one points upward and the other downward.

This orbital energy distribution will be easy once you learn the energy level diagram on the next page.

Understand, think, search...

17 Round table. Explain the difference between an orbit and an orbital.

18 Write the number of electrons in an atom with the following electron configuration:

1 s2 2 s2 2 p6 3 s2

19 How many orbitals in the highest energy level are full in an atom with the following configuration?

1 s2 2 s2 2 p6 3 s2 3 p3

What rule did you use?

QUANTUM MODEL OF THE ATOM 5

Energy level diagram

■ Energy level diagram

Energy level diagrams are aids for remembering the sequence of the orbitals in order of rising energy level. If we follow the order the diagrams indicate, we will see, for example, that after the 4 s orbital, the next ones to fill in are 3 d, 4 p and 5 s, followed by 4 d, 5 p, 6 s and 4 f.

■ Valence electrons

An element’s properties come from its electron configuration, but specifically from its valence electrons

The electrons in the last occupied level are called the valence electrons.

For magnesium, with electron configuration [Mg] = 1 s2 2 s2 2 p6 3 s2, the electrons in the 3s orbital, the last filled shell, are its valence electrons.

Problem solved

1. Given the atomic number of germanium (Z = 32):

a) Write the electron configuration of the neutral isotope of germanium.

b) Specify the valence electrons.

c) Write the electron configuration of the cation Ge2+

a) Neutral germanium has 32 electrons. We will write the complete electron level diagram and follow the arrows until we count 32 electrons. We obtain:

[Ge] = 1 s2 2 s2 2 p6 3 s2 3 p6 4 s2 3 d10 4 p2

b) The last level with electrons, in this case, is the fourth. The valence electrons are the two in the 4 s and the two in the 4 p orbitals.

c) The electron configuration of Ge2+ is:

[Ge2+] = 1 s2 2 s2 2 p6 3 s2 3 p6 4 s2 3 d10

Understand, think, search...

20 Explain why it is possible to have two electrons in the 2 s orbital and six in the 2 p orbitals.

21 Write the electron configuration of the neutral isotopes of lithium (Z = 3), sodium (Z = 11) and potassium (Z = 19).

22 Write the electron configuration of the Li+ cation.

23 We all contribute. Explain why the n = 4 level may have up to 32 electrons.

Note in the diagram how we draw the diagonal lines to specify the filling order.

24 Think and share with a partner. Write the electron configuration of the neutral isotopes of fluorine (Z = 9), chlorine (Z = 17), and bromine (Z = 35). What do you conclude?

25 Draw a diagram of sulfur’s atomic structure with circles to show orbitals and arrows to show sulfur’s valence electrons (Z = 16).

THE PERIODIC TABLE OF THE CHEMICAL ELEMENTS

6.1 Mendeleev’s periodic table

The order of the elements is based on their pattern of variation and chemical and physical properties, as observed by Mendeleev and Meyer in 1869. They listed the known elements in order of atomic mass and observed that some properties repeated. Thus, elements with similar properties appear grouped together on the table. Mendeleev also left gaps for undiscovered elements that were found later. This is an example of the predictive ability of science.

6.2 The current periodic table

Search for information

Search on the Internet for the traditional names of some of the groups on the periodic table. For example, halogens.

This was proposed by H. Moseley in 1913 and is almost identical to Mendeleev’s. The elements are organised in order of increasing atomic number and are grouped in:

• 7 periods or rows Elements of the same period have the same number of energy levels.

• 18 groups or columns Elements in a group have the same configuration of valence electrons.

Periodic table of the chemical elements

Noble gases

Write around. The picture below shows the pattern of variation of electron affinity and ionisation energy. But the noble gases break the pattern since they tend not to become ions or form bonds.

Figure out why. It will be a preview of material in the next unit.

6.3 Periodic properties and groups of elements

The periodic table contains:

• Metals. This is the largest group. They tend to lose electrons and become cations.

• Non-metals. These are ten elements that tend to form anions. They are not good conductors of heat or electricity.

• Semimetals and metalloids. These names mean ‘similar to a metal’. They share properties of metals and non-metals.

• Noble gases. There are on the periodic table. They are all gases and it is difficult for them to form compounds.

■ Periodic properties

The order of elements on the periodic table obeys a general, or periodic, law:

When we sort the elements in order of increasing atomic number, we observe periodic variation of some properties.

These are called periodic properties. In this unit we will study electron affinity and ionisation energy.

Electron affinity (EA) is the change in energy when an atom in a gaseous state acquires an electron, forming an anion. The greater the energy, the higher the likelihood of forming anions.

Non-metals have higher electron affinities since they tend to form anions.

The ionisation energy (IE) is the amount of energy that a gaseous atom absorbs when losing an electron and forming a cation. The lower this energy, the greater the likelihood of forming cations.

Understand, think, search...

26 Indicate the number of elements in each period of the periodic table.

27 Classify the following elements as metals, non-metals, semimetals or noble gases: iron, chromium, silicon, chlorine and argon.

28 Search for information about H. Moseley’s life and reflect and write about the involvement of scientists in war.

29 Order these elements in increasing order of electron affinity: Ca, Se, Ga, Br and Cu.

30 Why is an element with a high ionization energy unlikely to form cations?

Metal elements have lower ionization energies than non-metals since they tend to form cations.

So we may say that both properties, electron affinities and ionization energy, rise as we move right across a period and fall as we move downward in the same group.

6.4 The periodic table and electron configurations

Given the electron configuration of an element, we may place it on the periodic table. See, for example, the elements in group 14:

Note that all end with p2 which is the same as tin and lead. We may conclude that an element whose electron configuration ends in p2 is in group 14.

So the main energy level of an atom’s valence electrons is the same as the period of the element (figure below).

This relationship permits us to write an abbreviated electron configuration and predict an element’s chemical behaviour, using the periodic table.

The abbreviated electron configuration contains the symbol of the preceding noble gas and specifies only the valence electrons.

We may generally relate the configuration of an element’s valence electrons with the element’s position on the periodic table.

The picture on the left shows the electron configurations of the valence electrons in each block of the periodic table.

On it we can see that helium, the noble gas with the lowest atomic number, has an electron configuration different to that of the rest of the noble gases. It is an exception.

Understand, think, search...

31 Write the electron configuration of these representative elements and indicate their position on the periodic table: potassium (Z = 19), neon (Z = 10), aluminium (Z = 13), and sulfur (Z = 16).

32 Write the abbreviated electron configuration and specify the valence electrons of phosphorus (Z = 15), tin (Z = 50), iodine (Z = 53), and francium (Z = 87).

33 Of the elements in the previous exercises, which will form cations and which anions?

34 Is the element whose electron configuration ends in 4 s2 3 d 6, a metal, a non-metal or a noble gas?

35 Write the atomic number and symbol of the elements whose valence electrons are: a) 3 s2 3 p2, b) 2 s2, c) 4 s2 4 p5, d) 3 s2 3 p6. Which are noble gases?

Relationship between electron configuration and position on the periodic table

ATOMIC MASSES

The discovery of the electron led to Thomson’s atomic model. Rutherford’s model included the proton. Now we shall examine the implication of the discovery of the neutron.

7.1 The discovery of the neutron

Rutherford’s atomic model showed that the atomic number, Z, of an atom was approximately half the atom’s mass number. In 1932, Chadwick confirmed the existence of a new particle, the neutron.

The neutron is an electrically neutral particle with a mass similar to the proton which is found in the atomic nucleus.

This made it possible to relate an atom’s mass to its number of particles.

7.2 Mean atomic mass

The relative atomic mass is the sum of the masses of an atom’s protons and neutrons (we do not include the mass of electrons because it is so small in comparison to the mass of the proton and neutrons).

But not all atoms of an element have the same mass. Each element has several isotopes. So calculating the relative atomic mass, also known as the atomic weight, of an element requires accounting for the relative abundance of each isotope.

Problem solved

2. Uranium has three isotopes: 234U, 235U and 238U, with relative abundances of 0.0057 %, 0.72 % and 99.27 %, respectively. Calculate the relative atomic mass of uranium, in atomic mass units, u.

1 The atomic mass number is the mass in atomic mass units of each atom.

Understand, think, search...

36 Boron has two stable isotopes, B-10 and B-11. Using the definition of the theoretical mass of the atom and given the relative abundances of isotopes of 19.78 % and 80.22 % respectively, calculate the mean atomic mass of boron.

37 Calculate the relative abundance of the isotopes of chlorine, given that there are two, with atomic masses of 34.97 u and 36.97 u and that the mean atomic mass of chlorine is 35.45 u.

38 CAF. Explain why the values of the masses of the isotopes in the previous activity are not integer numbers of atomic mass units.

2 The contribution of each isotope to the mean atomic mass is: Contribution of U 234 :

As expected, the least abundant isotope contributes the least to the atomic mass.

3 Finally, add up the contribution of each isotope to obtain the mean atomic mass:

GUIDELINES PROBLEM SOLVING

Magnesium, with a relative atomic mass of 24.3 u, has three natural isotopes of atomic masses 24 u, 25 u, and 26 u. The most abundant is Mg-24, with a relative abundance of 78.99 %. What are the relative abundances of the other two isotopes?

SOLUTION

UNDERSTAND THE PROBLEM AND EXTRACT THE DATA

You cannot solve the problem until you understand the question. Recall that this is where you will find the data and quantities necessary to solve the problem.

• In this case it is a problem related to calculating the relative atomic mass. But it does not ask us for the relative atomic mass. It asks for the relative abundance of two types of magnesium.

• We must recall that the sum of relative abundances of isotopes must be 100 %.

• We know that we may obtain the relative atomic mass of an element from the masses of its isotopes and their relative abundance.

• The data given in the problem statement are:

– Mg-24: m = 24 u; abundance, 78.99 %

– Mg-25: m = 25 u; abundance, x

– Mg-26: m = 26 u; abundance, y

DRAW THE PROBLEM

In this case it is not a pure chemistry problem but an application of gravimetric calculations to the relative abundance of two isotopes. To better understand the exercise:

• We may draw the relative abundance of each isotope in a diagram.

• Alternatively, we may represent the contribution of each isotope to the relative atomic mass.

IDENTIFY THE APPLICABLE PHYSICAL LAWS

• In this case, it is more of a mathematical relationship than of a chemical one.

• Therefore, it is worth proposing the equations that relate the data in the problem statement and check if the dimensions are compatible. The problem has to do with relative atomic masses, and in particular with calculating the abundance of two of magnesium’s three isotopes.

OBTAIN THE ANSWER AND ANALYSE IT

• Once we have decided which equations relate the unknowns, we solve the system by the simplest means possible, such as substitution.

• We analyse the results.

• Solving x in the first equation we obtain:

x = 21.01 – y

Abundance: 100

% Contribution

So we need a system of equations:

Relationship between abundances: x + y + 78.99 = 100

Relationship of contributions:

• Substituting in the second equation: 0.25 · (21.01 – y) + 0.26 · y + 18.94 = 24.3

• The values we obtain are: y = 10.75; x = 10.26.

ATOMIC MODELS

In this section we present two tools for working with atomic models. The first will serve as a review of content we saw last year and the other will help us understand what an atomic spectrum is and its relationship with the

Bohr model. Using them, you will notice the utility of these applications for clarifying and consolidating new knowledge.

THE ATOM BUILDER

We will use the atom builder available on Anaya’s website. The application has two parts: ‘Build an atom’ and ‘Game’.

The first part, ‘Build an atom’, shows us all the possibilities of the application. It is divided into several parts:

• On the left-hand side, we have a diagram for building our atom, based on the electron-shell model.

• On the right-hand side, we get information about the atom we have built: its position on the periodic table, its symbol, its net charge and its atomic number.

• We may activate an option to display its name, whether it is neutral or an ion and if it has a stable or unstable nucleus.

LET’S PRACTISE

Activate the option to display all the information in the first part of the application (element, symbol, net charge and atomic number) and all the options on the right-hand box (name, ion/neutral, stable/unstable). Build several atoms. As a starting point we suggest: three protons, two neutrons and two electrons. You will obtain Li 3 5+ and you will see that it is an atom with an unstable nucleus.

As we can build atoms with up to ten protons, the application is limited to displaying atoms up to the second period on the periodic table. However, it is useful for visualising the charge of an ion, the atomic number of an atom and the notation used to convey those values.

Understand, think, search...

1 When we place electrons in the model, we cannot put more than two in the first layer. Why do you think that is?

2 Deactivate the display of all the information on the righthand side and specify the atom or ion in each case (writing its symbol, atomic number, atomic mass number and net charge):

a) 6 protons, 8 neutrons and 6 electrons.

b) 7 protons, 8 neutrons and 8 electrons. Check your results by activating the display on the right side of the application and write the electron configurations of the atoms.

3 Search for information about the carbon isotope in the previous activity and the utility of its instability.

MODELS FOR THE HYDROGEN ATOM

In this second part we will use a simulation of the hydrogen atom. We will go to the following website: https://phet.colorado.edu/es/simulation/ hydrogen-atom. We will have to download and install the application.

This application simulates the behaviour of hydrogen sample when struck with light. It simulates its behaviour in response to both white or monochromatic light.

White light contains the entire band of energy, while monochromatic light only has a narrow band of energy.

Energy is directly related to a parameter of light called wavelength which is a concept you will study in future years.

In the virtual experiment of the simulator, you measure photons, or energy packets, emitted by the hydrogen sample.

These photons correspond to different energy values, depending on their wavelength. To visualise this photon emission, we must check the ‘Show the spectrum’ box.

In the spectrum we may observe the photons with different energy values emitted by the hydrogen sample.

To understand what is happening inside the hydrogen atom and how the atomic spectrum works, we activate the Prediction option in the upper left corner.

THE MODEL’S PREDICTIONS

As we have indicated, for this section we must use the predictive part of the simulation. When we activate it, we note that we have several atomic models (billiard ball; plum pudding, referring to Thomson’s model, and others). For this exercise we will use the Bohr model.

We recommend that you select the option to show the electron energy level diagrams. That way we will see the photon emission and the transitions between energy levels at the same time.

Understand, think, search...

4 Use the Bohr model. First select the white light option, and then select the options to Show spectrum and Show energy diagrams. Observe what happens when a photon with sufficient energy strikes an electron in the first energy level. Describe it in as much detail as you can. You can accelerate the process using the bar on the bottom.

5 Reset the spectrum that you recorded in the previous exercise and select monochromatic light. Observe and write what happens when you use light with the following wavelengths: 94 nm, 440 nm and 700 nm.

Remember to reset the spectrum between observing each wavelength.

Then, answer the following questions:

a) At what wavelengths do transitions between energy levels occur?

b) Which of the three wavelengths matches the highest energy level?

c) Do all the emitted photons have the same amount of energy?

d) What conclusions can you draw?

SCIENCE WORKSHOP

Recreational science

The petites Curie

Introduction

Marie Curie, one of the most renowned women scientists in history, made an outstanding contribution to scientific and technical knowledge with a life marked by her tireless scientific work.

In 1903 she received the Nobel Prize in Physics, along with her husband and colleague Pierre Curie and Henri Becquerel, for the discovery of radioactivity. In 1911 she received the Nobel Prize in Chemistry, the awarding of which was surrounded by controversy.

Her capacity for hard work and the determination with which she faced the challenges she set herself in life would define her today as a great entrepreneur. These qualities are valuable in scientific activity to both conduct research and obtain the necessary funding for the research.

In the summer of 1914, Marie Curie decided that her contribution to France in the First World War would be the organisation of radiology services in field hospitals.

X-rays had been discovered in 1895 by Röntgen and over the following decades had been successfully applied to obtain images used to locate bone fractures and, in combat situations, shrapnel and bullets, without having to manipulate the wounds caused by these. However, carrying X-ray equipment to the front line was difficult, because of their size and the need to carry an electric generator to operate them.

Marie Curie extended the use and systematisation of X-rays to the battle front. To this end, she sought funding and donations of vehicles adapted for transporting the equipment. These vehicles contained not only the X-ray equipment but also dynamos to obtain electric current from the movement of the vehicle’s engine and a darkroom to develop the images obtained.

In addition, she organised a training centre for radiology technicians which several dozen women attended on a voluntary basis, as most of the male population was at the front. The fleet of “petites Curie” (as these mobile X-ray diagnostic units were known) consisted of 20 vehicles with 175 female operators, and Marie Curie herself carried out more than 1,200 radiological examinations.

Infographic

Marie Curie’s contributions to scientific and technical knowledge are extensively documented and have even been made into novels and films on several occasions.

Prizes

Search for information and create an infographic with the most relevant scientific and personal milestones in the exciting life of this extraordinary scientist, who was the first woman to receive a Nobel.

Marie Curie during the First World War in one of the petites Curie.

X-ray image of Anna Bertha Röntgen’s hand, considered the first X-ray image.

Practical work

Cathode rays and Discharge tubes

Procedure

Safety measures

Proposed problem

Verify the electric nature of cathode rays. Observe how discharge tubes containing different gases emit different coloured light.

You will need

• Discharge tubes

• Cathode ray tubes

• Magnet • Induction coil (Ruhmkorff coil) • DC power supply

Keep in mind that the induction coil is an electrical transformer that reaches high voltages. Do not touch it while it is on.

Experiment 1. The nature of cathode rays

• Connect the cathode ray tube to the induction coil. Then connect the coil to a DC power supply which has sufficient voltage.

• Connect the secondary electrodes of the cathode ray tube to another power source, so that you generate a potential difference perpendicular to that of the cathode rays. Write down what happens.

• Disconnect the secondary electrodes and move a magnet near the cathode ray tube. Write down what happens.

Helium discharge tube connected to the induction coil.

Understand, think, search...

1 Group write around. Connecting the secondary terminals of the cathode ray tube produces a potential difference.

a) In what other setting have you used potential differences? How is it related to the intensity of current in a conductor?

b) From what you’ve observed and the knowledge you used to answer the previous question, what conclusion can you draw about the nature of cathode rays?

2 Consequences and results. As we already know, there is a magnetic field around all magnets, and magnetic fields and electric currents interact. Given that concept, explain what happened when you moved the magnet near the cathode ray tube.

Cathode ray tubes.

Experiment 2. Discharge tubes

• Connect the induction coil to a DC power supply and connect the different discharge tubes one after the other to the coil’s terminals.

• Observe the light emitted by each discharge tube.

3 Review the fundamental ideas of Bohr’s atomic model and answer the following questions:

a) What is an atom in an excited state?

b) What do you think happens to the atoms of the gases in the discharge tubes when you apply a voltage?

c) Why does each gas emit different-coloured light?

CHALLENGES THAT LEAVE THEIR MARK

UNDERSTAND

Organise your ideas

Systemic concept map

1 Explain the transition of an electron from one energy level to the other using a nuclear atom model.

2 Complete the gaps A, B, C, D, E and F in the systemic concept map below, using the information from the unit.

Remember that you have the solutions of all the numerical activities in anayaeducacion.es.

The first atomic models

1 Explain how Thomson reached the conclusion that electrons have an electric charge and that it is negative.

2 Explain how researchers concluded that electrons were particles present in all atoms, forming part of matter.

3 Draw Thomson’s atomic model.

4 Which of the following drawings of the atom matches Rutherford’s atomic model? Justify your answer.

5 Explain why the experiments that led to the discovery of the electron did not involve changing elements from one type into another, while those that led to the discovery of the proton did.

6 In the Millikan oil drop experiment, the fact that the drops had a negative charge was fundamental. To achieve that, Millikan used ionizing radiation. Using what you learned in earlier years or through researching online, explain what ionization means.

7 What is the lowest possible value of an electrical charge? Express it as a fraction of a coulomb.

8 Indicate whether the following statements are true (T) or false (F) and explain why:

a) Ion formation may only be explained with Rutherford’s atomic model.

b) Any atomic model may explain any atomic phenomena.

c) Thomson’s atomic model assumes that no part of the atom has a positive charge.

d) Alpha radiation, just like electrons, has a positive electrical charge.

9 Timeline. Make a timeline of the discoveries of the subatomic particles. Include a diagram with the most important traits of each subatomic particle.

10 Are all the subatomic particles elemental? Justify your answer.

11 Indicate the main problem with Rutherford’s atomic model and what its biggest contribution is to our knowledge of the atom.

12 Say what this figure represents with regard to Rutherford’s atomic model:

18 What does it mean when an atom is in its ground state? Will it emit energy in that state? Indicate which drawing matches the ground state:

The quantum model of the atom

19 Briefly answer these questions about the quantum model of the atom:

a) Name the types of orbitals you know.

b) How many different orbitals are there at the n = 3 level?

c) How many electrons may an orbital hold?

d) How many electrons might fit in the n = 2 level? In which orbitals would each be?

20 Indicate whether the following statements are true (T) or false (F) and correct the false ones:

a) An orbital specifies the precise trajectory of an electron.

b) Each orbital has at most four electrons.

c) There are three p orbitals and nine f orbitals.

d) If an atom in its ground state has filled level 2, it has ten electrons.

Atomic spectra and Bohr’s atomic model

13 Let’s check. Explain the difference between a continuous spectrum, such as a rainbow, and a line spectrum, such as atomic spectra.

14 Explain the meaning of the following sentence: Energy in atoms is quantised.

15 CAF. If an atom in its ground state is struck with more energy than necessary to make the first electron transition, will there be an electron transition between those two orbits? Justify your answer.

16 Indicate whether the following statements about the Bohr model are true (T) or false (F) and explain why:

a) The electron orbits around the nucleus.

b) As the electron orbits the nucleus, it emits energy.

c) As the electron moves towards outer orbits, it always emits energy.

d) For an atom to be in an excited state, it must have previously absorbed at least a certain amount of energy.

17 The mirror. Explain the differences between the Rutherford and Bohr atomic models, using the following words: orbit, energy, continuous, stationary.

21 Indicate what is wrong with these box diagrams:

a) 7 7 2 s orbital.

b) 7 7 7 7 7 7 1 p orbitals.

c) 7 9 7 7 2 p orbitals.

22 Correct, if necessary, the following electron configurations:

a) 1 s2 2 s2 2 p8 3 s2

b) 1 s2 2 s2 2 p6 3 s2 3 p6 4 s1

c) 1 s2 2 s2 2 p6 3 s2 3 p6 4 s2 4 p6

d) 1 s2 2 s2 2 p6 3 s2 3 p6 4 s2 3 d6.

23 Write the electron configurations of the following elements:

a) Boron, Z = 5.

b) Aluminium, Z = 13.

c) Oxygen, Z = 8.

d) Silicon, Z = 14.

24 Draw a box diagram representing the valence electrons of magnesium, sodium, phosphorus and chlorine.

CHALLENGES THAT LEAVE THEIR MARK

25 Indicate the number of valence electrons in lithium, sodium, potassium and rubidium. Complete the table below with their electron configurations:

The periodic table and periodic properties

30 Write the electron configuration of the valence electrons of the elements in the last column of the previous exercise, given that oxygen’s (O) atomic number is Z = 8.

31 Draw a diagram of the periodic table and explain in it the relationships between the different groups of elements and the number of valence electrons in each group.

26 Indicate whether the following statements are true or false and correct the false ones:

a) An electron in the 2 px orbital has less energy than one in the 2 pz orbital.

b) The 5 d orbitals fill when the 4 f orbitals are full.

c) The s orbitals always have the lowest energy within an energy level.

d) There are three different types of orbitals in the n = 4 level.

27 Ions form through the gain or loss of electrons. Using the electron configurations of the following ions, specify their electric charges. In each case, after the electron configuration of each ion, the chemical element that it corresponds to has also been included.

a) 1 s2 2 s2 2 p6 3 s2 3 p6; ZCa = 20.

b) 1 s2 2 s2 2 p6; ZNa = 11.

c) 1 s2 2 s2 2 p6; ZAl = 13.

d) 1 s2 2 s2 2 p6 3 s2 3 p6; ZCl = 17.

28 1-2-4. From the results in the previous exercise, specify whether it is possible to identify the element of an ion from its electron configuration.

29 Indicate which of the following box diagrams show excited states.

32 The 6 Ws. Indicate the relationship between the number of electrons in each period of the periodic table and the number of electrons each orbital may store.

33 Make a table showing the period to which each noble gas belongs, including its symbol and electron configuration. To what group do the noble gases belong?

34 Correct these abbreviated electron configurations:

a) [Cs] = [Kr] 6 s1.

b) [Cr] = [Ar] 4 s2 4 d4.

c) [Sr] = [Kr] 4 s2.

d) [Pb] = [Xe] 6 s2 6 p2.

35 Write the abbreviated electron configurations of these elements, using the given information:

a) The element in group 15, fourth period.

b) The element in group 8, fourth period.

c) The second element in group 13.

d) The fourth element in group 2.

36 Given the following electron configurations, write the group and period to which each element belongs, the valence layer and the number of valence electrons.

a) 1 s2 2 s2 2 p6 3 s2 3 p6 4 s2 3 d10 4 p5.

b) [Ar] 4 s2 3 d 2 .

c) 1 s2 2 s2 2 p6 3 s2 3 p6 4 s2 3 d10 4 p6 5 s2 4 d10 5 p6 6 s1

d) [Rn] 5 s1

37 Write the abbreviated electron configuration of the shaded-in elements on the periodic table.

38 We all contribute. Write the abbreviated electron configuration of all the elements in group 17. What do they have in common? What else might we call this group?

39 Write the electron configurations of these ions and write which noble gas has the same configuration as each of these: Mg2+, K+, O2– and F–

40 Order these elements from least to greatest electron affinity: magnesium, silicon, sodium, sulfur, aluminium, chlorine and phosphorus. Indicate whether each of the elements in the preceding exercise would be more likely to form an anion or cation.

41 We have two elements, one with greater ionization energy:

a) Which will be likelier to form cations?

b) Which has greater electron affinity?

42 Order the alkaline metals from least to greatest ionization energy.

43 Round table. Other than the noble gases, which chemical element has the greatest electron affinity and greatest ionization energy? What does this mean?

44 Order the elements whose electron configurations follow from least to greatest electron affinity:

LEARNING SITUATION CHALLENGES THAT LEAVE AN IMPRINT

REFLECT

In this first unit you have completed all the groundwork for the final project: a timeline. This is a good point to stop and think about your work so far to make sure you have built a strong base for the project. To do so, download the questionnaire and assessment from anayaeducacion.es

TEST YOUR SKILLS

Carry out the competency assessment included at anayaeducacion.es.

Everyday Chemistry: What is the universe made of?

The matter we find on the Earth, the Moon, the rest of the solar system, the Sun and the stars is the same. We know the Moon’s composition because in 1969 humankind reached it and returned with samples for analysis on Earth. We also know what Mars and Venus are made of since space probes have reached them. Analysing asteroids fallen to Earth (called meteorites) has given us valuable information about the composition of the planets.

Still, humankind has not been able to send a crewed vehicle beyond the Moon, nor a space probe further than Voyager. So how do we know that the Sun does not contain matter different to that on Earth?

The answer is in part of this unit. Atomic spectra are the ‘fingerprint’ of each element and permit us to distinguish elements beyond any doubt.

So each specific element generates spectral lines, such as those we studied, depending on the formation of its atoms.

Spectroscopy and the Bohr model helped us understand the atom, which has helped us understand the universe.

On the web

• Search the Internet to find out what a spectroscope is and what it is used for.

• Examine the apparatus in the drawing and try to explain what is happening in it. Search for information if you need it, keeping in mind that the light source is a hydrogen lamp.

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