Principal Quantum Number Principal Quantum Number The principal quantum number symbolized as n is the first of a set of quantum numbers (which includes: the principal quantum number, the azimuthal quantum number, the magnetic quantum number, and the spin quantum number) of an atomic orbital. The principal quantum number can only have positive integer values. As n increases, the orbital becomes larger and the electron spends more time farther from the nucleus. As n increases, the electron is also at a higher potential energy and is therefore less tightly bound to the nucleus. This is the only quantum number introduced by the Bohr model. For an analogy, one could imagine a multistoried building with an elevator structure. The building has an integer number of floors, and a (well-functioning) elevator which can only stop at a particular floor. Furthermore the elevator can only travel an integer number of levels. As with the principal quantum number, higher numbers are associated with higher potential energy. Beyond this point the analogy breaks down; in the case of elevators the potential energy is gravitational but with the quantum number it is electromagnetic. The gains and losses in energy are approximate with the elevator, but precise with quantum state.
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The elevator ride from floor to floor is continuous whereas quantum transitions are discontinuous. Finally the constraints of elevator design are imposed by the requirements of architecture, but quantum behavior reflects fundamental laws of physics. Magnetic Quantum Numbers :- The magnetic quantum number describes the behavior of electron in a magnetic field. In the absence of external magnetic field, electrons/orbitals have same values of 'n' and 'l' but different values on 'm' have the same energies. They are called degenerate orbitals. However, in the presence of an external magnetic field, orbitals vary in their energies slightly. This is because the preferred orientation of the orbitals in space is a result of interaction of its own magnetic field with that of the external magnetic field. Magnetic quantum exists number due to angular momentum of electron, its motion can be linked to the flow of an electric current. This flow of current generates magnetic field, which can be intricated with an external morganatic or electric field. Because of this interaction, electrons orient themselves in a specific region around nucleus. These specific regions are known as orbitals. The orientation of electrons around the nucleus can be determined by using magnetic quantum number m. Spin Quantum Numbers This quantum number does not follow the wave mechanical treatment. Spin quantum number is related to spin of electrons. It’s equal to 12. This quantum number gives information about the direction of spin of electron. If electron rotates clockwise, the value of s will be +12 and sign will be (↑) an arrow. While in case of anticlockwise rotation of electron, the value of spin quantum number will be - 12 with down headed arrow (↓).
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Question 1: What are the permissible values for l and m when n = 3? Solution :For n = 3, the permissible values for 'l' and 'm' are: l = 0, 1, 2 For 'l' = 0 m = 0 (s-orbital) For 'l' = 1 M = +1, 0, -1 (p-orbital) For 'l' = 2 m = +2, +1, 0, -1, -2 (d-orbital) Question 2: Which orbital is specified by l = 2 and n = 3? Solution: For 'n' = 3 and 'l' = 2: 'l' = 2 means 'd' orbitals The given orbital is '3d'.
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