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C on te nt s
I auditioned for the Big Brother and all I got was a vague threat of a $5 Million lawsuit
f to in d po an tic n t is io gh ur iss f li he em n o an e io g th at in rd m rn a for ce ow ns on t a C iew tr v
62
resources
12 The boarding house
10 preface
e c a f e r P
Nobel Prizes in Chemistry, Physics and Medicine are awarded each year to scientists who “have
the third and final will of alfred B. nobel, 1895
conferred the greatest benefit to mankind.”
However, mankind hardly takes note. There is a fundamental disconnection between science and society. Scientists are engrossed in their quests, hidden in the recesses of their laboratories, while society is preoccupied with everyday problems. Science doesn’t explain, society doesn’t ask questions. In 1905 Albert Einstein reported his seminal discovery
A. Einstein, Annals of Physics 17, 132, 1905
on the photoelectric effect, for which he was awarded the Nobel Prize in Physics in 1921. In the same
10 s 11
year, James Joyce sent his first draft of Dubliners to Grant Richards publishing company in London. Today, like in 1905, society and science seem to run in parallel without ever crossing paths. Is it really so?
Alessandra Ravidá
ernin g an point heur of vie istic w tow the e ard miss ion a trans nd form ation of lig ht
conc
al be rt ei ns te in
12 s 13
al ic t Mrs. Mooney re d eo an h s t e se th ga n ng ee of di y w r r t ga eo be . re th ts ce s d n i a e a li ex sp rm el n ty fo w it o p ax c ve em M tin ha d e s e i s be l h t l d t s o a l i t d c c a d si an dy so rm an hy s fo bo es in i p a s d d on h se of iti ic bo un s s h o e e ce w of po at bl ro e st , pr ts ra p h e p e t A ite e d h ic y t n c t n i b n o e er tf ne co ed w rp id ye ag , n s e i , s n h m e n rm ot co ro rg ro te e ct la ct e l e e w y d el el tia er le ly a d i v e n h sp a et W sa of us pl o m s m u e to in co iti he fa nt o oc o l et r c e b i v be of cr m e es d us nu e to ak ns tic o m ne ti c g a n fu om en ctr giv e l a e of te d an sta e, m lu vo boarding house nite a fi
of er mb u n s ter ded me a gar r e r pa be the not can t for n e i c ion uffi inat m r as s e t e de plet ing to c om Accord . e t a t as of such energy is to lian theory, the Maxwel be considered a continuous spatial function
in the case of all pu rely electromagne tic phenomena includin g light, w hile the energy o shou f a pond ld, ac erable o cordi bject ng to the p of p resen hys t con icist cepti s, be ons sum repr esen car ted ried as a ele ove ctr r th on e ato s. T ms he an d ap en on erg de yo rab f le bo dy
ca nn ot sub b div e ide into d arb ma itra ny rily or a sma rbit ll pa rari ly rts, ener whi gy o le th fab e eam of lig from a ht point s ource ( accord ing to the Maxw ellian theory of light
or, more generally, according to any wave
er increasing usly spread an ev erates hich op w t, h g of li as e theory ns, h he wav T . e m nctio u volu f l patia ous s tion u n i t nta n e o c s re with rep na the n me i l o l n e he dw r rke al p ve c i wo ne pt o y l y ab rel pu y rob of p db ill e c w la d . rep an or y be e h t er oth n a
14 s 15
uo theory) is contin
tical ever, that the op pt in mind, how ke be ld ou sh It than ages rather to time aver r fe re s n io plete observat f the com In spite o . s e lu a v ed to eous as appli instantan y r o e th the ation of tc, it is confirm sion, e l r e ta n p e is n, d experim s with fractio ion, re perate t o c h le f ic e wh tion, r ad to f light diffrac eory o may le h s t n e o h i tt ct o the ble tha ial fun lied t nceiva s spat p o u p c o a l u il s t n s ti conti ation hen i sform nce w n e i a r r e t p d ith ex n and iate issio sso c ions w m t a e c i s f d n a ao on ctio contr vati omen rodu bser phen p o e e ed th th ce, elat that cen er r me s h e o t r t or o o s , flu ion and eem s n s , s o t t i i I t . h a g ht e em radi et li of lig h th viol ody t a b i r k t w blac y ul ed ect ys b with n a r n o c ode na ath me o of c n phe
transformation of
light are more re ad
16 s 17
ily understood if that the ener gy of light is discontinuou distribute sly d in space. In accord ance with to be co nsidere the assum d here, ption the ene spread rgy of a ing ou li ght ray t from a point distrib source uted o is ver an not con a fini tinuou increa te nu sly sing s mber p a c e but of en at po ergy consis ints i quan ts of n spa ta wh and c e , i c h ar whic whic e lo c a h mo h ca lized ve w n on com ithou ly be plet t e un d p i rodu vidin its. I the ced g, line n th and e fol of th a b s l to t o o oug rbed win his ht a gIw as poin nd t ish t be t h o pr of v e fa use esen iew cts ful whi , ho t to s ch h pin om g th ave e in at t led ves his me tiga app tors roa ch m in t hei ay r re sea rch . one assumes
ap pa re nt di ffe re nc e
in
th e
po si tio n
of a
n
ob je ct
of a
th e
w he n
vi e w ed
fr om
d i ffe r e nt of
nt
he pos ition
n ob j e c t w hen
rent e f f i md o r f ed view
po i nt s
are
nt di f f e r e n ce i
v i ew
the ap p
Paral view f o ts poin
on is ti o ep h t
dif fer e n ce in
of
an
th e ap p a ren t
n he w t ec j ob
ed iv ew m fro n re fi fe d
s int o tp
w vie f o
object when viewed from different points of view
llax: in e c n e er f f di t en r pa p a e th
an f o n o ti i s po e th
1
We start first with the point of view taken in the Maxwellian and
concerning a difficulty with regard to the theory of blackbody radiation
the electron theories and consider the following case. In a space enclosed by completely reflecting walls, let there be a number of gas molecules and electrons which are free to move and which exert conservative forces on each other on close approach: i.e. they can collide with each other like molecules in the kinetic theory of gases. is eq u iv al gas m ent to t he su olec ppo ule s s It is it a io n d ele n th well c at th expr known t trons a e ave re e essio hat rag e n k f in or t , with th qual to etic he ra e e tio o help of ach othe energies this r at f th of e a t r s h m s e um al rm p a a n d elect tion, He l equilib rr rical rium . cond Drude d er u c iv t iv e d ities of m a theor etica etals l
This assumption
Furthermore, let there be a number of electrons which
are bound to widely separated points by forces proportional to their
Polly was a slim girl
distances from these points. The bound electrons are also to participate in conservative
interactions with the free molecules and electrons when the latter come very close. We call the bound electrons “oscillators�: they emit and absorb electromagnetic waves of definite periods. According to the present view regarding the origin of light, the radiation
20 s 21
in the space we
≤
ν
of
y nc
re
ef
r fo
de
ist
in
A
et
he
or
n
α
ex
is
of
va
αν
e lu
d
r
an
la
fo rc e
ec
ft
io
ep
us
he
se
ro ba b
el
ili
ts o
ty
fv al
of
a
ue
so
ps
f
A
o
u ic rt pa
sc
ill
co
mp
on
ob ta in
en
to
va r
th
eZ
ew
th
on
xp an
d
e,
im
.W ee
ft
ts o
nn
er
st an
ma
in
n
ng
se
lo wi
ho
ef ol
ml yc
th
do
in
an
la te
d
at r
al
s or at
ill
gr ou
ic
cif
pe
if
e.,
, i.
..
). 2
(α 2
)f 1
α
f( 1
..
). 2
(A 2
)F 1
(A 1
F
=
. .)
mu
sp ac e
ic
nt
de
n pe
or
em
fs
so
se
es
pr oc
n
rp tio
so
ab
d
an
n
io
ss
mi
ee
th
,. 2
,α 1
α
fo r
be
in
tr
n
re
ur
c oc
er
h ot of
ely
s lo ec
of
ν
iff
fd
o ce
so
ue
l va
i at
di
h )t
r he .T
ts
se
nt
e er
fA
or
on
l wi
th
so
ue
l va of
m
e Th
α.
e
th
in
a lr
e qu
αν
d
an ν fA
e or on
up
..
n
ca
m
le
ro b
sp
Th i
n
te
ary
at a
itr
) 00 (19 99
gi
rb
ve
n
na
po
sio
if
pan
n
ex
1, ys. Ph n. An
ti
his
,.
gt
2
kin
,A
ma
1
es
f(A
gin ma
of
g
ei
T
(Z
ar
o
rin
n
≤
on
R N
n
ar yp
du
im
rv a
ee
s
r
w
n
≥
Aν
0
If
E=
)a ta
bit r
in t
et
te
tw
d
rie
si
h
d
:
of o
th
ei n
lb e
an
0
t=
a
in
T
t=
Fo u
er ie
hi c
an
2π
riods
sin 2 t πν + T αν
case being considered approximate a perfectly random state.
the pe
ν =∞
ν
closely this condition is fulfilled (namely, that the individual pairs of values) of Aν and αν are dependent
be ver y larg
e rela tive t o all
scilla tio
n tha t are pr
esent :
Z= ∑A
ν =1
(statistical) probabilities dW of the form: dW = f(a1, A2, . . . ,α1, α2, . . .)dA1dA2. . . dα1dα2. . . , The radiation is then as disordered as conceivable
T is t aken to
0
α
the tim e
case of dynamic n which is found for the are considering (radiatio ) must be identical h the Maxwellian theory wit e anc ord acc in m equilibriu s of all the relevant ion – at least if oscillator iat rad ody ckb bla the with ered to be present. frequencies are consid by emitted and absorbed disregard the radiation we , ing be e tim the r Fo dynamical equilibrium e into the condition of the oscillators and inquir . molecules and electrons eraction (or collision) of associated with the int e kinetic energy of es asserts that the averag The kinetic theory of gas e kinetic energy of st be equal to the averag an oscillator electron mu motion of an oscillator ule. If we separate the a translating gas molec er, we find for the ents at angles to each oth pon com ee thr o int on electr nents the expression e of these linear compo on of E y erg en e rag ave denotes the number of iversal gas constant. N where R denotes the un absolute temperature. m equivalent, and T the “real molecules” in a gra c energy of a free to two-thirds the kineti The energy E is equal the time average values because of the equality monatomic gas particle tor. If through any ial energies of the oscilla of the kinetic and potent should occur that radiation processes – it gh ou thr e cas r ou in – cause s age value greater or les tor takes on a time-aver illa osc an of rgy ene the uld ons and molecules wo ons with the free electr lisi col the n the , E n tha ent on the average from energy by the gas, differ lead to a gain or loss of is , dynamic equilibrium case we are considering zero. Therefore, in the rage energy E . h oscillator has the ave possible only when eac ument regarding the to present a similar arg We shall now proceed sent in the cavity. s and the radiation pre tor illa osc the en we bet interaction ics equilibrium in M. Plank, condition for the dynam the d ive der has nck Herr Pla be considered a ion that the radiation can sit po sup the r de un e this cas cess. completely random pro
0
3
2
ρν
ρν
L
2
8πν
8πν
T = E = Eν =
R 8πν 2 T N L3
3
L
R
N
ρν =
Eν = ν
dν = R 8π ∞ N 3T 2 L ∫ν dν 0
definite energy distribution between ether and matter.
but also state that in our model there can be not talk of a
equilibrium, not only fail to coincide with experiment,
These relations, found to be the conditions of dynamic
increasing or decreasing, the following relations must obtain:
If the radiation energy of frequency is not continually
part of the radiation with frequency between ν and ν + dν .
frequency, and ρνd ν the energy per unit volume of that
oscillation component), L the velocity of light, ν the
freedom) of an oscillator with eigenfrequency (per
where Eν is the average energy (per degree of
He found,
will be the radiation energy of the space, and in the limit we obtain
The wider the range of wave numbers of the oscillators, the greater
∞
22 s 23
∫ρ
=∞
We 3
wish to
11
T
=
ν
6. − 1 = 4. 0 × 1 86 10 − 6 56 ×1 0−
β
=
concerning show in the ρ following that Herr planck’s determination Planck’s determination of the fundamental constants is, of the fundamental to a certain extent, independent of his theory of blackbody radiation. constants
αν ν
e
2
α
β
Planck’s formula, which has proved M. Plank, Ann. Phys. 4, 561 (1901)
adequate up to this point, gives for ρν For large values of T/ν; i.e. for large wavelengths and radiation densities, this equation takes the form It is evident that this equation is identical with the one obtained ρν
=
α ν β
in Sec. 1 from the Maxwellian
2
T
and electron theories. By equating the coefficients of both formulas one obtains i.e.,
R 8π α = N L3 β
or
N=
β 8π R = 6.17 × 1023 α L3
24 s 25
an atom of hydrogen weigh s 1/N grams = 1.62Ă… x 10−24 g. This is exactly the valu e found by Herr Planck , which in tu rn agrees w ith values found by other me thods. W e therefo the con re arrive clusion: at the grea ter the e the wav nergy de elength nsity an of a rad d iation, t theore he mor tical p e useful d rincip les w to be o the e hav : for s e emp mall w l oyed dens a v e le turn o ities, ngths ut howe a n d In th s v m e a r ll rad , thes e fol iation e prin lowi ciples ng w conc fail u e sh erni s com all c ng b onsi plete for t lack der t ly. he e bod he e y ra mis xper diat sion imen ion w and tal fa itho prop cts u t aga invo tion king of t h a mo e ra del diat ion itse lf.
3 concerning the entropy of radiation
The following tre atment is to be fo und in a famous work by Herr W . Wien and is intro duced here only for the sake of compl eteness. Suppose we have radiation occupy ing a volume υ. We assume th at the observable properties of the radiation are completely dete rmined when th e radiation density This assumption an arb ρ(ν) is given for al itrary one. l frequencies. Siisnc radiation of diffe e rent frequencies are to be consid ered independent of each other when there is no trans fer of heat or work, the entropy of th e radiation can be represented by where ϕ is a func tion of the variabl es ρ and ν. ϕ can be redu ced to a function of a single variable through formulation of th e condition that the entropy of the radiation is unaltered during adiabatic compression be tween reflecting walls. We shall no t enter into this pr oblem, however, but shall directly inv estigate the derivati on of the function ϕ from th e blackbody radia tion law. In the case of blac kbody radiation ρ, is such a func tion of ν that the entro py is maximum for a fixed value of energy; i.e.,
From this it follo ws
as a function of ν
that for every ch oice of δρ
where λ is inde pendent of ν. In the case of blackb ody radiation, theref ore, δϕ/δρ is inde pendent of ν. The following eq uation applies w hen the tempera ture of a unit volume of blackbody radi ation increases by dT or, since δϕ/δρ is independent of ν.
this simplest One will n aturally cling to
g as it is not assumption as lon
ent. controverted experim
∞
S = ν∫ 0
sugar and
( ρ,ν )dν
butter safe under lock and key
∞
δ∫ 0
( ρ,ν )dν = 0
providing 0
∞
∫ 0
δ − λ δρ dν = 0 δρ
ν =∞
dS =
δ d ρdν δρ ν =0
dS =
δ dE δρ
∫
28 s 29
∞
δ ∫ ρ dν = 0
i l i ve e W “
na
s
ty e i c o
ex
i te quis
ly d
de epen
nt o
nc e i c ns
e
and
tech nolo g y, i n wh ich h a rd ly a nyon e kn anything about science and technology� Carl Sagan
ows
1 δ = δρ T
Since dE is equal to the heat
1 dE T
added and since the process is
dS =
reversible, the following statement also applies By comparison one obtains
This is the law of blackbody radiation. Therefore one can derive the law of blackbody radiation from the function ϕ, and, inversely, one can derive the function ϕ by integration, keeping in mind the fact that ϕ vanishes when ρ=0.
ρ = αν 3e
−β
ν T
1 1 ρ ln =− T βν αν 3
S =v
( ρ,ν ) = − βνρ
ln
ρ −1 αν 3
E ( ρ,ν )dν = − βν
ln
E −1 υαν 3dν
asymptotic from for the entropy of monochromatic radiation at low radiation density
From
existing observations of the blackbody
4
radiation, it is clear that the law originally postulated by Herr W. Wien, is not exactly valid. It is, however, well confirmed experimentally for large values of ν/T. We shall base our analysis on this formula, keeping in mind that our results are only valid within certain limits. This formula gives immediately and then, by using the relation obtained in the preceeding section, Suppose that we have radiation of energy E, with frequency between ν and ν+dν, enclosed in volume υ. The entropy of this radiation is: If we confine ourselves to investigating the dependence of the entropy entropy of the radiation at volume υ0, we obtain This equation shows that the entropy of a monochromatic radiation of sufficiently low density varies with the volume in the same manner as the entropy of an ideal gas or a dilute solution. In the following, this equation will be interpreted in accordance with the principle introduced into physics by Herr Boltzmann, namely that the entropy of a system is a function of the probability its state.
S − S0 =
υ E ln βν υ0
34 s 35
on the volume occupied by the radiation, and if we denote by S0 the
5 She was sure she would win
molecularlar-theoretic entropy by molecu of n io lat lcu ca e In th theoretic d “probability” in ently use the wor qu fre e w ds ho investigation met s of ed in the calculu from that employ g rin ffe di e ns se a of the obability” “gases of equal pr dependence probabilities. In particular etically established when been hypoth have frequently of the zed are definite odels being utili entropy one theoretical m an a conjecture. duction rather th de a it rm pe to enough of gases lled per that the so-ca and dilute I will show in a separate pa lly adequate for the solutions on “statistical probability” is fu ena, and I hope that the volume treatment of thermal phenomlogical difficulty that eliminate a by doing so I will mann’s Principle. plication of Boltz obstructs the ap ulation and ly a general form here, however, on will be given. ry special cases application to ve
If it is rea sonable to speak of the probab ility of the state of a system, an d futhermo re if every entropy incr ease can be understood as a transiti on to a state of higher probability, then the en tropy S1 of a syst em is a fun ction of W , the p 1 robability o f its instantane ous state. If we have two noninte racting syst ems S1 and S , w e can write 2 If one consi ders these two system s as a single system of e ntropy S and probab ility W, it fo llows that S = S1 + S 2 = (W ) The la st equation says that th e and states o f the two sy stems are W = W1 + W2 indep endent of e ach other. From these equation it (W1 â‹…W2 ) = 1 (W + follows that 1) 2 (W2 ) The quanti ty C is there fore a universal co nstant; the kinetic theory of g ases show s its value to be R/N, where the constants R and N hav e been defi ned above . If S0 denote s the entro py of a system in so me initial st ate and W denotes th e relative p robability o f a state of e ntropy S, w e obtain in g eneral First we tr eat the foll owing
S1 =
1
S2 =
2
(W ) (W ) 1
2
and finally 1
(W ) = C ln (W ) + const
2
(W ) = C ln (W ) + const
1
1
2
2
(W ) = C ln (W ) + const
S − S0 =
R lnW N
special case. We consider a number (n) of movable points (e.g., molecules) confined in a volume υ0. Besides these points, there can be in the space any number of other movable points of any kind. We shall not assume anything concerning the law in accordance with which the points move in this space except that with regard to this motion, no part of the space (and no direction within it) can be distinguished from any other. Further, we take the number of these movable points to
solution, possesses an entropy S0. Let us imagine transferring all n
υ
anything else being changed in the system. This state obviously possesses a different entropy (S), and now wish to evaluate the entropy difference with the help of the Boltzmann Principle. We inquire: How large is the probability of the latter state relative to the original one? Or: How large is the probability that at a randomly chosen instant of time all n movable points in the given volume υ0 will be found by chance in the volume υ? For this probability, which is a “statistical probability”, one obviously obtains:
= W
movable points into a volume υ (part of the volume υ0) without
υ
0
This system, which, for example, can be an ideal gas or a dilute
n
be so small that we can disregard interactions between them.
tod ay is t
he t e
chn olo gy o f
tom orro w” Ed wa rd Te lle r
“Th e sc ienc e of
By applying the Boltzmann Principle, one then obtains It is noteworthy that in the derivation of this equation, from which one can easily obtain the law of Boyle and Gay–Lussac as well as the analogous law of osmotic
If E is the energy of the system, one obtains:
S
−
S
0
+
motion of the molecules.
n ln
υ
had to be made as to a law of
N
υ
−d ⋅ (E − TS ) = pdυ = TdS = RT
pressure thermodynamically, no assumption
R
0
n dυ therefore N υ pυ = R n T N
exp e wing follo of th nce e d ic epen mat he d hro c o for t e mon lum y of e vo p h o t r n ent form ono the iati n i rad ula this orm f tes i l r a r ew ene iple If on rinc he g t p h n wit man ion: this oltz clus B s n e e r o h pa gc for t and win com ollo cy ν f one n f e e i u th and ls in freq s at wal n of rive g r o i n a t i t l one adia flec tota tic r y re the a b t m a d h a se chro ity t d in nclo ono abil oun is e b f If m o E e r t b rgy he p υ)a will ene υ 0, t me 0 s rgy e u e l n m o i v lu ne a nt the a vo atio inst t of r radi n a e er s (p cho eυ urth f y m l e u w vol dom at: his ran e th mt d o any r u l F c con atic om r h noc ow Mo of l n o i iat hin rad wit ( y of sit den nge a r of the ty idi l a v ’s en Wi
6 S − S0 =
υ E ln βν υ0
R S − S 0 = ln N S − S0 =
υ W= υ0
υ υ0
N E R βν
R lnW N
N E R βν
40 s 41
interpretation of the expression for the volume dependence of the entropy of monochromatic radiation in accordance . 4, In Sec e with boltzmann’s nd th e fou w principle ion ress
R
N 0
e
3
ν
3
βν
− T
− T
d
βν
e
ν
erage ion with the av blackbody radiat ule olec am f o N) ergy (R/ n e 2 c 3 / s ti in kine is ta f nal er o i t b t t a a sl e o de o el tran Th on . , m tu e a ni ntu tur ul a g r m a a r pe m fo qu e tem n y g e e i ra rg am eW ve ene es h h a t t at to he an rt ng i o f d or cc a le, hi w T,
∞
αν
αν βν
the ra rm for di od at mu con io yn l sis a n a ) mi ted be ca h of a a l l ve ya nu s st mb ene ho rgy er of i ug qua nd nta epe h it of m We s nd a gni till w ent tud ish t e o com Rβν /N. pare the a vera ge magnitude of the energ y quanta of the
∫ =
If th m e on en oc tr o h ra rom py d o a ia de tio tic f pe nd n s
0
∫ ∞
d 3 R N T
42 s 43
energy quanta. We shall examine this . llowing in the fo n o ti s e qu
m ag co in ni ve ns tu st is d ig e tin at Rβ e g ν/ w of N he tra en ,t th ns h e for er e ma th ne rgy tio e xt q la no ob uan w f li so vi gh ou ta o ta fe re m a iss s st f lso that ep io they of n su can an ch be i d an nter pret atu ed o re r ex plai ned by considerin g light to cons ist of such
is to
me e olu th v a h e on g er ium u o w th n ed as atio m us di ra uo n ti on c s di
to the result
through photoluminescence
light is transformed
when monochromatic
let us assume that,
just obtained,
both the incident and emitted light
frequency. The transformation process is to be
Rβν/N, where ν denotes the relevant
consist of energy quanta of magnitude
reparation into light of a different frequency,
concerning stokes’s rule According
7
44 s 45
kinds,
other
energy of
etc., as well as to
of frequencies n3 , n4
emission of light quanta
give rise to the simultaneous
the incident light quanta can
is possible that the absorption of
– a light quantum of frequency ν2; it
low densities of incident energy quanta
generates by itself – at least at sufficiently
energy quantum of frequency ν1 is absorbed and
interpreted in the following manner. Each incident
His instinct urged him to remain free
of the quantum cannot be greater than that
incident light
that quantum; it follows okes’s Rule. ell–known St w e th is is Th ording to d that acc ze si a h p m e e strongly under It should b t emitted h g li f o ty e quanti s eption th ndition ther co our conc (o n io t ina to the w illum tional ns of lo r o io it p d o r n p co t ust be ciden ach in tant) m s e n e o c c n s si ing roces light, remain ident tary p c n n i e e m e f th ction an el gth o the a ause stren f c o l l i y l w t here nden ntum lar, t depe y qua u n g i c t r i , e t n d e ar in ligh ent . In p ted k a a d l i t u c n t s in ua g e po y of gy q of th rdin nsit ener e t t cco n n i e A d . e i t c th inc effe her t for rom ent limi of ot c r s ns f e e o i r w t o o es: ia lu ol cas dev he f t be n , g l e e l n i t v i w ci ow abo o ex foll orth ry t e f a h t s t es se e in nec ion abl ept v i c e n o onc he c re c a to t e Rul es’s k o St
ν
1
≤ ≤
1
ν R β N
ν R β N
2
or
ν
2
e.g., heat. It do es not ma tter wh at inter medi ate proc esse s giv e rise to t his fin al r esu lt. I the f flu ore sce nt sub sta n ce no is ta pe rpe sou tua rce l of e ne the rgy pri , nc ipl co eo ns er v f a en tio er n gy of re th q uir at the es e an ne rgy em of itt ed en erg y
48 s 49
1. when the number of simultaneous ly interacting energy quanta per unit volume is so lar ge that an energy quantu m of emitted light can rece ive its energy fro m several incident e n e rgy quanta 2. when ; the incid ent (or e m such a itted) lig compos ht is not of ition th at it co radiat r respon ion wit ds to b hin th lackbod e rang that i y e of va s to s ay, fo li d it y r exam of Wie is pro n’s La ple, w duce w, hen th d by a bod that e inci dent l for th y of s ight uch h e wa Wie igh te velen n’s L m g ths u perat aw i ure nder pos s no c o sibi l n o s nger idera lity tion valid com to t man . Th he c e la s ds s onc t-me pec epti is n ial i ntio on w ot e nter ned x e clud est. hav den Acc ed t e ou sity o hat rdin tlin can ed, g a “n exh bla the on-W ibit ckb p oss ien an e ody ibili radi ner rad ty atio gy b iati n ” e on o h f a very vior wit hin low diff eren the ran t fro ge mt of v hat alid of a ity of W ien ’s L aw.
ca nn ot an ds
lin
�
ep ay ar at life Fr ed an . k Ro sa lin d
nd uld e no t b ver yd es
cie nc ea ho
“S
The usual conception that the energy of light
8
is continuously distributed over the space through which it propagates, encounters very serious difficulties when one attempts to explain the photoelectric phenomena, as has been pointed out in Herr Lenard’s pioneering paper.According to the concept that the incident
P. Lenard, Ann. Phys., 8, 169, 170 (1902)
light consists of energy quanta of magnitude Rβν/N, however, one can conceive of the ejection of
concerning the emission of cathode rays through illumination of solid bodies
electrons by light in the following way. Energy quanta penetrate into the surface layer of the body, and their energy is transformed, at least in part, into simplest way to imagine this is that a light quantum delivers its entire energy to a single electron:
50 s 51
kinetic energy of electrons. The
If one assumes that the individual electron is detached from a neutral molecule by light with the performance of a certain amount of work, nothing in the relation derived above need be changed; one can simply consider P’ as the sum of two terms.
R βν − P N Πε =
we shall assume that this is what happens. The possibility should not be excluded, however, that electrons might receive their energy only in part from the light quantum. An electron to which kinetic energy has been imparted in the interior of the body will have lost some of this energy by the time it reaches the surface. Furthermore, we shall assume that in leaving the body each electron must perform an amount of work P characteristic of the substance. The ejected electrons leaving the body with the largest normal velocity will be those that were directly at the surface. The kinetic energy of such electrons is given by In the body is charged to a positive potential Π is surrounded by conductors at zero potential, and if Π is just large enough to prevent loss of electricity by the body, if follows that: where ε denotes the electronic charge, or where E is the charge of a gram equivalent of a monovalent ion and P is the potential of this quantity
of negative electricity relative to the body. If one takes E = 9.6 x 103, then Π ⋅ 10−8 is the potential in
R βν − P N
volts which the body
ΠE = R βν − P
assumes when irradiated in a vacuum. In order to see whether the derived relation yields an order of magnitude consistent with experience, we take P = 0, ν = 1.03 x 1015 (corresponding to the limit of the solar spectrum toward the ultraviolet) and β = 4.866 x 10−11. We obtain Π ·107 = 4.3 volts, a result agreeing in order magnitude with those of Herr Lenard. If the derived formula is correct, then Π , when represented in Cartesian coordinates as a function of the frequency of the incident light, must be a straight line whose slope is independent of the nature of the emitting substance. As far as I can see, there is no contradiction between these conceptions and the properties of
of everything else, delivers its energy of electrons, then the velocity distribution of the ejected electrons will be independent of the intensity of the incident light; on the other hand the number of electrons leaving the body will, if other conditions are kept constant,
52 s 53
energy quantum of the incident light, independently
Phys. 8, pp. 163, 185, and Table 1, Fig. 2 (1902)
P. Lenard, Ann.
the photoelectric observed by Herr Lenard. If each
in de te be vi ns pr at at i t t op he yo io Re m Fo le or n w a f co as fo m tio s rf t d ith he fro e ar re ts m ob na lu to c k i pl go r n o or m vi o s eg cid P. Le l to m nc et th ou i s es S n o e n i a el er to m en ard the g e fv rd ce s of y ila ke ni it on t l , An as a nc t t t n ig n. o lid rt ha s’s o he e su g ht e i h o n di s i h y . t m R i q d t n y y be po sc ul ho ua iv po pt du o e e t us i ft se nt io du t h n c c h et he ed n, a an se et as al ic of ic d on su la be by el al al t ab w e he ec m m bo ca ob ov e s a t i r u e d d t n o tf ta nd ho e, e ci ns th in or de on de ar at .I s, t i n h f e es th ra tl in on ab ob e ys ig e pl ov en ta h , d a ti w e. in er oe ce s hi s gy s de of ch by n of ot liv th is an e er m th al l e a a d ke e og st in eq ou th v is er ua s se co tio ns pr n: id oc er e s at s io ns :
In
Phys. 8, p. 150 and pp. 166-168 (1902)
ΠE + P ≤ R βν
s ay w l e a th is h c E Π hi w d, , r a ce en en L r r ffe er di H l ia by nt d e e t at po tig e s th ve ce in n es si nc ν, β a t R bs an su h e rt th ΠE + P ≥ R βν te f a o e , r g se ca tly n e ca th ifi In n g si
cathode rays must traverse in order to produce visible light, amounts in 54 s 55
some cases to hundreds and in others to thousands of
, 12 9,
46
an electron
) 03
(19
goes into the
pr od u erg ctio yq no f ua nta man yl . igh t
kinetic energy of
s., hy
.P
nn
,A
rd
a en
be assumed that the
en
L P.
volts. It is therefore to
9 concerning the ionization of gases by ultraviolet light solid bodies
We sha ll have to assum e that , the ion ization o f a gas b y ultrav iolet light, an in dividual li ght energy qu antum is u sed for the ionizatio n of an indiv idual gas molecule. From this is fo llows immediately th at the work of ionization (i.e., the work th eoretically need ed for ionization) of a mo lecule cannot be gr eater than the energy of an ab sorbed light quantu m capable of
R βν ≥ J
58 s 59
producing this effect. If one de notes by J th e (theoretical) w ork of ionizatio n per gram equivalent, th en it follows that: According to Lenard’s mea surements, however, th e largest e ffective waveleng th for air is approxim ately 1.9 x 10 −5 cm: the refore: An up per lim it for the w ork o f ioniz ation can als o be
R βν = 6.4 × 1012 erg ≥ J
of gases the ionization potential for negative ions is, however, five times greater.
d ntials of rarefie tion pote57) the ioniza(Lie om p. fr 2, 190 ed g, in pzi ta ob izitĂŤt in Gasen the smallest J. Stark, Die Electr ng to J. Stark gases. Accordi r (at ials for ai zation potent In the interior observed ioni 10 V. One es) is about od an m u n plati 12 as an ins 9.6 x 10 ta b o re fo re the is nearly r J, which fo it m li r uppe found the value equal to another here is T . e v o b a the uence conseq al iment exper of ing test ich wh ms se e to
She waited on patiently
L
ν Rβ = j
Come down, dear. Mr. Doran wants to speak to you
eat of gr If tance. impor d bsorbe every a antum ergy qu light en , the molecule ionizes a lation must following re tity een the quan obtain betw mber ht L and the nu of absorbed lig d gas j: ules of ionize of gram molec ationship is correct, this rel If our conception relevant gases which (at the must be valid for all n. ion without ionizatio appreciable absorpt frequency) show no
60 s 61
me e to b
Resources
Concerning an heuristic point of view toward the emission and transformation of light by Albert Einstein was first published in German in the Annalen der Physik (Volume 17, pp. 132-148) in 1905 and subsequently translated in English for the American Journal of
I auditioned for the Big Brother and all I got was a vague threat of a $5 Million lawsuit by Josh Gross was posted on the Idahobased weekly newspaper, Boise Weekly,
on Thursday, May 10, 2012 at 11:08 am. http://www.boiseweekly.com/Cobweb/ achives/2012/05/10/i-auditioned-for-big-brotherThe boarding house is a short story from and-all-i-got-was-a-vague-threat-of-a-5-million-lawsuit the collection, Dubliners, by James Joyce. It was first submitted for publication on 1905 and eventually published in June 1914.
62 s 63
Physics (Volume 33, Issue 5, pp. 367-374) in 1965.