A system of physical chemistry - Index of

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A system of physical chemistry - Index of

THE QUANTUM THEORY 37

where ^ is a universal constant (Planck's constant) having the numerical

value 6 "5 x lo"^^ erg- seconds.^

Now the smaller the unit the greater the probability that a resonator

will possess at least one or some quanta. If we consider a material

system, made up of molecules, atoms, and electrons, such a system

possesses resonators of various dimensions, i.e. capable of vibrating with

different frequencies. Such a system can absorb or emit a range (or

spectrum) of vibration frequencies. Considering the very short waves,

i.e. large vibration frequency, the quantum c corresponding to this is

large, and hence the chance that a resonator possesses even one

quantum of this size is less than in the case of longer waves, where

each quantum is a smaller magnitude. Less energy of the short wave

type will therefore be emitted than that of the longer wave type.

That is, the energy of the radiation emission curve falls off in the short

wave region. In this way Planck explains the observed diminution in

energy emitted in the visible and ultra-violet region, as shown in

Lummer and Pringsheim's curves. Further, in the region of extremely

long waves v is relatively very small, and hence the size of the unit € is

small, so that for extremely long waves the actual energy contribution

made by this region will be small. We should therefore expect on

Planck's view the energy wave-length curve to pass through a maximum,

as is actually the case.

Starting out with Planck's hypothesis of the discrete nature of absorption

and emission of radiation, it is now necessary to see what

radiation formula may be deduced ; in other words, what theoretical

expression can be deduced for the distribution of energy in the spectrum

of a body emitting temperature-, i.e. black-body-radiation. For an

exact and complete account, the reader is referred to Planck's Theory

of Heat Radiation. We can only here attempt an abbreviated and

approximate deduction, based upon a new method employed by Jeans

{Phil. Mag., 20, 953, 1910)-

If a vibration— that is, a very small spectral region lying between

X and A-f d\, which corresponds experimentally to monochromatic

radiation— can possess the following amounts of energy, viz. o, c, 2e

. . . etc., then the ratio of the probabilities of these events, as in the

usual gas theory calculations, is—

I : ,?-^/*'r : ^"2*/*"^ : etc.

where e is the base of natural logarithms, A a constant, namely, the

gas constant per molecule, and T the absolute temperature. This

means that if we represent by " i " the number of vibrations possessing

no energy at all, then the number of vibrations, each of which possesses

one unit of magnitude c, will be ^~^'*'^, and so on. Instead of thinking

of vibrations in "space," let us think of the resonators or vibrations of

' Planck {Amtalen der Physik. [4], 4, 553, 1901) has shown that the magnitude

of f is a function oiv by applying Wien's displacement law toan expression obtained

by him for the entropy of a system. The reader should also consult Planck's

Theory of Heat Radiation, 2nd edition.

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