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 **of**f 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.