A system of physical chemistry - Index of

o 6 A SYSTEM OF PHYSICAL CHEMISTRY

Pringsheim's curve, Fig. 53, Vol. II.) to be a very small fraction **of** the

whole (even at fairly high temperatures). The main part **of** the energy

is confined to the infra-red region. These long waves are considered

as emitted and absorbed by the atoms 01 the substance being set in vibra-

tion. These statements apply only to the continuous spectrum given

out by a black body in the first instance and in general by heated

metals. Planck's resonators for the infra-red may therefore be identified

with the atoms (electrically charged) ; for the ultra-violet, with the

electrons. But Planck in the theoretical treatment **of** the subject has

regarded his resonators as linear^ that is, he only considers the energy

caused by vibration in a single direction. Such a vibration entails one

degree **of** freedom. If we were to apply the equipartition principle to

a **system** **of** such linear resonators, to each resonator, we would ascribe

RT units **of** energy made up **of** ^RT kinetic energy and an equivalent

quantity **of** potential. It is only for extremely long waves that the

equipartition principle holds (as is shown by the degree **of** applicability

'

**of** Lord Rayleigh's formula for radiation), and that only for a limited

temperature range. The essence **of** Planck's view is that it discards t/ie

equipartition principle. It will be noted that the linear resonators **of**

Planck are considered to possess only one-third **of** the total vibrational

energy **of** the actual atoms (**of** a solid), each **of** which possesses three

degrees **of** freedom— as already pointed out in connection with the

values for atomic heat.

According to Planck, the material resonators considered do not

react with, or are not influenced by, iiifinitely small quantities **of** radiation

energy, using the word infinitely in its strict sense. Planck's

attains a

hypothesis may be stated thus : // is necessary that f/ie energy

finite value t in order that the resonators composing the material **system**

may be able to absorb it or emit it. (As already mentioned, Planck

later modified this statement by supposing absorption to be continuous,

but emission discontinuous, i.e. in quanta.) It will be clear how this

hypothesis modifies the principle **of** equipartition **of** energy among

various degrees **of** freedom. To any degree **of** freedom which actually

possesses energy we cannot ascribe less than one quantum and the

(c),

actual quantity possessed will be an integral multiple **of** one quantum.

With this distribution **of** energy some **of** the degrees **of** freedom may

possess no energy at all, i.e. the ^^^//partition idea breaks down.

The term " the quantum " requires now to be considered. Although

we speak **of** this as the unit **of** (radiant) energy, it must be clearly

understood that // is not a fixed and constant quantity **of** energy.

According to Planck, the quantum e, i.e. its size or magnitude, is a

function **of** the vibration frequency (either **of** the radiation, supposing

this to be monochromatic, or what amounts to the same thing, the

frequency **of** the resonator). In fact, according to Planck, there is

direct proportionality between the magnitude **of** € and the frequency v,

this proportionality being expressed in Planck's fundamental relation—

€ = hv