A system of physical chemistry - Index of

40

A SYSTEM OF PHYSICAL CHEMISTRY

E =

Let us write E^ = -rr-, then E = J (•

It will thus be seen that Ea is a rate (the rate **of** X).

change **of** E with

We might also define it as the density **of** the energy radiated from

a spectral region the wave-length limits **of** which differ by unity. This,

though correct, is **physical**ly inconceivable. It would entail the existence

**of** a spectrum the wave-length limits **of** which differ i by cm., a difference

enormous compared to any actual limits reached. It is therefore much

less confusing to think **of** Ea as being the small energy-density increment

AE divided by the correspondingly small spectral width A\ (or

more accurately ^ as above). The expressi6n E^^A or ^ dk is there-

fore the energy-density **of** the radiation between \ and X -h dk. Planck

gives an analogous significance to the term Uvdv. Thus the densityenergy-

**of** the total spectrum may be written—

or writing «,, = ^- , E

E =

=

The term iii, is also a rate, or it may be defined as the density **of** the

energy radiated from a spectral region, the limits **of** the vibration fre-

a different order

quency differing by unity. Numerically ii^, is **of** quite

**of** magnitude from Ea. Thus, since X = -, where c is the velocity **of**

light, it is evident that -y = -.„ so that on increasing v by unity

{i.e. corresponding to the production **of** u,, x i energy-density units)

the wave-length decreases by the amount —,.

This gives a result **of** the

order lo"^^ in the case in which the infra-red wave-length region A = i/x

is considered. Since Ea is the energy-density corresponding to a wavelength

difference **of** U7iity, the term Ea is lo^^ Uv for the region in which

the vibration frequency differs by unity.

The shortest wave-length i.e. **physical**ly possible, the shortest wavelength

capable **of** being emitted or absorbed by an atomic-electronic

mechanism (such as that associated with a is molecule), **of** the order **of**

magnitude **of** very hard X-rays, namely, io~® cm. This sets a limit,

therefore, to the width **of** spectrum which can be regarded as possessing

a **physical** meaning. It is interesting to see what this limiting width is