A system of physical chemistry - Index of

196

A SYSTEM OF PHYSICAL CHEMISTRY

molecule possesses therefore in all five degrees **of** freedom as on the older

theory. It will be observed that Krligerdoes not take into account any

vibration **of** the nuclei with respect to one another along the path or

figure-axis joining their centres. Calling the molecular heat C„, then, in

the region **of** temperature in which the equipartition principle holds, it

follows that C„ is given by the relation—

C„ = 5R/2 = 4-96.

It will be recalled that the molecular heat **of** hydrogen in the neighbourhood

**of** 0° C. is 4"9 to 5*2 cals., whilst at 2000° abs. it is **of** the order

6-5 cals.

Kriiger further points out that the two degrees **of** freedom which correspond

to the precessional vibrations can be treated from the quantum

standpoint just as in the analogous case **of** the vibrations **of** a solid : that

is, the energy content decreases with falling temperature and converges

to zero at zero temperature. A marked decrease in energy content

with lowering **of** temperature has been shown experimentally to be the

case with hydrogen by Eucken [Siizungs. Akad. IViss., Berlin, 191 2,

p. 14 {cf. Chap. IV.)), The curve obtained by Eucken for the molecular

heat points to a single frequency independent **of** the temperature.

For the special

case **of** the hydrogen molecule in which the optical

properties yield quantitative values for the gyroscopic properties, the

angular velocity **of** precession may be calculated and compared with

that obtained from the specific heat data. For this it purpose is necessary

to use the numerical values which Bohr has calculated for the constants

**of** the hydrogen molecule {Th7. Mag., [vi.], 26, 487, 191 3 (^ Chap. V.)).

For the angular momentum **of** a single rotating electron, fir^ifr' (where

r = the radius **of** the electron's path, if/' = the angular velocity **of** its

rotation, and jx the electronic mass), we have the value—

hl2Tr = I •06 X lo~27.

For the radius r **of** the electron's path Bohr finds the value x io~^cm.,

and for i//' the value 3-86 x 10^*^ per second. [The latter quantity is

just 27rw, where w has been defined in Chapter V. as the frequency **of**

revolution **of** the electron, and possesses the value 6*2 x 10^^ for the

electron **of** the hydrogen atom. Bohr has shown {cf. Chap. V.) that,

for the electrons **of** the hydrogen molecule, w is i*i times the w for the

single electron **of** the atom. We should therefore employ a slightly

greater value for t/^' than that adopted by Kriiger.] Further, Bohr has

calculated that 2^, the distance apart **of** the two atoms, is 0*635 x io~^cm.,

the mass **of** the atom having the value i'64 x lo"^* gram, the mass

**of** the electron being 8-97 x lo"'^^ gram. It follows therefore that A,

the moment **of** inertia **of** the atoms perpendicular to the figure axis,

is 2 X 1-64 X io~'^* X (0-317 x io~^)^ or 3*30 x io~*^ Similarly

moment **of** inertia, C, **of** the two electrons is given by—

2 X 8-97 X io~'-" x (5'52 X 10 ^)- or 5-43 X 10 -44