A system of physical chemistry - Index of

194

A SYSTEM OF PHYSICAL CHEMISTRY

bringing in the quantum theory which not only accounts for the series

laws but also quantitatively for the Rydberg constant in terms **of** the

Planck constant h, the charge e, and the mass **of** y. the electron. According

to Bohr, one or more electrons rotate round the nucleus **of** an

atom in a fixed path with the angular momentum h\2Tr or a whole

multiple there**of**, the different angular momenta corresponding to

rotations **of** the electrons in paths **of** different diameter. This theory

has been applied with success by Warburg {Verh. d. D. phys. Ges., 15,

1259 (1913)) to explain the Stark electrical effect. Recently Debye

has employed a similar atomic model to calculate the dispersional

properties **of** hydrogen in particular. The general dispersion formula

has been given by Sommerfeld {Elster atid Geitel Festschrift, p. 549

(1915)).

If the^e models correspond to it

reality, follows that such atoms, and,

as a special case, the hydrogen molecule, must possess gyroscopic properties.

In the following treatment it will be shown that the gyroscopic

properties **of** gaseous molecules, in particular the hydrogen molecule,

are **of** considerable importance for the theory **of** gases, especially in connection

with the problem **of** molecular heat **of** gases, and are capable **of**

solving certain difficulties which exist at the present time.

On Bohr's theory the hydrogen molecule consists **of** two positively

charged hydrogen nuclei with two electrons rotating round the line

joining the centres **of** the nuclei, each electron possessing an angular

momentum **of** /^/27r. The hydrogen molecules behave therefore as

small gyroscopes, which are at the same time free from forces such as

gravity, for the gas is almost perfect. What is particularly significant

from the standpoint **of** kinetic theory is the behaviour **of** such molecular

gyroscopes under collisioris.

The translational motion **of** such freely moving molecules, each with

three degrees **of** freedom, is naturally the same whether the molecules

possesses gyroscopic properties or not. But we have now to consider

the nature **of** the remaining degrees **of** freedom which must be attributed

to the molecule in order to account for its molecular heat. There are

at least two degrees **of** freedom to be accounted for. These, as has

been pointed out in Chapter IV., have been ascribed by Bjerrum to rota-

tion **of** the molecule as a whole. But, as Kriiger goes on to say,

according to the lundamental equations **of** gyroscopic theory, a gyroscope

cannot carry out any rotations, but it can be put into a state **of** vibration

which, in the case **of** a symmetrical gyroscope free from external forces

— the case here considered—

corresponds to regular precession, i.e. precessional

vibrations. Kriiger's theory consists in substituting the idea

**of** precessionaP vibrations **of** the atoms in place **of** rotation **of** the

molecule as a whole, in order to account for the two remaining degrees

**of** freedom. The advantage **of** this comes in. as we shall see later, in

connection with monatomic molecules. In the case considered the

precessional vibration **of** the atoms is regarded as due to a vibration **of**

each electron perpendicular to its own orbit whilst it still keeps on fol-

^ See the footnote on p. 23 **of** Chap. I.

II