A system of physical chemistry - Index of


A system of physical chemistry - Index of



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 thereof, 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


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.


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