A system of physical chemistry - Index of

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A system of physical chemistry - Index of

APPENDIX in f97

C can therefore be neglected compared with A.

velocity

Hence for the angular

of precession we have—

, I-o6 X

- 27 ID

V = n 2TrA = TT = 3'2i X 10^*.

3*30 X 10 ~ ^"^ "^

The angular velocity v of precessional vibration is related to the /requency

v of precessional vibration in a very simple manner, viz.—

v = v/27r.

Hence v = — = 7— ^ = 5^ •11 x 10^^.

27r 6-28

This is expression obtained by equating the angular momentum to

hlzTT. This, however, only holds for a single electron. Hence for the

two electrons of the hydrogen molecule we get just twice the value for v —

v = I "006 X 10^'

(revised value given in Kriiger's second paper).

Thus, with the help of Bohr's results, i.e. results in agreement with the

optical properties of the hydrogen molecule, Kriiger has obtained a

value for the vibrational frequency exhibited by the molecule in virtue

of precessional vibrations. We have now to see how far this value

is borne out by a consideration of the molecular heat of hydrogen.

of the mole-

Eucken has applied the quantum theory to the problem

cular heat of hydrog'en in the simple form originally suggested by

Einstein for the case of solids, i.e. we have to do with a single vibration

frequency which ought to agree with the value of v' obtained above,

if Kriiger's argument is correct.

The formula employed by Eucken is—

(^)'

X e^^'\r

To make this agree with observed values it is necessary to write

x lo^^.

^v = 430, and, since ^ = 4'86 x io~^^, it follows that v' = 8-85

The agreement between the two values for v is satisfactory.

The equation obtained by Kriiger on the basis of the gyroscopic

theory of the molecule has also been obtained by Nernst {Verh. d. D.

phys. Ges., 18, 83, (191 6)) based on quite different considerations, involving

rotation of the molecule. Nernst points out that in the case

of hydrogen a more correct value for fiv'

is 450, whence v is 9"3 x lo^^.

This agrees even more closely with the value obtained by Kriiger on

the basis of precessional vibrations.

The above considerations hold good, naturally, not only for hydrogen

but for all gas molecules in which rotating electrons exist, and, accord-

ing to Bohr, the series spectra, which are a general property of gases,

are due to such rotating electrons. The diminution of approximately

5 per cent, in the molecular heats of nitrogen and carbon monoxide

between 273° and 90° abs. observed by K. Scheel and W. Heuse {Ann.

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