A system of physical chemistry - Index of

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A system of physical chemistry - Index of

THE QUANTUM THEORY 45

stant for the Balmer series in the hydrogen spectrum,^ viz. 3"29o x to^''

according to Millikan, the value of Planck's constant h may be calculated

with a high degree of precision. The value given by Millikan is—

h — 6"547 ± o"oii X io~""

which is in close agreement with that "observed" by Millikan (6*56)

and by Webster (6 "5 3).

The Significance of the Constant k, and a Determination of t/ie Number

of Molecules in one gram-molecule.

Consider once more the Planck expression for the energy of vibration

of a large number of similar resonating particles emitting monochromatic

radiation, viz.—

The expression W*^ — i may be expanded thus—

kT + Kir) + ^^s^'^' p^^'"'"-

If now we are dealing with a system vibrating at very high tempera-

ture it will be seen that the above expression becomes 7=. That is,

at high temperatures—

— Ne

2U = — = N/^T.

c

Ft

Exactly the same result is obtained at less high temperatures if the

system is vibrating very slowly, for in this case v is small (relatively),

and since e = hv the quantity € is likewise small. In both cases the

quantity c vanishes from the expression for the sum of the energies of

the vibrating particles,

absolute temperature.

this energy being simply proportional to the

Under these conditions we reobtain the rt suits

of the ordinary kinetic theory, i.e. the principle of equipartition of

energy, it being no longer necessary to consider the energy as other

than continuous. The principle of equipartition of energy is therefore

true as a limiting case for large values of T, and for small values of v.

Suppose that we are dealing with a solid radiating energy at a temperature

sufficiently high that the energy of vibration of the resonators could

be represented by N^T. The resonators, as employed by Planck, are

linear, i.e. they possess i degree of freedom, to which one would ascribe

(if the equipartition principle applied, i.e. if T is sufficiently high) %^RT

kinetic and -jRT potential, in all RT units of energy per gram-mole or

1

Cf. Bohr's theory of the atom (Chap. V.), according to which Rydbarg's constant

= •ZTr''e*mjh:\

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