A system of physical chemistry - Index of

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A system of physical chemistry - Index of

THE QUANTUM THEORY 43

both of which have been experimentally verified. Planck's expression

is thus a very comprehensive one.^

Some Numerical Vahies.

At this point it is of interest to calculate the values of the two

fundamental constants h and k which occur in Planck's equation, h

is the universal proportionality-factor connecting the energy e of a

quantum with the frequency v ; -^, as will be shown later, is the gas

constant R, reckoned not for a gram-mole but for a single molecule.

The calculation may be carried out as follows.

Kurlbaum {Wied. Ann., 65, 759, 1898) has found by experiment

that the total energy emitted from i square centimetre of a "black

body" in i second, the temperature of the body being 100° C. and

that of the air being taken as 0° C, amounts to 1 0-073 watt/cm.^, that

is—

S = Sioooc.- Sooc.= 4"2 X 7'3i

Stefan's Law we obtain—

X 10^ ergs/cm. ^-sec.

By applying

Hence

S = (^(373^ - 273*).

42 X 7*31 X 10^ ergs

(373* - 273*) cm. ^-sec. -degrees*.

The physical significance of a is evidently the total radiation

emitted from a black body per second, when the temperature difference

between the black body and the surroundings is i degree, the

temperature of the black body being 1° absolute, the surroundings

being at 0° absolute. Corresponding to this emission at 1° absolute,

' To emphasise further the fact that Planck's formula is at variance with the

of freedom, it is inter-

principle of e^ja'partition of energy among various degrees

esting to calculate the energy of an electron vibrating with a frequency identical

with that of the ultra-violet region when light is emitted, and compare this energy

with the energy of an atom or of a gaseous molecule possessing the mean kinetic

energy characteristic of ordinary temperature (say 300° absolute), {cf. J. Stark,

Zeitsch. physik. Client., 86, 53, 1913)- The frequency y for the ultra-violet region

will be about 5 x lo^^ per second. Planck's expression for the mean energy of a

single resonator is, as we have already seen—

U = hvlkr

€ I

For ordinary (low) temperatures—T = 300°— this expression reduces to

hv

U = hve *T| since v is large and T small. The mean energy of an electron

resonator is therefore U, where U = i x 10""^* ergs. The mean kinetic energy of

a gas molecule at the ordinary temperature = ~kT = 6 x 10""^^ ergs, so that instead

of equipartition of energy we find that the energy of the electron vibrating in the

atom or molecule is only one five-hundredth part of the mean kinetic energy of

translation of the molecule itself.

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