A system of physical chemistry - Index of

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A system of physical chemistry - Index of

APPENDIX II 185

within an infinitesimally small amount of energy from arrival in a

"critical" state, and of these a portion will radiate almost instantane-

ously, or eject an electron. Thus Planck avoids Einstein's revolutionary

postulate on the atomicity of energy.

We saw above that the number of oscillators whose energy lies between

€ and £ + Sc is—

and so the number whose representative points lie between the «th and

the {n + i)th ellipse is A/^^-('*+2)'"'/ftTj the number whose points are

in the next ring are Khe - ^" + 8)''^'/*t_ That is, of all those which acquire

an amount of energy between nAv and {n + i)/iv, the fraction e-^"!^'^

pass the {n + i)th "critical" state and acquire an amount of energy

between {n -f i)hv, and {n + 2)hv. So ^-''^/^t {§ the chance of no

emission taking place, and therefore i - e-h^l^T: is the chance that an

emission will take place. By postulate {c) above, we have—

g- hvfhx

=

J _ /U(.'),

g-h.lkr

where / is a constant to be determined, i.e.—

therefore by equations (8) and (10) —

dh{v) ve^ hv

^ "df ^ 3^^''-/*T - I

V

= -

^ '

!:!:(l(.) ^j:)

2,m\ 2 /

. . . (13)

Now for small values of v, -^ is small and L(v) approaches the value

kT, hv being therefore negligible in comparison with L(v) ;

values of v—

so for small

phv—jT-' = — L(v) . . . . ^ '

(12a)

dt 3W

Now Hertz has shown that in this case (for here by postulate {b)

the classical methods are applicable) the rate of emission of a vibrating

^ . 87rVe2

electric doublet is equal to the fraction —3— of its own energy.^ But

in equilibrium the rate of emission is equal to rate of absorption, therefore

Hertz's result gives us for our case—

^L(v) 87r2,.2^dt

T,c^nt

^ '

1 Wied. Ann., 36, p. 12, 1889.

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