A system of physical chemistry - Index of

By equation (i)

APPENDIX II i8i

(i - e kr)

hv

III'

I — e^kr

^kr

. (5)

T E / X

//!/

= = •• L(v) ^ N 7.^^ .... (6)

^*T _ I

it follows that—

^i-) = y^-nr. c .... (7)

M _ I

an equation which agrees well with observed results, if, as has already

been noted, h is put equal to 6-55 x 10 "2''. It should be evident now

that Planck escapes from the Rayleigh-Jeans conclusion entirely by

his hypothesis **of** discontinuity in the exchanges **of** energy between the

oscillators and the medium. Had he assumed that c^ €3 - ^v ^s ~ ^21

etc., are infinitesimally small, he would have found for L(i/) in (6) the

limit **of** the right-hand expression as hv approaches zero, which is just

kT, and so have arrived back at equipartition and the previous dis-

crepancy. His essential point is, in fact, the assumption that k is

finite, i.e. that the " elementary region **of** the condition diagram " has

a finite size. So that in a sense Planck's theory is more an innovation

in the method **of** probabilities, and need not be confined to radiation

problems. This point will be touched on later.

Two obvious criticisms **of** this first line **of** argument have been

advanced. First, equation (i) is obtained by an application **of** electromagnetic

equations which rest on the assumption **of** a continuous exchange

**of** energy between oscillators and medium. But as Campbell

in his Modern Electrical TJieory (2nd edition) points out, this may not

be a fatal flaw in the reasoning. Maxwell's equations may be quite

true for average values **of** the electric and magnetic quantities involved

without implying their absolute validity at all instants in the immediate

neighbourhood **of** one oscillator, and so equation (i) might still stand as

an equality **of** average values, even though the discontinuity assumed by

Planck existed for individual doublets and their near environment. It

should be noted, however, in passing, that at a high temperature, say

2000° C., the quantum **of** energy for high-grade light **of** the order

r = 10^^ is 30 times as large as the average energy **of** an oscillator in

these conditions.

The second objection is that to produce the enormously great

number **of** qualities which are known to exist in complete radiation, we