A system of physical chemistry - Index of

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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

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