A system of physical chemistry - Index of

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A system of physical chemistry - Index of

I So A SYSTEM OF PHYSICAL CHEMISTRY

If we integrate this over the narrow ring in the diagram between

two ellipses determined by values of the energy c and € + 8e, we have

for the number of oscillators whose energies lie between « and e + he, the

expression—

«

Of course, on the assumption of infinite divisability of the energy, the

total number of oscillators, N, should be-

QO

— e krae.

But the essence of Planck's idea is that this integral should be replaced

by a convergent series. For, according to his ideas, the representative

points can only be found on the ellipses corresponding to energies

tj, €2. fa • • • «») etc., where cj is the quantum of energy and = t,, « •

tj ;

they will lie nowhere between these ellipses. The points will, as it were,

jump from ellipse to ellipse. The areas of these ellipses are of course—

I'

-, -, etc., or -i, 2-, 3-', etc..

and the various rings between them have all a common area. It is a

feature of Planck's theory that he gives this area a constant value for

all oscillators of any period, and denotes it by the letter " /i," so that—

e^ == /iv,

€3 = 3/z.', etc.

The integral expression N above must now be replaced by the

series—

A.r

N =

V

A

11 «2

"

. fl + -

e-kr[i,^ f^) +

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