A system of physical chemistry - Index of

48 .4 SYSTEM OF PHYSICAL CHEMISTRY

expecting interference on the Einstein view is very considerable, especially

when it is recalled that interference can be produced — as in

certain experiments **of** Michelson— with a difference **of** path **of** 40 cms.,

a distance which is enormously great compared with one wave-length.

Planck's Later Quantum Hypothksis.

Planck's Modified Equation for the Energy **of** an Oscillator.

[Cf Max Planck, Ber. d. Deut. physik. Gesell., 13, 138, 191 1.)

The essential modification here introduced is that while emission

**of** radiant energy takes place in quanta, and therefore discontinuously,

absorption can take place continuously. Planck was led to consider

this as more probable than the older view, one important reason

having to do with the question **of** time. Supposing absorption took

place in quanta only, then an oscillator might be exposed to radiation

so weak as not to yield even one quantum, under which condition the

oscillator would absorb no energy at all. This would be especially true

for large values **of** v (large units). Further, even in those cases in

which absorption could occur, it is conceivable that in weak radiation

there might be a time interval.

On the former view the energy U **of** an oscillator could be expressed

by U = «€, where n is an integer. If absorption is continuous, the

total energ)' can no longer be regarded as an exact multiple **of** €, but

could in general be regarded as consisting **of** ne units plus a quantity p

over. That is—

U = /«€ -f p.

Now the limits for the value **of** p are zero and one e. If we are

considering a large number ot oscillators p will have an average value

e

- or — , so that we can write—

2 2

=rz hv

U = //€ — -1- .

2

On the older view Planck's equation for U is—

hv

u ,hv\kt

which evidently corresponds to Hi.

The new expression for U can therefore be written—

Planck points out several consequences **of** this new expression.