## The quantum hypothesis

Perhaps there is a law of nature which forbids some high frequency modes of vibration. This law must be such that the

number of modes is limited by the condition to form stationary waves, but as the wavelength gets shorter and the frequency increases, this number increases rapidly. As we have seen in Section 11.2.5, this leads to the ultraviolet catastrophe.

There can be only one conclusion:

### Something prohibits higher frequencies.

higher the frequency, the more modes are forbidden. Then only a fraction of the high frequency oscillators will be active. This law could apply also to the vibrating charges in the walls of the cavity (and everywhere else, for that matter).

In a letter written in 1901 Planck wrote: '...the whole procedure was an act of despair because a theoretical interpretation had to be found at any price, no matter how high that might be.'

The proposed law of nature was that an oscillator can only have energy consisting of an integral number of quantum units. The value of such a quantum depends on the frequency of of the oscillator, and is

Planck's quantum postulate: E = hf, where f = frequency of the oscillator

Planck presented his postulate, less than two months after his previous 'comment', at a German Physical Society meeting on 14 December 1900, a date now often regarded as 'the birthday of quantum theory'.

Planck obtained a value for his constant, h = 6.55 x 10-34 Js, which best fitted the data on the radiation spectrum then available. The modern value of this fundamental constant is

Planck's constant h = 6.625255 x 10-34 Js

'Much less simple was the interpretation of the second universal constant of the radiation law, which as the product of energy and time, I called the elementary quantum of action '

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