A beam of atoms emerges from an oven that is at a temperature T. The distribution of the speeds of the atoms in the beam is proportional to . (a) We have to show that the distribution of the de Broglie wavelengths of the atoms is proportional to , and (b) that the most probable de Broglie wavelength is

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(a)

The distribution of the speeds of the atoms in the beam is proportional to . That is the number of atoms in the beam having speed between and is given by the equation

The relation between speed v of atoms and their de Broglie wavelength is

,

where m is the mass of the atom. We thus have the relation

We define a function by the relation

.

Therefore,

That is

(b)

We find the most probable value of by requiring the condition

This gives