#### 12.9 Forms of the Distribution Function *f*(*λ*)

From purely thermodynamic reasoning, Wien arrived at the relation

*e*_{λ}, = λ ^{−5}*f*(*λT*)

where *e*_{λ} is the monochromatic emissive power of a black body within the wavelength range *λ* to *λ + dλ* and at absolute temperature *T*.

#### 12.9.1 Wien's Formula

Wien arrived at the following relation

on certain arbitrary assumptions; these assumptions are as follows:

- The radiation was produced by oscillators of atomic dimensions.
- The frequency of the emitted waves was proportional to the kinetic energy of the oscillators.
- The intensity in any particular wavelength range was proportional to the number of oscillators ...