Prior to Planck’s derivation of the distribution law for black-body radiation, Wien found empirically a closely related distribution function which is very nearly but not exactly in agreement with the experimental results, namely ρ =(a/λ⁵)e^−b/λkT. This formula shows small deviations from Planck’s at long wavelengths. (i) By fitting Wien’s empirical formula to Planck’s at short wavelengths determine the constants a and b. (ii) Demonstrate that Wien’s formula is consistent with Wien’s law (Problem 7A.3) and with the Stefan–Boltzmann law (Problem 7A.6).

Data in Problem 7A.6

Use the Planck distribution to deduce the Stefan–Boltzmann law that the total energy density of black-body radiation is proportional to T⁴, and find the constant of proportionality.