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Energy per unit volume per unit frequency of a blackbody radiation is
S = 2π(kT)^3/(c^2h^2) * x^3/(e^x-1), (1)
where x = hf/(kT)
As the energy of a photon is hf, the number of photons per unit volume per unit frequency is
N = S/(hf) = 2π(kT)^2/(c^2h^2) * x^2/(e^x-1) (2)
Its maximum is when dN/dx = 0. Differentiating equation (2) we obtain the condition ...
This solution answers questions addressing frequency, wavelength and energy density.