Wien's displacement law

For a blackbody, the wavelength at which $B_{\lambda }(T)$ is largest obeyswhere $b$ is Wien displacement constant.

For the frequency version of Planck law, differentiating $x^3/(e^x-1)$ gives $3(1-e^{-x})=x$ at its nonzero maximum. Here $x=h\nu /(k_{B}T)$, so the peak frequency is proportional to temperature. This peak differs from converting the peak of the wavelength version by $\nu =c/\lambda$, because spectral densities transform with a Jacobian.

The Wien displacement constant is the constant of proportionality $b$ in ${\lambda }_{\max }T=b$.