Wien Displacement Law

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Wien Displacement Law for a Blackbody Spectrum

The Wien displacement law refers to a relation between the position of the peak of the emission of a blackbody spectrum and the blackbody temperature (they are inversely related). The peak energy ($E$), frequency ($\nu$), or wavelength ($\lambda$) in a blackbody emission spectrum can be shown to be related to the blackbody temperature ($T$) by setting the derivative of the blackbody (Planck) function to zero. (The solution is not analytic, however). The relation

Following are various convenient forms for the Wien displacement law.

Energy and frequency form:

\[
E_{\rm max} \equiv h\nu_{\rm max} = 2.82kT
\]

or

\[
\frac{\nu_{\rm max}}{T} = 5.88 \times 10^{10} \ {\rm Hz \ deg^{-1}}
\]

Wavelength form:

\[
\lambda_{\rm max} T = 0.290 \ {\rm cm \ deg}
\]

or

\[
\lambda_{\rm max} T = (5000 \ {\rm Angstrom})(5800 \ {\rm Kelvin})
\]

All are equivalent forms of the Wien displacement law.