Show that the Planck radiation law agrees with the Rayleigh-Jeans formula for large wavelengths.
Strategy We use Equation (3.23) for the Planck radiation law, let \lambda \rightarrow \infty for the term involving the exponential, and see whether the result agrees with Equation (3.22).
\ell(\lambda, T )=\frac{2 \pi c k T}{\lambda^{4}} (3.22)
\ell(\lambda, T)=\frac{2 \pi c^{2} h}{\lambda^{5}} \frac{1}{e^{h c / \lambda k T}-1} (3.23)