Planck’s radiation law for the spectral energy density of blackbody radiation is (u_\lambda d\lambda = \dfrac{8\pi hc}{\lambda^5}\dfrac{1}{\exp!\left(\dfrac{hc}{\lambda k_B T}\right)-1}, d\lambda). From this general expression, the classical and limiting radiation laws can be obtained by considering appropriate physical limits. For Rayleigh–Jeans law, we consider the long wavelength or low frequency limit, i.e., (\lambda) is large. In this case the quantity (\dfrac{hc}{\lambda k_B T}) is very small compared to unity. Using the series expansion of the exponential function, (\exp(x) \approx 1 + x) for (x \ll 1). Hence, [ \exp!\left(\frac{hc}{\lambda k_B T}\right) - 1 \approx \frac{hc}{\lambda k_B T}. ] Substituting this approximation into Planck’s law gives [ u_\lambda d\lambda = \frac{8\pi hc}{\lambda^5}\left(\frac{\lambda k_B T}{hc}\right)d\lambda = \frac{8\pi k_B T}{\lambda^4} d\lambda. ] This is the Rayleigh–Jeans law, which predicts that the spectral energy density is proportional to temperature and varies