[UPSC IFoS 2018] Black Body Radiation (Q449, 10M)

Explain Planck's formula for black-body radiation. Use this formula to show that energy radiated per unit time per unit area in the range d\lambda of \lambda is e(\lambda, T) = \left( \frac{2\pi c^2 h}{\lambda^5} \right) (e^{\beta hc / \lambda} - 1)^{-1} d\lambda