Stimulated emission — UPSC Physics Optional CSE 2020 Paper I

Briefly discuss the postulates of Einstein to explain stimulated emission. Derive an expression for Einstein's A and B coefficients and show that the ratio of coefficients of spontaneous versus stimulated emission is proportional to the third power of frequency of radiation. Why is it difficult to achieve laser action in higher frequency ranges such as X-rays? Can there be a temperature at which the rates of spontaneous and stimulated emission are equal? Illustrate with wavelength \lambda = 5000\,\mathring{\mathrm{A}}.