A vibrational transition of a gas at radiates at

PHYSICS · Multi-part · Fermi University Physics · Atomic, Molecular & Optical Physics · Radiative transitions, external fields and collisions · Radiative transitions, external fields and collisions

Deriving the Spectrum, Ch Radiative transitions and lifetimes

Problem

A vibrational transition of a gas at

T = 300\,\mathrm{K}

radiates at

\lambda = 10.6\,\mu\mathrm{m}

, with spontaneous rate

A_{21} = 0.30\,\mathrm{s^{-1}}

(the only decay channel of the upper level). Treat the gas as immersed in blackbody radiation at

300\,\mathrm{K}

. ((a)) Compute

\hbar\omega_{21}/k_{\rm B}T

for this line at

300\,\mathrm{K}

. ((b)) Using the Einstein relations, find the ratio of the stimulated emission rate to the spontaneous emission rate in this thermal field. ((c)) Find the lifetime of the upper level, and the actual stimulated emission rate it experiences in the

300\,\mathrm{K}

radiation field.

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