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Properties of Atoms. Spectra.

Problem 6.129

Atomic lithium of concentration n=3.6⋅1016 cm−3n=3.6 \cdot 10^{16} \mathrm{~cm}^{-3} is at a temperature T=1500 KT=1500 \mathrm{~K}. In this case the power emitted at the resonant line's wavelength λ=671nm(2P→2S)\lambda=671 \mathrm{nm}(2 P \rightarrow 2 S) per unit volume of gas is equal to P=0.30 W/cm3.P=0.30 \mathrm{~W} / \mathrm{cm}^{3} . Find the mean lifetime of Li atoms in the resonance excitation state.

Reveal Answer
τ=(nℏω/P)(g/g0)e−ℏω/kT=65 ns, where g and g0are the degeneracy ratios of the resonant and the basic level.\tau=(n \hbar \omega / P)\left(g / g_{0}\right) \mathrm{e}^{-\hbar \omega / k T}=65 \mathrm{~ns}, \text { where } g \text { and } g_{0} \text {are the degeneracy ratios of the resonant and the basic level.}
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