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Properties of Atoms. Spectra.

Problem 6.126

Find the ratio of the number of atoms of gaseous sodium in the state 3P3 P to that in the ground state 3S3 S at a temperature T=T= =2400 K=2400 \mathrm{~K}. The spectral line corresponding to the transition 3P→3 P \rightarrow →3S\rightarrow 3 S is known to have the wavelength λ=589nm.\lambda=589 \mathrm{nm} .

Reveal Answer
6.126.N˙/N0=(g/g0)e−ℏω/hT=1.14⋅10−4,where g and g0 are the statistical weights (degeneracy ratios) of the levels 3P and 3S respectively (g=6,g0=2)\begin{aligned} &6.126 . \dot{N} / N_{0}=\left(g / g_{0}\right) e^{-\hbar \omega / h T}=1.14 \cdot 10^{-4}, \text {where } g \text { and } g_{0}\\ &\text { are the statistical weights (degeneracy ratios) of the levels } 3 P \text { and }\\ &3 S \text { respectively }\left(g=6, g_{0}=2\right) \end{aligned}
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