All Problems

Properties of Atoms. Spectra.

Problem 6.126

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

Reveal Answer
6.126.N˙/N0=(g/g0)eω/hT=1.14104,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}