= Solution
Population can move between the levels by electron-impact excitation and de-excitation, spontaneous emission, radiative absorption and stimulated emission. Other collision partners and radiative cascades can matter in a fuller atom. In the elementary <coronal approximation>, the plasma is dilute, optically thin, steady, and weakly illuminated at the transition frequency. Electron impacts predominantly excite the lower level, while spontaneous emission predominantly empties the upper level; collisional de-excitation and photon trapping are negligible. The population balance is
$$
n_eC_{12}N_1=A_{21}N_2,\qquad\boxed{\frac{N_2}{N_1}=\frac{n_eC_{12}}{A_{21}}.}
$$
A key condition is $n_eC_{21}\ll A_{21}$, together with insignificant external pumping and competing channels. A Maxwellian electron <Maxwell-Boltzmann distribution> lets the tabulated rate coefficient be expressed using one <temperature>.
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