Discussion
At \( 2500 \ \mathrm{K} \), the fraction of sodium atoms in the excited state at \( 589 \ \mathrm{nm} \) is roughly
Answer: C
Applying the Boltzmann distribution with a 2.1 electron volt gap:
\[ \begin{aligned} \frac{N^{*}}{N_{0}} &\approx e^{-2.1/kT} \\ &\approx 6\times10^{-5} \end{aligned} \]
which is six parts in a hundred thousand. Essentially every atom is in the ground state, which is why absorption by the ground state is so much more reliable than emission from the excited one - and why atomic absorption is less sensitive to flame temperature than atomic emission.
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