(Solution) - A large number of hydrogen atoms are in thermal equilibrium -(2025 Original AI-Free Solution)

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A large number of hydrogen atoms are in thermal equilibrium. Let n2/n1, be the ratio of the number of atoms in an n = 2 excited state to the number of atoms in an n = 1 ground state. At what temperature is n2/n1 equal to
(a) 10-12;
(b) 10-8;
(c) 10-4?
(d) Like the sun, other stars have continuous spectra with dark absorption lines (see Fig. 38.12). The absorption takes place in the star's atmosphere, which in all stars is composed primarily of hydrogen. Explain why the Ballmer absorption lines are relatively weak in stars with low atmospheric temperatures such as the sun (atmosphere temperature S800 K) but strong in stars with higher atmospheric temperatures.