A particular (hypothetical) atom has only two atomic levels, separated in energy by 3.2 eV. In the atmosphere of a star there are of these atoms per in the excited (upper) state and atoms per in the ground (lower) state. We have to calculate the temperature of the star’s atmosphere.

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Let the temperature of the star be . By the Boltzmann law, we have

where is the difference in energies of the excited state and the ground state. Therefore, we have

Taking natural log of both sides in the above equation, we get