A large collection of hydrogen atoms is initially excited to the fifth Bohr orbit and is then allowed to de-excite through all possible transitions. Which pair is closest to the maximum and minimum photon energies that can appear in the emitted spectrum?
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Question

A large collection of hydrogen atoms is initially excited to the fifth Bohr orbit and is then allowed to de-excite through all possible transitions. Which pair is closest to the maximum and minimum photon energies that can appear in the emitted spectrum?

Options

G1 Physics · Accepted Answer

The maximum photon energy comes from the largest available energy drop, from the fifth orbit to the ground state: E(max) = 13.6[1−1 ÷ 5²] = 13.6×24 ÷ 25 = 13.056 eV. The minimum photon energy comes from the smallest spacing among the populated levels, between the fifth and fourth levels: E(min) = 13.6[(1 ÷ 4²)−(1 ÷ 5²)] = 13.6[(1 ÷ 16)−(1 ÷ 25)] = 13.6×9 ÷ 400 = 0.306 eV. Correct option: A.