Question
An ensemble of hydrogen atoms has electrons randomly occupying the n = 1, 2, 3, and 4 levels.
(a) As electrons move to lower-energy levels, how many distinct wavelengths can the ensemble emit? (b) Find the minimum and maximum photon energies among the transitions counted in (a). (c) Calculate the frequency and wavelength corresponding to each of the two photon energies from (b).
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The question is Chemistry 2e Chapter 6 exercise 28 with its original three-part grouping: line count, both energy limits, then the two frequencies and wavelengths. Calculations use the textbook 2.18 × 10⁻¹⁸ J Bohr constant and do not model intensities, selection rules, or fine structure. Rounded constants or rounding the photon energy early can give slightly different last digits; all displayed results here come from the stated constants without intermediate rounding.