The arrows in the figure depict the transition of an electron in the H atom. Which transition requires the absorption of the highest energy photon?

Question

BlackTom AI · Accepted Answer

To determine which transition requires the absorption of the highest energy photon, we compare the energy gaps between the initial and final levels for each upward (absorption) transition.
Option A: n = 1 to n = 3. The energy difference is ΔE = E3 − E1 = (-13.6/9) − (-13.6/1) = 13.6 × (1 − 1/9) ≈ 12.09 eV. This is a large gap, indicating a high-energy photon is absorbed.
Option B: n = 2 to n = 6. Here, ΔE = E6 − E2 = (-13.6/36) − (-13.6/4) = 13.6 × (1/4 − 1/36) = 13.6 × (8/36) ≈ 3.02 eV. Although substantial, this energy is much smaller than the 12.09 eV for 1→3, so it does not require the highest energy photon among the options.
Option C: n = 3 to n = 2. This transition moves downward (from a higher n to a lower n), which corresponds to emission of a photon, not absorption. Therefore it does not describe an absorption process at all, and cannot be the highest-energy absorption event.
In summary, the upward transition with the largest energy gap is from n = 1 to n = 3, which requires the absorption of the highest energy photon among the given choices.

The arrows in the figure depict the transition of an electron in the H atom. Which transition requires the absorption of the highest energy photon? 单项选择题

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