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?

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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.

CHEM 110 Section 3 (PM) SP25 Pre-Lecture 6 Quiz C02-1-3

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?

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