An electron having kinetic energy 12.5 eV collides with a ground-state hydrogen atom. The collision leaves the hydrogen atom in a bound excited state, and atomic recoil may be neglected. What is the maximum amount of kinetic energy that the incident electron can lose in a single such collision?
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Question

An electron having kinetic energy 12.5 eV collides with a ground-state hydrogen atom. The collision leaves the hydrogen atom in a bound excited state, and atomic recoil may be neglected. What is the maximum amount of kinetic energy that the incident electron can lose in a single such collision?

Options

G1 Physics · Accepted Answer

The maximum allowed energy loss occurs when the atom is excited to the highest bound level accessible with 12.5 eV. For the third orbit: ΔE₃ = 13.6[1−1 ÷ 9] ≈ 12.09 eV. For the fourth orbit: ΔE₄ = 13.6[1−1 ÷ 16] = 12.75 eV. Because 12.75 eV exceeds the incident energy, the fourth orbit cannot be reached. Hence the largest possible bound-state excitation is to the third orbit, and the maximum energy loss is 12.09 eV. Correct option: B.