An electron having kinetic energy 13.0 eV collides with hydrogen atoms initially in their ground states. Neglect recoil and consider only collisions in which the atom remains bound after the collision. How many different excited Bohr states of hydrogen can be reached in a single collision?
Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model
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Question

An electron having kinetic energy 13.0 eV collides with hydrogen atoms initially in their ground states. Neglect recoil and consider only collisions in which the atom remains bound after the collision. How many different excited Bohr states of hydrogen can be reached in a single collision?

Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model

G1 Physics · Accepted Answer

For excitation to a bound level n, ΔEₙ = 13.6[1−1 ÷ n²] ≤ 13.0 eV. For n = 2: ΔE₂ = 10.2 eV, possible. For n = 3: ΔE₃ ≈ 12.09 eV, possible. For n = 4: ΔE₄ = 12.75 eV, possible. For n = 5: ΔE₅ = 13.6[1−1 ÷ 25] = 13.056 eV, which exceeds 13.0 eV. Therefore only n = 2, 3 and 4 are accessible excited states. Hence N = 3.