An electron having kinetic energy 50 eV collides with He⁺ ions initially in their ground states. Neglect recoil and ionisation, and count only distinct bound excited states that can be reached in one collision. How many such excited states are energetically accessible?
Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model
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Question

An electron having kinetic energy 50 eV collides with He⁺ ions initially in their ground states. Neglect recoil and ionisation, and count only distinct bound excited states that can be reached in one collision. How many such excited states are energetically accessible?

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

G1 Physics · Accepted Answer

For He⁺, Eₙ = −54.4 ÷ n² eV. For n = 2: ΔE₂ = 40.8 eV, possible. For n = 3: ΔE₃ ≈ 48.36 eV, possible. For n = 4: ΔE₄ = 54.4[1−1 ÷ 16] = 51.0 eV, which exceeds 50 eV. Therefore only the second and third excited states are accessible. Hence N = 2.