An electron with kinetic energy 15.00 eV collides inelastically with a hydrogen atom initially in its ground state and excites the atomic electron to the third Bohr orbit. Neglect atomic recoil. If the scattered incident electron is left with kinetic energy (N ÷ 100) eV, find N.
Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model
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Question

An electron with kinetic energy 15.00 eV collides inelastically with a hydrogen atom initially in its ground state and excites the atomic electron to the third Bohr orbit. Neglect atomic recoil. If the scattered incident electron is left with kinetic energy (N ÷ 100) eV, find N.

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

G1 Physics · Accepted Answer

Excitation energy from the ground state to the third orbit is ΔE = 13.6[1−1 ÷ 3²] = 13.6×8 ÷ 9 ≈ 12.0889 eV. Initial projectile kinetic energy: Kᵢ = 15.00 eV. With recoil neglected, K_f = Kᵢ−ΔE = 15.00−12.0889 ≈ 2.9111 eV. Thus, K_f ≈ 291 ÷ 100 eV. Hence N = 291.