A hydrogen atom of mass approximately u collides with a stationary He⁺ ion of mass approximately 4u. The electron in He⁺ is initially in its ground state. Using the non-relativistic threshold condition, what minimum kinetic energy must the incident hydrogen atom have to excite the He⁺ electron to its second Bohr orbit? If the answer is N eV, find N.
Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model
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Question

A hydrogen atom of mass approximately u collides with a stationary He⁺ ion of mass approximately 4u. The electron in He⁺ is initially in its ground state. Using the non-relativistic threshold condition, what minimum kinetic energy must the incident hydrogen atom have to excite the He⁺ electron to its second Bohr orbit? If the answer is N eV, find N.

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

G1 Physics · Accepted Answer

For He⁺, Z = 2. Ground-state energy: E₁ = −54.4 eV. Second-orbit energy: E₂ = −13.6 eV. Required excitation energy: ΔE = 40.8 eV. Projectile mass m ≈ u. Target mass M ≈ 4u. Threshold energy: K(threshold) = 40.8[1+1 ÷ 4] = 40.8×1.25 = 51.0 eV. Hence N = 51.