alleryFor Bohr's hydrogen-like atom, what is the velocity of electron in n-th orbit (in terms of fine structure constant α and c)?
Av_n = c / Z
Bv_n = c α Z / n (where α ≈ 1/137)
Cv_n = c
Dv_n = c × n
Answer & Solution
Correct answer: B. v_n = c α Z / n (where α ≈ 1/137)
v_n = (1/n) × (Zα c) where α = e²/(4πε₀ ħc) ≈ 1/137 is the fine structure constant.
**For H ground state:** v₁ ≈ c/137 ≈ 2.19 × 10⁶ m/s.
Relativistic effects small for light atoms, but become significant for heavy atoms (high Z).
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