For Bohr's hydrogen-like atom, what is the velocity of electron in n-th orbit (in terms of fine structure constant α and c)?
- v_n = c / Z
- v_n = c α Z / n (where α ≈ 1/137)
- v_n = c
- v_n = c × n
Show answer and 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).