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Question

What is the angular momentum of an electron in the \( n = 2 \) state of a hydrogen atom? (Use \( h =
6.6 \times 10^{-34} \, \text{J·s} \))

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Explanation

**Quantization basis** de Broglie standing wave requires constructive interference, integer wavelengths in orbit, otherwise destructive, so only certain radii allowed r_n = n² a₀, a₀=0.53 Å, angular momentum L = n h/2π, de Broglie explains why orbits are stationary - electron wave closed on itself. L = n (h/2π) . For n = 2 : L = 2 × (6.6 × 10⁻³⁴/2 × 3.14) ≈ 2.1 × 10⁻³⁴ J·s . Using E_n = -13.6/n² eV, r_n = n² a₀, L = n h/2π, R = R₀ A^¹/³, BE = Δm c² and 1 u = 931.5 MeV, evaluation yields 2.1 × 10⁻³⁴ J·s, consistent with

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