Practice question
Question
What is the speed of an electron in the \( n = 3 \) orbit of a hydrogen atom if its speed in \( n = 1
\) is \( 2.2 \times 10^6 \, \text{m/s} \)?
Explanation
**De Broglie hypothesis** λ = h/p, p=mv momentum, suggests electron as wave, in Bohr model circumference 2πr = n λ, standing wave condition, n wavelengths fit into orbit, for n=6, 6 wavelengths, for n=4, 4 wavelengths, explains quantization of angular momentum L = r p = r h/λ = r h n/(2πr)= n h/2π = n ħ, physical basis for Bohr quantization. v_n = (v₁/n) . For n = 3 : v₃ = (2.2 × 10⁶/3) ≈ 7.33 × 10⁵ m/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
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