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MHT CET 2026 (16 Apr, Shift 1) · Bohr Model: Orbits, Speed & Angular Momentum

Bohr Model: Orbits, Speed & Angular Momentum question from MHT CET 2026 (16 Apr, Shift 1)

Q22MHT CET 2026 · 16 APR · SHIFT 1Medium

Bohr Model: Orbits, Speed & Angular Momentum

Using Bohr's atomic model, the orbital period of electron in hydrogen atom in the nnth orbit is (ϵ0\epsilon_0=permittivity of free space, h=Planck's constant, m = mass of electron, e = electronic charge)

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Answer: (a)

  1. rn=ε0n2h2πme2r_n = \frac{\varepsilon_0 n^2 h^2}{\pi m e^2}, vn=e22ε0nhv_n = \frac{e^2}{2\varepsilon_0 nh}
  2. T=2πrnvn=2π⋅ε0n2h2πme2⋅2ε0nhe2T = \frac{2\pi r_n}{v_n} = 2\pi\cdot\frac{\varepsilon_0 n^2 h^2}{\pi m e^2}\cdot\frac{2\varepsilon_0 nh}{e^2}
  3. T=4ε02n3h3me4T = \frac{4\varepsilon_0^2 n^3 h^3}{m e^4}
  4. So the answer is (a).
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