In the Bohr model, an electron moves in a circular orbit around the… | MHT CET 2021 (23 Sep, Shift 1)

Q89MHT CET 2021 · 23 SEP · SHIFT 1Medium

Bohr Model: Orbits, Speed & Angular Momentum

In the Bohr model, an electron moves in a circular orbit around the nucleus. Considering an orbiting electron to be a circular current loop, the magnetic moment of the hydrogen atom, when the electron is in nth excited state, is

(e = electronic charge, m ${}_{e}$ = mass of the electron, h = Planck's constant)

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Answer: (d)

$M = \frac{evr}{2} = \frac{e}{2m_e}(m_e v r) = \frac{e}{2m_e}L$
Bohr: $L = \frac{nh}{2\pi}$
$M = \left(\frac{e}{2m_e}\right)\frac{nh}{2\pi}$ , so the answer is (d).

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