The gyromagnetic ratio of an electron in a hydrogen atom, according to Bohr model is

The gyromagnetic ratio of an electron in a hydrogen atom, according to Bohr model is
  1. decreases with the quantum number ' $n$ '
  2. independent of which orbit it is in
  3. negative
  4. positive

Solution

$\begin{aligned} & \text { Gyromagnetic ratio }=\frac{\text { Magnetic Moment }}{\text { Angular Momentum }} \\ & =\frac{\mathrm{iA}}{\mathrm{mvr}}=\frac{\left(\frac{\mathrm{e} \omega}{2 \pi}\right)\left(\pi \mathrm{r}^2\right)}{\mathrm{m}(\mathrm{r} \omega) \mathrm{r}}=\frac{\mathrm{e}}{2 \mathrm{~m}} \end{aligned}$ It is independent of the orbit of the electron

Asked in: MHT CET 2021 (20 Sep Shift 1)

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