The gyromagnetic ratio of an electron in a hy | vedclass

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(B) The gyromagnetic ratio is defined as the ratio of the magnetic moment $\mu$ to the angular momentum $L$ of the electron.$	ext{Gyromagnetic ratio}

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independent of which orbit it is in

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(B) The gyromagnetic ratio is defined as the ratio of the magnetic moment $\mu$ to the angular momentum $L$ of the electron.$	ext{Gyromagnetic ratio} = \frac{\mu}{L} = \frac{iA}{mvr}$Using the Bohr model,the current $i = \frac{e}{T} = \frac{e \omega}{2 \pi}$ and the area $A = \pi r^2$.The angular momentum $L = mvr = mr(r \omega) = mr^2 \omega$.Substituting these values:$\frac{\mu}{L} = \frac{(\frac{e \omega}{2 \pi})(\pi r^2)}{mr^2 \omega} = \frac{e}{2m}$Since $e$ and $m$ are constants,the gyromagnetic ratio is independent of the orbit $n$ of the electron.

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

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