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(C) Let $R$ be the radius of the circular path. The magnetic moment $M$ is given by $M = i 	imes A$.Since the current $i = \frac{e}{T} = e f$,where $

Vedclass · Accepted Answer

$\left(\frac{e}{2 m}\right) \frac{n h}{2 \pi}$

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(C) Let $R$ be the radius of the circular path. The magnetic moment $M$ is given by $M = i 	imes A$.Since the current $i = \frac{e}{T} = e f$,where $f$ is the frequency,we have $M = (e f) 	imes (\pi R^2)$.Using $f = \frac{v}{2 \pi R}$,we get $M = e 	imes \left(\frac{v}{2 \pi R}ight) 	imes (\pi R^2) = \frac{e v R}{2}$ $\ldots$ $(i)$.According to Bohr's postulate,the angular momentum $L = m v R = \frac{n h}{2 \pi}$.Therefore,$v R = \frac{n h}{2 \pi m}$ $\ldots$ $(ii)$.Substituting $(ii)$ into $(i)$,we get $M = \frac{e}{2} 	imes \left(\frac{n h}{2 \pi m}ight) = \left(\frac{e}{2 m}ight) \left(\frac{n h}{2 \pi}ight)$.

In the Bohr model,an electron of mass $m$ moves in a circular orbit around the proton. Considering the orbiting electron as a circular current loop,find the magnetic moment of the hydrogen atom when the electron is in the $n$th orbit. (Assume $h$ is Planck's constant)

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