In a hydrogen atom,an electron of charge e re | vedclass

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Question

(A) The magnetic moment of a revolving electron is given by $\mu_e = i 	imes A$,where $i$ is the equivalent current and $A$ is the area of the orbit.

Vedclass · Accepted Answer

$\frac{e v r}{2}$

Vedclass · Answer

(A) The magnetic moment of a revolving electron is given by $\mu_e = i 	imes A$,where $i$ is the equivalent current and $A$ is the area of the orbit.Since the electron revolves with speed $v$ in an orbit of radius $r$,the time period $T$ is given by $T = \frac{2 \pi r}{v}$.The equivalent current $i$ is $i = \frac{e}{T} = \frac{e v}{2 \pi r}$.The area of the orbit is $A = \pi r^2$.Substituting these values into the magnetic moment formula:$\mu_e = \left( \frac{e v}{2 \pi r} ight) 	imes (\pi r^2) = \frac{e v r}{2}$.Thus,the magnetic moment associated with the electron is $\frac{e v r}{2}$.

In a hydrogen atom,an electron of charge $e$ revolves in an orbit of radius $r$ with speed $v$. Then,the magnetic moment associated with the electron is

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