1)

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 


A) $\frac{evr}{2}$

B) 2 evr

C) evr

D) $\frac{evr}{3}$

Answer:

Option A

Explanation:

Magnetic moment of  revolving electron,

   $\mu_{e}=i \times A$

 where, i= current and A= area

 $\therefore$ $\mu_{e}=\frac{e}{T} \times \pi r^{2}$      (As current, i= $\frac{charge}{time}=\frac{e}{T}$)

 where, T= time period of revolution and r= radius of orbit

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$\mu_{e}=\frac{e}{2\pi r} \times v \times \pi r^{2}$

 ( $\because$   Time period (T)= $\frac{ distance }{ speed}$)

 where, v= velocity of revolving electron

$\Rightarrow$    $\mu_{e}=\frac{evr}{2} $

 Hence, the magnetic moment of revolving electron is $\frac{evr}{2}$