In the Bohr model,an electron moves in a circ | vedclass

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(D) The current $i$ produced by an electron moving in a circular orbit is given by $i = \frac{e}{T}$,where $T$ is the time period of revolution. Since

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$\left(\frac{e}{2 m_{e}}\right) \frac{nh}{2 \pi}$

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(D) The current $i$ produced by an electron moving in a circular orbit is given by $i = \frac{e}{T}$,where $T$ is the time period of revolution. Since $T = \frac{2 \pi r}{v}$,we have $i = \frac{ev}{2 \pi r}$.The magnetic moment $M$ of a current loop is $M = iA$,where $A = \pi r^2$ is the area of the orbit.Substituting the values,$M = \left(\frac{ev}{2 \pi r}\right) (\pi r^2) = \frac{evr}{2}$.Multiplying and dividing by the mass of the electron $m_{e}$,we get $M = \frac{e}{2 m_{e}} (m_{e}vr)$.According to Bohr's quantization condition,the angular momentum $L = m_{e}vr = \frac{nh}{2 \pi}$.Substituting this into the expression for $M$,we get $M = \frac{e}{2 m_{e}} \left(\frac{nh}{2 \pi}\right)$.

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