The angular momentum of an electron in a give | vedclass

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Question

(A) The angular momentum $J$ of an electron of mass $m$ moving in an orbit of radius $r$ with velocity $v$ is given by $J = mvr$.Kinetic energy $(KE)$

Vedclass · Accepted Answer

$\frac{J^2}{2mr^2}$

Vedclass · Answer

(A) The angular momentum $J$ of an electron of mass $m$ moving in an orbit of radius $r$ with velocity $v$ is given by $J = mvr$.Kinetic energy $(KE)$ is given by $KE = \frac{1}{2} mv^2$.We can express $KE$ in terms of $J$ by substituting $v = \frac{J}{mr}$ into the $KE$ formula:$KE = \frac{1}{2} m \left( \frac{J}{mr} \right)^2 = \frac{1}{2} m \left( \frac{J^2}{m^2r^2} \right) = \frac{J^2}{2mr^2}$.Thus,the correct option is $(A)$.

The angular momentum of an electron in a given orbit is $J$. Its kinetic energy will be:

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