The kinetic energy of the electron in an orbi | vedclass

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(B) In a hydrogen atom, the electrostatic force of attraction between the nucleus (charge $+e$) and the electron (charge $-e$) provides the necessary

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$e^2/r$

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(B) In a hydrogen atom, the electrostatic force of attraction between the nucleus (charge $+e$) and the electron (charge $-e$) provides the necessary centripetal force for the electron to move in a circular orbit of radius $r$.According to Coulomb's law, the electrostatic force is $F = \frac{1}{4\pi\epsilon_0} \frac{e^2}{r^2}$.The centripetal force required for circular motion is $F = \frac{mv^2}{r}$.Equating these two forces: $\frac{mv^2}{r} = \frac{1}{4\pi\epsilon_0} \frac{e^2}{r^2}$.Multiplying both sides by $r/2$, we get $\frac{1}{2}mv^2 = \frac{1}{4\pi\epsilon_0} \frac{e^2}{2r}$.The kinetic energy $K$ is given by $K = \frac{1}{2}mv^2 = \frac{e^2}{8\pi\epsilon_0 r}$.Since $e$, $\pi$, and $\epsilon_0$ are constants, the kinetic energy $K$ is proportional to $e^2/r$.

The kinetic energy of the electron in an orbit of radius $r$ in a hydrogen atom is proportional to ($e$ = electronic charge).

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