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(C) According to Bohr's postulate,the angular momentum of an electron in the $n^{th}$ orbit is given by $m v r_n = \frac{n h}{2 \pi}$.For the second o

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$\frac{h^2}{32 \pi^2 m a_0^2}$

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(C) According to Bohr's postulate,the angular momentum of an electron in the $n^{th}$ orbit is given by $m v r_n = \frac{n h}{2 \pi}$.For the second orbit $(n = 2)$,the radius is $r_2 = n^2 a_0 = 2^2 a_0 = 4 a_0$.Substituting these values: $m v (4 a_0) = \frac{2 h}{2 \pi} = \frac{h}{\pi}$.Solving for velocity $v$: $v = \frac{h}{4 m \pi a_0}$.The kinetic energy $(KE)$ is given by $KE = \frac{1}{2} m v^2$.Substituting $v$: $KE = \frac{1}{2} m \left( \frac{h}{4 m \pi a_0} \right)^2 = \frac{1}{2} m \cdot \frac{h^2}{16 m^2 \pi^2 a_0^2} = \frac{h^2}{32 m \pi^2 a_0^2}$.

The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is [$a_0$ is Bohr radius]:

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