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(B) The time period of revolution $T$ is given by $T = \frac{2\pi r}{v}$.The radius of the $n^{th}$ Bohr orbit is $r = \frac{n^2 h^2 \varepsilon_0}{\p

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$\frac{n^3}{Z^2}$

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(B) The time period of revolution $T$ is given by $T = \frac{2\pi r}{v}$.The radius of the $n^{th}$ Bohr orbit is $r = \frac{n^2 h^2 \varepsilon_0}{\pi m Z e^2}$.The velocity of the electron in the $n^{th}$ Bohr orbit is $v = \frac{Z e^2}{2 \varepsilon_0 n h}$.Substituting these into the expression for $T$:$T = \frac{2\pi (\frac{n^2 h^2 \varepsilon_0}{\pi m Z e^2})}{(\frac{Z e^2}{2 \varepsilon_0 n h})} = \frac{4 \varepsilon_0^2 n^3 h^3}{m Z^2 e^4}$.Since $h, \varepsilon_0, m,$ and $e$ are constants,we have $T \propto \frac{n^3}{Z^2}$.

The time of revolution of an electron around a nucleus of charge $Ze$ in the $n^{th}$ Bohr orbit is directly proportional to

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