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(D) The time period of revolution of an electron in a Bohr orbit is given by $T = \frac{2\pi r}{v}$.We know that the radius of the orbit $r \propto n^

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$8T$

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(D) The time period of revolution of an electron in a Bohr orbit is given by $T = \frac{2\pi r}{v}$.We know that the radius of the orbit $r \propto n^2$ and the velocity of the electron $v \propto \frac{1}{n}$.Substituting these relations into the time period formula: $T \propto \frac{n^2}{1/n} = n^3$.For the ground state $(n_1 = 1)$,the time period is $T_1 = T$.For the first excited state $(n_2 = 2)$,the time period is $T_2$.Using the proportionality $T \propto n^3$,we have $\frac{T_2}{T_1} = \left(\frac{n_2}{n_1}\right)^3$.$\frac{T_2}{T} = \left(\frac{2}{1}\right)^3 = 8$.Therefore,$T_2 = 8T$.

The period of revolution of an electron in the ground state of a hydrogen atom is $T$. The period of revolution of the electron in the first excited state is

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