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(B) According to Bohr's model,the time period $T$ of an electron in the $n^{th}$ orbit is proportional to $n^3$,i.e.,$T \propto n^3$.For the hydrogen

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$27: 64$

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(B) According to Bohr's model,the time period $T$ of an electron in the $n^{th}$ orbit is proportional to $n^3$,i.e.,$T \propto n^3$.For the hydrogen atom,the ground state corresponds to $n=1$.The first excited state is $n=2$,the second excited state is $n=3$,and the third excited state is $n=4$.We need the ratio of the time periods for the second excited state $(n_1 = 3)$ and the third excited state $(n_2 = 4)$.Using the relation $T_1/T_2 = (n_1/n_2)^3$,we get:$T_1/T_2 = (3/4)^3 = 27/64$.Therefore,the ratio is $27: 64$.

The ratio of the time periods of the revolution of the electrons in the second and third excited states of a hydrogen atom is

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