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(D) According to Bohr's model,the radius of the $n^{th}$ orbit is given by $R_n \propto n^2$.Given $R_1 = R$ and $R_2 = 4R$,we have $\frac{R_1}{R_2} =

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$1/8$

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(D) According to Bohr's model,the radius of the $n^{th}$ orbit is given by $R_n \propto n^2$.Given $R_1 = R$ and $R_2 = 4R$,we have $\frac{R_1}{R_2} = \frac{R}{4R} = \frac{1}{4}$.Since $R_n \propto n^2$,we have $\frac{n_1^2}{n_2^2} = \frac{1}{4}$,which implies $\frac{n_1}{n_2} = \frac{1}{2}$.The time period $T$ of an electron in the $n^{th}$ orbit is given by $T_n \propto n^3$.Therefore,the ratio of the time periods is $\frac{T_1}{T_2} = \left( \frac{n_1}{n_2} \right)^3$.Substituting the values,$\frac{T_1}{T_2} = \left( \frac{1}{2} \right)^3 = \frac{1}{8}$.

In a hydrogen atom,an electron transitions from an orbit of radius $R$ to an orbit of radius $4R$. What is the ratio of their time periods?

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