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(A) In Bohr's model,the radius of the $n^{th}$ stationary orbit is given by the formula $R_n = a_0 \frac{n^2}{Z}$,where $a_0$ is the Bohr radius and $

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$0.25$

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(A) In Bohr's model,the radius of the $n^{th}$ stationary orbit is given by the formula $R_n = a_0 \frac{n^2}{Z}$,where $a_0$ is the Bohr radius and $Z$ is the atomic number.Since $a_0$ and $Z$ are constant for a given atom,the radius is proportional to the square of the principal quantum number: $R_n \propto n^2$.For the second orbit $(n_1 = 2)$,the radius is $R_1 \propto 2^2 = 4$.For the fourth orbit $(n_2 = 4)$,the radius is $R_2 \propto 4^2 = 16$.Therefore,the ratio is $\frac{R_1}{R_2} = \frac{n_1^2}{n_2^2} = \frac{2^2}{4^2} = \frac{4}{16} = \frac{1}{4} = 0.25$.

Let $R_1$ be the radius of the second stationary orbit and $R_2$ be the radius of the fourth stationary orbit of an electron in Bohr's model. The ratio $\frac{R_1}{R_2}$ is

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