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(C) According to Bohr's theory,the radius of an orbit is $r \propto n^{2}$ and the velocity of an electron is $v \propto \frac{1}{n}$.Time period $T$

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(C) According to Bohr's theory,the radius of an orbit is $r \propto n^{2}$ and the velocity of an electron is $v \propto \frac{1}{n}$.Time period $T$ is given by $T = \frac{2 \pi r}{v}$.Substituting the proportionality relations,$T \propto \frac{n^{2}}{1/n} = n^{3}$.Since $r \propto n^{2}$,we have $n \propto r^{1/2}$,so $T \propto (r^{1/2})^{3} = r^{3/2}$.Therefore,the ratio of time periods is $\frac{T_{1}}{T_{2}} = \left(\frac{R_{1}}{R_{2}}\right)^{3/2}$.Given $R_{1} = R$ and $R_{2} = 4R$,we get $\frac{T_{1}}{T_{2}} = \left(\frac{R}{4R}\right)^{3/2} = \left(\frac{1}{4}\right)^{3/2} = \frac{1}{8}$.

In an atom,two electrons move around the nucleus in circular orbits of radii $R$ and $4R$. The ratio of the time taken by them to complete one revolution is

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