In two hydrogen atoms A and B, the electrons are revolving around the nucleus in circular orbits of

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In two hydrogen atoms A and B, the electrons are revolving around the nucleus in circular orbits of radius r and 4r, respectively. The ratio of times taken by them to complete one revolution is

Accepted Answer

$\frac{r_{1}}{r_{2}} = \frac{n_{1}^{2}}{n_{2}^{2}} \Rightarrow \frac{r}{4r} = \frac{n_{1}^{2}}{n_{2}^{2}} \Rightarrow \frac{n_{1}}{n_{2}} = \frac{1}{2}$

$\therefore\frac{T_{1}}{T_{2}} = \frac{n_{1}^{3}}{n_{2}^{3}} = \frac{1}{8}$

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