Two electrons are revolving around a nucleus at distances r and 4r. What will be the ratio of their periods?

# Two electrons are revolving around a nucleus at distances r and 4r. What will be the ratio of their periods?

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### Solution:

$\begin{array}{l}{\mathrm{T}}^{2}\propto {\mathrm{r}}^{3}\\ \frac{{\mathrm{T}}_{\mathrm{r}}}{{\mathrm{T}}_{4\mathrm{r}}}={\left(\frac{\mathrm{r}}{4\mathrm{r}}\right)}^{3/2}=\frac{1}{8}\end{array}$

Here, T is the time period and r is the radius.

Sum of ratio is 1+8=9.

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