Question

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

(assume that electrons exert negligible force on each other )

• A. 1:4
• B. 4:1
• C. 1:8
• D. 8:1

Answer 1

The correct option is C 1:8

$\begin{array}{c}{r}_1=R\\ r_2=4R\end{array}$

$\text{We know that radius,}r\propto n^2\because r_2=4r_1\Rightarrow n_2=2r_1\text{We also know that}v\propto \frac{1}{n}\Rightarrow v_1=2v_2$

$\text{Tinme}=\frac{\text{Distance}}{\text{speed}}=\frac{2\pi r}{v}$

$\therefore \frac{T_1}{T_2}=\frac{2\pi r_1}{v_1}\times \frac{v_2}{2\pi r_2}=\frac{r_1\times 0.5v_1}{v_1\times 4r_1}=\frac{1}{8}$