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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
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B
4:1
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C
1:8
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D
8:1
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Solution

The correct option is C 1:8
$$\begin{array}{l}r_{1}=R \\r_{2}=4 R\end{array}$$

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

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

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

Physics

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