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

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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