In an atom, the two electrons move round the nucleus in circular orbits of radii

Question

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

Options:

A . 14

B . 41

C . 81

D . 18

Answer: Option D
:
D
Time period

T \propto \frac{n^{3}}{Z^{2}}

For a given atom (Z = constant) So

T \propto n^{3}

......... (i) and radius

R \propto n^{2}

......... (ii)

∴

From equation (i) and (ii)

T \propto R^{3 / 2} \Rightarrow \frac{T_{1}}{T_{2}} = {(\frac{R_{1}}{R_{2}})}^{3 / 2} = {(\frac{R}{4 R})}^{3 / 2} = \frac{1}{8}

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