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

• A. 1/4
• B. 4/1
• C. 8/1
• D. 1/8

Answer 1

Answer: (D)

1/8

Answer 2

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) $T \propto R^{3/2}$

⇒ $\frac{T_{1}}{T_{2}} = \left( \frac{R_{1}}{R_{2}} \right)^{3/2} = \left( \frac{R}{4R} \right)^{3/2} = \frac{1}{8}$