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. $\frac{1}{4}$
• B. $\frac{4}{1}$
• C. $\frac{8}{1}$
• D. $\frac{1}{8}$

Answer 1

The correct option is D $\frac{1}{8}$

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)
$\therefore$ From equation (i) and (ii) $T\propto R^{3/2}\Rightarrow \frac{T_1}{T_2}={\left(\frac{R_1}{R_2}\right)}^{3/2}={\left(\frac{R}{4R}\right)}^{3/2}=\frac{1}{8}$