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)

$1/8$

$\frac{R_1}{R_2}=\frac{n_1^2}{n_2^2}=\frac{1}{4}$ $\therefore \frac{n_1}{n_2}=\frac{1}{2}$
$\frac{T_1}{T_2}={\left(\frac{n_1}{n_2}\right)}^3={\left(\frac{1}{2}\right)}^3=\frac{1}{8}$