Question

In an atom two electrons move around 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. $1:8$
• D. $8:7$

Answer 1

Answer: (C)

$1:8$

Time period, $T\propto {\left(R\right)}^{3/2}$

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

Thus the ratio of time period is $1:8$