Question

In an atom two electrons move around the nucleus in circular orbitals of radii $R$ and $4R$. The ratio of the time taken by them to complete one resolution is:

• A. $1:4$
• B. $4:1$
• C. $1:8$
• D. $8:7$

Answer 1

The correct option is C $1:8$

As we know,

$r_n\propto n^2$

so here, $n_1=1;n_2=2$

Also,

$T=\frac{2\pi r_R}{u_n}=\frac{2\pi r_1\times n^2}{u_1/n}$

or $T\propto n^3$

$T_1/T_2=1^3/2^3=1:8$

Hence, the correct option is $\text{C}$