Question

In Bohr's model of the hydrogen atom, the ratio between the period of revolution of an electron in the orbit of $n=1$ to the period of revolution of the electron in the orbit $n=2$ is?

• A. $2:1$
• B. $1:2$
• C. $1:4$
• D. $1:8$

Answer 1

The correct option is D $1:8$

Time period of a revolution is given by,

$T=\frac{2\pi r}{V}$

and we know that radius, r is given by

$r=\frac{n^2{h}^2}{4{\pi }^{2}mkZ{e}^2}$
Similarly, velocity v is given by

$V=\frac{2\pi kZ{e}^2}{nh}$
Substituting values of r and v, we get,

$T=\frac{2\pi n^2{h}^2}{4{\pi }^{2}mkZ{e}^2}=\frac{2\pi kZ{e}^2}{nh}T=\left(c\right)n^{3}orT\propto n^3\&ifn=1T_1=1n=2T_2=8\to T_1:T_2=1:8$