Question

The angular speed of the electron in the $n^{th}$ orbit of Bohr hydrogen atom is

• A. directly proportional to $n^2$
• B. Directly proportional to $n$
• C. Inversely proportional to $n^3$
• D. Inversely proportional to $n$

Answer 1

Answer: (D)

We know velocity of electron in the $n^{\text{th }}$ orbit is $v_n=r_n{w}_n$
$w_n$ is angular velocity
$w_n=\frac{v_n}{v_n}$
Also, $v_n=\frac{z{e}^2}{2{\epsilon }_{0}nm}$
$\therefore w_n=\frac{z{e}^2}{2{\epsilon }_{0}nm}$
$\therefore w_n\propto \frac{1}{n}$