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)

Inversely proportional to $n$

Answer 2

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, $v_{n} =\frac{z e^{2}}{2 \varepsilon_{0} n m}$
$\therefore w_{n} =\frac{z e^{2}}{2 \varepsilon_{0} n m}$
$\therefore w_{n} \propto \frac{1}{n}$