Question

For an electron moving in $n^{\text{th}}$ orbit of hydrogen atom, the angular velocity is proportional to,

• A. $n^3$
• B. $\frac{1}{n}$
• C. $n^2$
• D. $n$

Answer 1

The correct option is D $n$

According to second postulate of Bohr's theory,
$mvr=\frac{nh}{2\pi }$

As, $v=r\omega$

$\Rightarrow m\left(rw\right)r=\frac{nh}{2\pi }$

$\Rightarrow m{r}^{2}w=\frac{nh}{2\pi }$

$\therefore \omega \propto n$

Hence, $\left(D\right)$ is the correct answer.

Why this Question? This question is based on the concept of angular velocity of an electron concept and how it varies with its principle quantum number.