Question

The angular speed of electron in the $n$th orbit of 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: (C)

$mvr=\frac{nh}{2\pi }$
$\Rightarrow m\omega r^2=\frac{nh}{2\pi }$
$\Rightarrow \omega \propto \frac{n}{r^2}$
As, $r\propto n^2$
$\therefore \omega \propto \frac{1}{n^3}$