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)

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