Question

The product of linear momentum and angular momentum of an electron of the hydrogen atom is proportional to $n^x$, where x is

• A. 0
• B. 1
• C. -2
• D. 2

Answer 1

The correct option is A 0

For Bohr's model of hydrogen atom,

$mvr=\frac{nh}{2\pi }$

and $\frac{kZ{e}^2}{r^2}=\frac{m{v}^2}{r}$

Eliminating $r$ from the equations gives,

$v=\frac{2\pi kZ{e}^2}{nh}$

Thus linear momentum $=mv\propto \frac{1}{n}$

Angular momentum $=mvr=\frac{nh}{2\pi }\propto n$

Thus, Linear Momentum $\times$ Angular Momentum $\propto n^0$