Question

The angular momentum of electron in hydrogen atom is proportional to

• A. $\sqrt{r}$
• B. $\frac{1}{r}$
• C. $r^2$
• D. $\frac{1}{\sqrt{r}}$

Answer 1

The correct option is A $\sqrt{r}$

Angular momentum $=mvr$
Velocity of an electron $=\frac{k}{n}$
where from radius of orbit $=c{n}^2$
$n=\sqrt{\frac{r}{c}}$
Angular momentum $=m\times \frac{k}{n}\times r=\frac{cmk}{\sqrt{n}}r$
$\Rightarrow$ Angular momentum $=a\sqrt{r}$ where a is a constant
$\Rightarrow$ Angular momentum $\propto \sqrt{n}$