Question

The angular momentum of an electron in hydrogen atom is proportional to

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

Answer 1

Answer: (A)

$\sqrt{r}$

we know that angular momentum $L\propto n$ [$n$ is principal quantum number]

and we also know that radius of an orbit $r\propto n^2$

$\Rightarrow r=c\times n^2$ [$c$ is some constant]

$\Rightarrow n=\sqrt{\frac{r}{c}}$

$\Rightarrow n\propto \sqrt{r}$

now we know that $L\propto n$ but $n\propto \sqrt{r}$

$\Rightarrow L\propto \sqrt{r}$