Question

$L$ is angular momentum of an electron which is revolving around the nucleus of H-atom in the first orbit having radius $r$. The angular momentum of same electron when it is revolving in bigger orbit of radius $9r$ is:

• A. $3L$
• B. $\frac{9L}{2}$
• C. $\frac{9L}{4}$
• D. $9L$

Answer 1

The correct option is A $3L$

For an electron $L=m_{e}vr$
Where, v and r are dependent on principal quantum number n
We know: $r\propto n^2$ and $v\propto \frac{1}{n}$
If $r$ becomes a nine times than velocity decreases by $3$ times.
$L_f=\left(me\right)\left(\frac{v}{3}\right)\left(9r\right)$
$=3L$