Question

The angular momentum of an electron in a hydrogen atom is proportional to : (Where r is the radius of orbit of electron) 

(1) \(\sqrt{\mathrm{r}}\)

(2) \(\frac{1}{\mathrm{r}}\)

(3) r

(4) \(\frac{1}{\sqrt{\mathrm{r}}}\)  

Answer 1

Correct option is : (1) \(\sqrt{\mathrm{r}}\)  

\(F_c = \frac{mv^2}{r}\)

\(\frac{Kq_1q_2}{r^2}= \frac{mv^2}{r}\)

\(mv^2r^2= Kq_1q_2r\)

\(\frac{L^2}{m}=Kq_1q_2r\)

\(L \propto\sqrt{r}\)