Question

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

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

Answer 1

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

In hydrogen atom,

The radius of n^th orbit is

$r_n\propto \frac{n^2}{Z}$

where, Z is atomic number

so,

$n={\left(Z{r}_n\right)}^{\frac{1}{2}}..........\left(1\right)$

Angular momentum is given by,

$L=\frac{nh}{2\pi }..........\left(2\right)$

Put value of n from (1) to equation (2)

$L=\frac{{\left(z{r}_n\right)}^{\frac{1}{2}}h}{2\pi }$

$L\propto r^{\frac{1}{2}}$

$L\propto \sqrt{r}$