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

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Solution

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

(Where r is the radius of orbit of electron) [2024]

1 $\frac{1}{r}$

2 $r$

3 $\sqrt{r}$

4 $\frac{1}{\sqrt{r}}$

Ans.
(3)

The radius of $n^{t h}$ orbit is, $r \propto \frac{n^{2}}{Z}, \Rightarrow n \propto \sqrt{Z r}$ ...(i)

  where, Z is atomic number.

  Angular momentum is given by, $L = \frac{n h}{2 π}$ ...(ii)

  Put value of $n$ from (i) to equation (ii),

$L = \frac{\sqrt{Z r} h}{2 π} = (\frac{\sqrt{Z} h}{2 π}) \sqrt{r} \Rightarrow L \propto \sqrt{r}$

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