Question

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

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

Answer 1

Answer: (A)

$\sqrt{r}$

Answer 2

According to Bohr’s model of the hydrogen atom, the angular momentum $L$ of an electron in an orbit is quantized and given by:

$L = n\hbar,$

where $n$ is the principal quantum number and $\hbar$ is the reduced Planck’s constant.
For a hydrogen atom, the radius of the $n$-th orbit is given by:

$r_n \propto n^2.$

Therefore, we can express $n$ in terms of $r$:

$n \propto \sqrt{r}.$

Substituting this into the expression for angular momentum:

$L \propto n \propto \sqrt{r}.$

Hence, the angular momentum of an electron in a hydrogen atom is proportional to $\sqrt{r}.$