Question

What is the angular momentum of a hydrogen atom in

(a) a $6s$state and

(b) a $4f$state? Give your answers as a multiple of U.

Short answer

(a). The angular momentum of a hydrogen atom in $6s$is role="math" localid="1650308924182" $0$.

(b). The angular momentum of a hydrogen atom in$4f$is$\sqrt{12}ħ$

Step-by-step solution

Part (a) step 1: Given Information

The angular momentum of a hydrogen atom in a $6s$state .

Part (a) step 2: Simplify

Now, finding the angular momentum of a hydrogen atom in a$6$sstate.
We know that the $6s$state is described as $n=6$and $l=0$.

Therefore, from the equation for the orbital angular momentum, we have:

$$\begin{gathered} L=\sqrt{l\left(l+1\right)}ħ \\ L=\sqrt{0\left(0+1\right)}ħ \\ L=0 \end{gathered}$$

Part (b) step 1: Given Information

The angular momentum of a hydrogen atom in a $4f$state .

Part (b) step 2:Simplify

We have to find the angular momentum of the hydrogen atom in a $4f$state.

know that, the $6s$state is described as $n=4$and$l=3$ .
$$\begin{gathered} L=\sqrt{l\left(l+1\right)}ħ \\ L=\sqrt{3\left(3+1\right)}ħ \\ L=\sqrt{3\left(4\right)}ħ \\ L=\sqrt{12}ħ \end{gathered}$$