Answer
See work below.
Work Step by Step
The Bohr model says that the angular momentum of a H atom in the n=2 state is $L_{Bohr}=2\hbar$.
In quantum mechanics, the magnitude of the angular momentum depends only on $\mathcal{l}$.
$$L=\sqrt{\mathcal{l}(\mathcal{l}+1)}\hbar$$
The possible values of $\mathcal{l}$ are from 0 to (n-1).
There are 2 possible values of $\mathcal{l}$, which are 0 and 1, for n = 2.
There are 2 possible values of the angular momentum for n = 2.
$$L_{qm}=\sqrt{0(1)}\hbar=0$$
$$L_{qm}=\sqrt{1(2)}\hbar=\sqrt{2}\hbar $$
