Answer
Largest: $\sqrt{30}\hbar $
Smallest: 0
Work Step by Step
The possible values of $\mathcal{l}$ are from 0 to (n-1).
For n = 6, that means $\mathcal{l}$ ranges from 0 to 5.
The magnitude of the angular momentum depends only on $\mathcal{l}$.
$$L=\sqrt{\mathcal{l}(\mathcal{l}+1)}\hbar$$
Find the minimum and the maximum
$$L_{min}=\sqrt{0(1)}\hbar=0$$
$$L_{max}=\sqrt{5(6)}\hbar=\sqrt{30}\hbar $$
