Electrons are speeded up by 150 V and hit a crystal whose rows of atoms are 0.215 nm apart…

Step 1. The wavelength. $\lambda = \dfrac{1.227}{\sqrt{150}}\ \text{nm} = 0.100\ \text{nm}$.

Step 2. The first order. $\sin\varphi = \dfrac{0.100\ \text{nm}}{0.215\ \text{nm}} = 0.466$, so $\varphi = 27.8^\circ$.

Step 3. The second order. $\sin\varphi = \dfrac{2 \times 0.100\ \text{nm}}{0.215\ \text{nm}} = 0.932$, so $\varphi = 68.7^\circ$.