Question

The angle between $(100)$ and $(110)$ planes of $FCC$ lattice is

• A. $90^{\circ}$
• B. $0^{\circ}$
• C. $45^{\circ}$
• D. $120^{\circ}$

Answer 1

Answer: (C)

Angle between $(100)$ and $(110)$ planes of $f c c$ lattice is
$\cos \varphi=\frac{h_{1} \,h_{2}+k_{1} \,k_{2}+l_{1}\, l_{2}}{\sqrt{h_{1}^{2}+k_{1}^{2}+l_{1}^{2} \sqrt{h_{2}^{2}+k_{2}^{2}+l_{2}^{2}}}}$
$\cos \varphi=\frac{(1 \times 1)+(0 \times 1)+(0 \times 0)}{\sqrt{(1)^{2}+(0)^{2}+(0)^{2}} \sqrt{(1)^{2}+(1)^{2}+(0)^{2}}} $
$\cos \varphi=\frac{1}{\sqrt{2}} $
$\Rightarrow \varphi=45^{\circ}$