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 $fcc$ lattice is
$\cos \phi =\frac{h_1{h}_2+k_1{k}_2+l_1{l}_2}{\sqrt{h_1^2+k_1^2+l_1^2\sqrt{h_2^2+k_2^2+l_2^2}}}$
$\cos \phi =\frac{(1\times 1)+(0\times 1)+(0\times 0)}{\sqrt{(1{)}^2+(0{)}^2+(0{)}^2}\sqrt{(1{)}^2+(1{)}^2+(0{)}^2}}$
$\cos \phi =\frac{1}{\sqrt{2}}$
$\Rightarrow \phi =45^{\circ }$