Q. Copper has face-centred cubic (fcc) lattice with interatomic spacing equal to 2.54 $\mathring{\mathrm{A}}$. The value of lattice constant for this lattice is
A) 1.27 $\mathring{\mathrm{A}}$
B) 5.08 $\mathring{\mathrm{A}}$
C) 2.54 $\mathring{\mathrm{A}}$
D) 3.59 $\mathring{\mathrm{A}}$
Explanation
(d) Interatomic spacing for a fcc lattice
$r = \left\lbrack \left( \frac{a}{2} \right)^{2} + \left( \frac{a}{2} \right)^{2} + (0)^{2} \right\rbrack^{\frac{1}{2}} = \frac{a}{\sqrt{2}}$
$a$ being lattice constant.
$\therefore = \sqrt{2}r = \sqrt{2} \times 2.54 = 3.59\ \mathring{\mathrm{A}}.$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.