Question

A metal crystallises in face centred cubic structure with metallic radius $\sqrt{2}A^\circ$. The volume of the unit cell (in $m^3$) is

• A. $4 \times 10^{-10}$
• B. $6.4 \times 10^{-29}$
• C. $4 \times 10^{-9}$
• D. $6.4 \times 10^{-30}$

Answer 1

Answer: (B)

For FCC,

Atomic radius $(r)=(\sqrt{2} a) / 4$

$\Rightarrow \sqrt{2} \times 10^{-10}=(\sqrt{2} a ) / 4$

$\Rightarrow a =\left(4 \times \sqrt{2} \times 10^{-10}\right) / \sqrt{2}=4 \times 10^{-10} m$

Volume of unit cell $= a ^{3}=\left(4 \times 10^{-10}\right)^{3}$

$=64 \times 10^{-30} m ^{3}=6.4 \times 10^{-29} m ^{3}$