Question

An element $X$ (Atomic weight = 80 g/mol) has a $fcc$ structure. Calculate the number of unit cells in $8g$ of $X$

• A. $0.4\times N_4$
• B. $0.25\times N_A$
• C. $4\times N_A$
• D. $0.025\times N_A$

Answer 1

The correct option is D $0.025\times N_A$

Since,
$80g$ of X has $N_A$ atoms.

$\text{Number of atoms in 8 g of X}=\frac{8}{80}\times N_A=\frac{N_A}{10}$
For a fcc unit cell :
$\text{Number of atoms in unit cell}=(8\times \frac{1}{8})+(6\times \frac{1}{2})=4$

$\therefore$
$\text{Number of unit cells}=\frac{\text{Total number of atoms}}{\text{Number of atoms present in unit cell}}$

$\text{Number of unit cells}=\frac{N_A}{10\times 4}=0.025\times N_A$