Question

Suppose the mass of a single Ag-atom is $m$. Ag metal crystallises in fcc lattice with unit cell of length $a$. The density of $Ag$ metal in terms of $a$ and $m$ is

• A. $\frac{4m}{a^{3}}$
• B. $\frac{2m}{a^{3}}$
• C. $\frac{m}{a^{3}}$
• D. $\frac{m}{4a^{3}}$

Answer 1

Answer: (A)

$\frac{4m}{a^{3}}$

Answer 2

Given that,
Mass of single Ag-atom $=m$
Unit cell length $=a$
Total atoms present per unit cell of fcc lattice $=4$
Therefore, mass of unit cell becomes $4 m$.
Volume of unit cell $=a^{3}$
Density( $\rho)=\frac{\text { Mass of unit cell }}{\text { Volume of unit cell }}$
$=\frac{4 m}{a^{3}}$