Question

An element X (atomic weight $=24\, g / mole$ ) forms face centred cubic lattice. If the edge length of the lattice is $4 \times 10^{-8} cm .$ and the observed density is $2.40 \times 10^{3}\,kg / m ^{3}$ The $\%$ age occupancy of lattice point by $X$ element is-

• A. $96 \%$
• B. $84 \%$
• C. $75 \%$
• D. $2.5 \%$

Answer 1

Answer: (A)

$\rho=\frac{Z \times M}{a^{3} \times N_{A}}=\frac{4 \times 24}{\left(4 \times 10^{-8}\right)^{3} \times 6 \times 10^{23}}$

$=\frac{4 \times 24}{64 \times 10^{-24} \times 6 \times 10^{23}}$

$\rho=2.5\, g / cm ^{3}$ or $2.5 \times 10^{3} kg / m ^{3}$

$\%$ age occupancy $=\frac{2.4 \times 10^{3}}{2.5 \times 10^{3}} \times 100=96 \%$