Question

An element $X$ (atomic mass $=24gm/mol$) forms a face centered cubic lattice. If the edge length of the lattice is $4$ x ${10}^{-8}$ $cm$ and the observed density is $2.40$ x ${10}^3$ $kg{m}^3$ then the percentage occupancy of lattice points by element $X$ is : (Use $N_A$ $=$ $6$ x ${10}^{23}$)

• A. $96$
• B. $98$
• C. $99.9$
• D. None of the above

Answer 1

Answer: (A)

$96$

Theoretical density $=\frac{Z.M}{N_A.a^3}$
$=\frac{4\times 24\times {10}^{-3}}{6\times {10}^{23}\times (4\times {10}^{-10}{)}^3}$
$=2.5\times {10}^{3}kg/m^3$
$\%occupancy=\frac{Observeddensity}{Idealdensity}\times 100$
$=\frac{2.4\times {10}^3}{2.5\times {10}^3}\times 100=96\%$