Question

An element crystallizes in a structure having FCC unit cell of an edge length $200$ pm. Calculate the density (in g cm${}^{-3}$) if $200$ g of this element contain $5\times {10}^{24}$ atoms.

• A. $5$
• B. $30$
• C. $10$
• D. $20$

Answer 1

The correct option is D $20$

Molecular mass of the given element is $=\frac{200\times 6\times {10}^{23}}{5\times {10}^{24}}=24$
$density=\frac{zM}{N_A\times (a\times {10}^{-10}{)}^3}$
$density=\frac{4\times 24}{6\times {10}^{23}\times (200\times {10}^{-10}{)}^3}$
$density=20{\text{g cm}}^{-3}$