Question

Metallic gold crystallises in fcc lattice. The edge length of the cubic unit cell is $4.07$ $\mathring{A}$. What is the density (in g cm${}^{-3}$) of gold?

• A. $10.2$
• B. $19.4$
• C. $7.4$
• D. $13.6$

Answer 1

The correct option is B $19.4$

$z=4\text{(for}fCC)$

$M=197\text{(for gold)}$

$a=4.07\text{A( given)}$

$=407pm$

$P=\frac{2\times M}{Na\times a^3\times {10}^{-30}}g{cm}^{-3}$

$=\frac{4\times 191}{6.022\times {10}^{23}\times (401{)}^3\times {10}^{-30}}$

$=\frac{7899}{401}=19.4g{cm}^{-3}$