Question

Copper crystallises in a face centred cubic lattice with a unit cell length of $361\text{pm}$. The density of copper is: (Atomic mass of $Cu=63\text{u})$.
[0.77 Mark]

• A. $8.89{\text{g/cm}}^3$
• B. $1.28{\text{g/cm}}^3$
• C. $12.31{\text{g/cm}}^3$
• D. $4.12{\text{g/cm}}^3$

Answer 1

The correct option is A $8.89{\text{g/cm}}^3$

By using the relation,
$D=\frac{Z\times M}{a^3\times N_A}$
Where,
D = density of the solid
M=Atomic mass
a= edge length
For FCC, $Z=4$
$N_A=6.02\times {10}^{23}$
$a=361\text{pm}=361\times {10}^{-12}\text{m}=361\times {10}^{-10}\text{cm}$
$\therefore D=\frac{4\times 63}{(361\times {10}^{-10}{)}^3\times 6.02\times {10}^{23}}=8.89{\text{g/cm}}^3$