Question

Copper crystallizes in fcc structure and the edge length of the unit cell is $3.61A^o$. Hence the density of copper is:
(atomic mass of $Cu=63.5gmo{l}^{-1}$)

• A. $5.17gc{m}^{-3}$
• B. $0.72gc{m}^{-3}$
• C. $7.09gc{m}^{-3}$
• D. $8.97gc{m}^{-3}$

Answer 1

The correct option is D $8.97gc{m}^{-3}$

The density $\rho =\frac{Z\times M}{N_0\times a^3}$
$Z=4atoms=$ number of Cu atoms in one fcc unit cell.
$M=63.5g/mol=$ atomic mass of copper.
$N_0=6.023\times {10}^{23}atoms/mole=$ Avogadro's number.

$a=3.61A^o=3.61\times {10}^{-8}cm=$ edge length of the unit cell.

The density $\rho =\frac{Z\times M}{N_0\times a^3}$

The density $\rho =\frac{4atoms\times 63.5g/mol}{6.023\times {10}^{23}atoms/mole\times (3.61\times {10}^{-8}cm{)}^3}$

The density $\rho =8.97gc{m}^{-3}$