Question

Copper crystallises into a fcc lattice with edge length $3.61\times {10}^{-8}cm$. Show that the calculated density is in agreement with its measured value of $8.92gc{m}^3$.

Answer 1

Copper crystallizes into a fcc lattice with edge length $3.61\times {10}^{-8}$ cm.

Fcc unit cell has $4$ atoms per unit cell.

Cu has atomic mass of $63.5$ g/mol.

Avogadro's number is $6.023\times {10}^{23}$.

The calculated density is as below:

$D=\frac{ZM}{a^3{N}_0}=\frac{4\times 63.5}{(3.61\times {10}^{-8}{)}^3\times 6.022\times {10}^{23}}=8.97gc{m}^{-3}$

This is close enough to the measured value of $8.92gc{m}^{-3}$.