Question

X-ray diffraction studies show that copper crystallises in an fcc unit cell with cell edge of $3.608\times {10}^{-8}$ cm. In a separate experiment, copper is determined to have a density of $8.92mc{m}^{-3}$, calculate the atomic mass of copper.

Answer 1

Atomic mass of Cu

Given:

Cell edge, $a=3.608\times {10}^{-8}cm$
And density of copper, $d=8.98gc{m}^{-3}$

In case of $fcc$ lattice, number of atoms per unit cell, $z=4$

We know that $N_A=6.022\times {10}^{23}mo{l}^{-1}$

Therefore, $\text{M}=\frac{{\text{dN}}_A{a}^3}{z}$

By Putting the values, we get,

$\text{M}=\frac{8.92gc{m}^{-3}\times 6.022\times {10}^{23}mo{l}^{-1}\times (3.068\times {10}^{-8}cm{)}^3}{4}$

$\text{M}=63.1gmo{l}^{-1}$

Hence, the atomic mass of copper $=63.1u$

Final answer: The atomic mass of copper is $=63.1u$.