Question

The unit cell of copper corresponds to a face centered cube of edge length $3.596\mathrm{\AA }$ with one copper atom at each lattice point. The calculated density of copper in $\mathrm{kg}/{\mathrm{m}}^3$ is

Answer 1

Density:

• The density of a substance indicates how dense it is in a given area.
• Mass per unit volume is the definition of a material's density.
• In essence, density is a measurement of how closely stuff is packed.
• It is a particular physical characteristic of a specific thing.
• The Greek scientist Archimedes made the discovery of the density principle.

The expression used for the calculation of density of Copper:

$\begin{array}{l}d=\frac{Z\times M}{N_A\times a^3}\end{array}$

putting values in the above expression to calculate the density of Copper-

$\begin{array}{rcl}\mathrm{d}& =& \frac{\mathrm{Z}\times \mathrm{M}}{{\mathrm{N}}_{\mathrm{A}}\times {\mathrm{a}}^3}\\ & =& \frac{4\times 63.54}{1000\times 6.022\times {10}^{23}\times {\left(3.596\times {10}^{-10}\right)}^3}\\ & =& 9076\mathrm{kg}/{\mathrm{m}}^3\end{array}$

Therefore, the density of copper is $9076\mathrm{kg}/{\mathrm{m}}^3$.