Question

Copper, a monovalent, has molar mass $63.54\, g / mol$ and density $8.96 \,g / cm ^3$. What is the number density $n$ (in $m ^{-3}$ ) of conduction electron in copper ______$\times 10^{26}$

Answer 1

If $M$ is the molar mass and $\rho$ is the density then volume of one mole
$V=\frac{M}{\rho} $.
The number of atoms per unit volume
$=\frac{N_A}{V}=\frac{N_A}{M / \rho}=\frac{N_A \rho}{M}$
$=\frac{\left(6.02 \times 10^{23}\right) \times(8.96)}{63.54}$
$=8.49 \times 10^{22} cm ^{-3} $
$=8.49 \times 10^{28} m ^{-3}$
As each copper (monovalent) atom has one electron, so number of electrons per unit volume
$=8.49 \times 10^{26} m ^{-3}$