Question

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

Answer 1

Answer: 8.49

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
$=\frac{N_A}{V}=\frac{N_A}{M/\rho }=\frac{N_A\rho }{M}$
$=\frac{\left(6.02\times 10^{23}\right)\times (8.96)}{63.54}$
$=8.49\times 10^{22}c{m}^{-3}$
$=8.49\times 10^{28}{m}^{-3}$
As each copper (monovalent) atom has one electron, so number of electrons per unit volume
$=8.49\times 10^{26}{m}^{-3}$