Copper, a mono valent, has molar mass $63.54gm/mole$  and density $8.96gm/c{m}^3$ , the number density of conduction electrons in copper is  $n\times {10}^{28}/m^3$. Find ‘n’

$$\begin{gathered} Monovalent means each atom contributes one conduction electron. \\ \therefore No. of conduction electrons =No. of atoms \end{gathered}$$

$$\begin{gathered} From mole concept we know that, \\ No. of moles = \frac{Mass}{Molar Mass} = \frac{No of atoms}{Avogadro No.} \end{gathered}$$

$\Rightarrow \frac{Density \times Volume}{Molar Mass} = \frac{No of atoms}{Avogadro No.}$

$\Rightarrow \frac{No of atoms}{Volume} = \frac{Avogadro No.\times Density}{Molar Mass}$$=\frac{6.023\times {10}^{23}\times 8.96}{63.54} per c{m}^3$

$$\begin{gathered} = 0.849\times {10}^{23} per c{m}^3 \\ =0.849\times {10}^{29} per m^3 \\ =8.49\times {10}^{28} per m^3 \end{gathered}$$