A current of 10 A is passing through a metallic wire of cross-sectional area 4 x 10^-6 m².  If  the density of the aluminium conductor is 2.7 gl cc, considering aluminium gives 1 electron per atom for conduction, then find the drift velocity of the electrons if molecular weight of aluminium is 27 g

Given, current, I = 10 A

Area of cross-section,   $A=4\times {10}^{-6}{\mathrm{m}}^2$

Density of conductors,  $\rho =2.7\mathrm{g}/\mathrm{cc}=2.7\times {10}^3\mathrm{kg}/{\mathrm{m}}^3$

Molecular weight of aluminium,  $M_w=27\mathrm{g}=27\times {10}^{-3}\mathrm{kg}$

If n be the total number of electrons in the conductor per unit volume, then

$n=\frac{\text{Total number of electrons}}{\text{Volume of conductor}\left(V\right)}$

$=\frac{\text{Number of atoms per mole}\times \text{Number of moles}}{V}$

$=\frac{\text{Avogadro number}}{V}\times \left(\frac{M}{M_w}\right)$

$=6\times {10}^{23}\times \frac{\rho }{M_w}=6\times {10}^{23}\times \frac{2.7\times {10}^3}{27\times {10}^{-3}}$

$\therefore n=6\times {10}^{28}$

We know that, drift velocity,

$v_d=\frac{I}{neA}=\frac{10}{6\times {10}^{28}\times 1.6\times {10}^{-19}\times 4\times {10}^{-6}}$

$=2.6\times {10}^{-4}\mathrm{m}/\mathrm{s}$