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An aluminium wire having across sectional area of $4 \times 10^{- 6} m^{2}$ carries a current of 5A. The drift speed of electrons in the wire is $x \times 130 μ m \sec^{- 1} .$ The density of aluminum is $2.7 g c m^{- 3} .$ Assume that one conduction electron is supplied by each atom. Find the value of $x$ .

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Detailed Solution

Density of Aluminium, $ρ = 2700 k g / m^{3}$

In 1m³ volume, mass is 2700 kg.

Number of moles, $n = \frac{m}{M} = \frac{2700}{27 \times 10^{- 3}} = 10^{5}$

Number of atoms, $N = n N_{A} = 10^{5} \times 6.023 \times 10^{23} = 6.023 \times 10^{28}$

Electron density, $n' = \frac{6.023 \times 10^{28}}{1}$

$v_{d} = \frac{I}{n e A} = \frac{5}{6.023 \times 10^{28} \times 1.6 \times 10^{- 19} \times 4 \times 10^{- 6}}$

$\Rightarrow v_{d} = 1.3 \times 10^{- 4} m / s = 130 \times 10^{- 6} m / s$

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