Question

Every atom makes one free electron in copper .If 1.1 ampere current is flowing in the wire of copper having 1mm diameter then find the drift velocity of the free electrons.

Answer 1

density of copper = 9 × 10³ kg/m³

first, we have to find number of atoms per unit volume.

atomic weight of copper = 63g/mol
= 63 × 10^-3 kg/mol

volume of 1 mole of copper = mass of 1 mole of copper/density of 1 mole of copper

= 63 × 10^-3/9 × 10³ = 7 × 10^-6 m³

number of electrons in 1 mole of copper = 29 × 6.023 × 10²³

so, number of electrons per unit volume = 6.023 × 10²³/7 × 10^-6
= 8.6 × 10^28 /m³

now use formula, $v_d=\frac{i}{neA}$

here, i = 1.1 A , n = 24.95 × 10^29/m³
e = 1.6 × 10^-19 C and A = π(1/2 × 10^-3)²

so, vd = 1.1/{8.6 × 10^28 × 1.6 × 10^-19 × 3.14 × 1/4 × 10^-6 }

= 4.4/{24.95 × 1.6 × 3.14 × 10³}

= 0.1 × 10^-3 m/s

hence, drift velocity = 10^-4 m/s