Question

The experimentally observed value of electrical conductivity of a metal is of the order of 107Ω-1m-1. Calculate relaxation time for the electron-ion collisions. Given e= 1.6 x 10-I9c, m=9.1 x10-31 kg and n = 1028m-3.

Answer 1

we know the formula,

$\tau=\frac{\sigma m}{ne^2}$

• $\sigma$ is electrical conductivity.
• m is mass of electron
• n is number of electrons per unit volume
• e is charge on electron
• $\tau$ is time of relaxation

here, $\sigma$ = 10^7Ω-¹m-¹

m = 9.1 × 10-³¹ Kg

n = 10^28 m-³

e = 1.6 × 10^-19 C

so, $\tau$ = {10^7 × 9.1 × 10^-31}/{10^28 × (1.6 × 10^-19)²}

= 3.55469 × 10-¹⁴ sec

hence, time of relaxation is 3.55469 × 10-¹⁴ sec.