Question

The number densities of free electrons in three conductors X, Y and Z are in the ratio 4:1:8 and their electrical conductivities are in the ratio 2:1:2. For which conductor will the relaxation time of free electrons be (a) maximum (b) minimum?

Answer 1

Answer:

(a). $\mathsf{\tau_{max} = X}$

(b). $\mathsf{\tau_{min} = Z}$

Explanation:

Conductivity, $\boxed{\mathsf{\sigma{\propto{n{\tau}}}}}$

$\mathsf{\sigma_x{\propto{n_x{\tau_x}}}}$

$\mathsf{\sigma_y{\propto{n_y{\tau_y}}}}$

$\mathsf{\sigma_z{\propto{n_z{\tau_z}}}}$

$\mathsf{\tau_x{={\dfrac{2}{4}} = {\dfrac{1}{2}}}}$

$\mathsf{\tau_y{={\dfrac{1}{1}} = 1}}$

$\mathsf{\tau_z{={\dfrac{2}{8}} = {\dfrac{1}{4}}}}$

Here, n = Number Density

τ = Relaxation time