The mobility of free electrons (charge= e, mass= m and relaxation time = τ) in a metal is proportional to

Question

The mobility of free electrons (charge= e, mass= m and relaxation time = τ) in a metal is proportional to (A)  (e/m)τ (B)  (m/e)τ (C)  (e/mτ) (D)  (m/eτ)

Tardigrade Admin · Accepted Answer

Drift velocity per unit electric field is called mobility of electron ie, μ = (vd/E) = (E/ρ neE) Now, ρ = (m/ne2 τ) ∴ μ = (ne2 τ/mne) = (e τ/m)

Q. The mobility of free electrons (charge= e, mass= m and relaxation time = $τ$ ) in a metal is proportional to

$\frac{e}{m} τ$

$\frac{m}{e} τ$

$\frac{e}{m τ}$

$\frac{m}{e τ}$

Drift velocity per unit electric field is called mobility of electron
$i e, μ = \frac{v _{d}}{E} = \frac{E}{ρ n e E}$
Now, $ρ = \frac{m}{n e ^{2} τ}$
$∴ μ = \frac{n e ^{2} τ}{mn e} = \frac{e τ}{m}$

Q. The mobility of free electrons (charge= e, mass= m and relaxation time = τ) in a metal is proportional to

me​τ

em​τ

mτe​

eτm​