Question

Which of the following statements is true about mobility of charge carriers in a metal ?

• A. Mobility increases with increase in applied electric field.
• B. Mobility decreases with increase in temperature.
• C. Mobility is independent of the mass of the charge carrier.
• D. Mobility increases with increase in temperature

Hint:

In metals, drift velocity $v_d = \mu E$. Since relaxation time $\tau$ drops at higher temperatures, mobility $\mu = \frac{e \tau}{m}$ decreases continuously with rising temperature.

Answer 1

The Correct Option is B

Concept:
• Mobility $\mu$ of a charge carrier is defined as the magnitude of drift velocity per unit applied electric field: $\mu = \frac{v_d}{E}$.

• In terms of relaxation time $\tau$ and carrier mass $m$: $\mu = \frac{e \tau}{m}$.

Step 1: Analyze temperature dependence of mobility
As temperature increases, thermal vibrations of lattice ions intensify.
Collision frequency of electrons increases, leading to a decrease in average relaxation time $\tau$.
From $\mu = \frac{e \tau}{m}$, a decrease in relaxation time $\tau$ causes mobility $\mu$ to decrease.

Step 2: Evaluate other statements
- Mobility is independent of applied electric field $E$ in low-field regime ($\mu = \text{constant}$).
- Mobility depends inversely on carrier mass $m$ ($\mu \propto \frac{1}{m}$).
- Mobility decreases (not increases) with temperature rise in metals.

Step 3: Conclusion
The statement "Mobility decreases with increase in temperature" is true, corresponding to option (B).