Question

The electrical conductivity of a metal \(\sigma\) is given by:

• A. \(\sigma=\dfrac{ne\tau}{m}\)
• B. \(\sigma=\dfrac{ne^2\tau}{m}\)
• C. \(\sigma=\dfrac{ne}{\tau m}\)
• D. \(\sigma=\dfrac{ne^2}{\tau m}\)

Hint:

In Drude theory, conductivity increases with electron concentration \(n\) and relaxation time \(\tau\).

Answer 1

The Correct Option is B

Concept:
According to Drude free electron theory, electrical conductivity of a metal is: \[ \sigma=ne\mu \] where \(\mu\) is electron mobility.

Step 1: Write electron mobility. \[ \mu=\frac{e\tau}{m} \] where, \[ e=\text{charge of electron} \] \[ \tau=\text{relaxation time} \] \[ m=\text{mass of electron} \]

Step 2: Substitute mobility in conductivity expression. \[ \sigma=ne\left(\frac{e\tau}{m}\right) \] \[ \sigma=\frac{ne^2\tau}{m} \] \[ \therefore \text{Correct Answer is (B)} \]