Question

Mobilities of electrons and holes in a sample of intrinsic germanium at room temperature are \( 0.36 \, \text{m}^2 \, \text{V}^{-1} \, \text{s}^{-1} \) and \( 0.17 \, \text{m}^2 \, \text{V}^{-1} \, \text{s}^{-1} \), respectively. The electron and hole densities are each equal to \( 2.5 \times 10^{19} \, \text{m}^{-3} \). The electrical conductivity of germanium is

• A. 4.24 S/m
• B. 2.12 S/m
• C. 1.09 S/m
• D. 0.47 S/m

Hint:

Electrical conductivity is directly proportional to the charge carriers' density and mobility. Higher mobilities lead to higher conductivity.

Answer 1

The Correct Option is B

Step 1: Formula for conductivity.
The electrical conductivity \( \sigma \) of a material is given by the formula: \[ \sigma = q (n_e \mu_e + n_h \mu_h) \] where \( q \) is the charge of an electron, \( n_e \) and \( n_h \) are the electron and hole densities, and \( \mu_e \) and \( \mu_h \) are their mobilities.

Step 2: Calculations.
Substitute the given values to calculate the conductivity of germanium. The answer is 2.12 S/m.