Question

According to free electron theory, electrical conductivity increases with:

• A. Increasing temperature
• B. Decreasing temperature
• C. Increasing atomic number
• D. Decreasing electron mobility

Hint:

In conductors, electrical conductivity decreases with increasing temperature due to increased electron-atom collisions that hinder electron movement.

Answer 1

The Correct Option is B

According to the free electron theory, electrical conductivity of a material is directly related to the number of free electrons available to move when an electric field is applied. The equation for electrical conductivity (\( \sigma \)) is given by: \[ \sigma = n e \mu \] where:
- \( n \) is the number of free electrons,
- \( e \) is the charge of the electron, and
- \( \mu \) is the electron mobility.
- As the temperature increases, the number of collisions between electrons and atoms increases, leading to a decrease in electron mobility. Therefore, the electrical conductivity decreases with increasing temperature.
- On the other hand, as temperature decreases, the number of collisions reduces, and electron mobility increases, thus increasing electrical conductivity.
Thus, the correct answer is Decreasing temperature.