Question

On increasing the temperature of a conductor, for free electrons ______ increases.

• A. drift velocity
• B. mobility
• C. relaxation time
• D. thermal speed

Hint:

Higher temperature $\rightarrow$ More "chaos" (Thermal Speed) $\rightarrow$ More collisions $\rightarrow$ Lower Relaxation Time $\rightarrow$ Higher Resistance.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
In a conductor, free electrons are in constant random motion due to thermal energy. When the temperature increases, the kinetic energy of these electrons also increases.
Step 2: Detailed Explanation:
The average thermal speed ($v_{rms}$) of an electron is proportional to the square root of the absolute temperature ($T$): $$v_{rms} = \sqrt{\frac{3k_B T}{m}}$$ As temperature rises, the electrons move faster and collide more frequently with the positive ions of the lattice. These frequent collisions actually decrease the relaxation time ($\tau$) and the mobility ($\mu$), while the random thermal speed increases.
Step 3: Final Answer:
The thermal speed increases.