Question

Consider free electron gas, the order of excitation energy for an electron to jump from level \(1\) to level \(2\) is:

• A. \(2k_B T\)
• B. \(\dfrac{k_B T}{2}\)
• C. \(k_B T\)
• D. \(\dfrac{3}{2}k_B T\)

Hint:

Thermal excitation energy is generally of the order of \(k_B T\).

Answer 1

The Correct Option is C

Concept:
In a free electron gas, thermal excitation energy is of the order of thermal energy.

Step 1: Thermal energy scale.
The characteristic thermal energy scale is: \[ k_B T \] where, \[ k_B=\text{Boltzmann constant} \] \[ T=\text{absolute temperature} \]

Step 2: Excitation energy.
For an electron to jump from a lower energy level to a higher energy level due to thermal excitation, the energy involved is generally of the order of: \[ k_B T \]

Step 3: Final answer. \[ \therefore \text{Correct Answer is (C)} \]