Question

Which of the following statements are correct at \(T=0\ \text{K}\)?
A. Fermi function is a step function,
B. Chemical potential is equal to Fermi energy,
C. Chemical potential is equal to half of Fermi energy.

• A. A and B Only
• B. B and C Only
• C. A and C Only
• D. C Only

Hint:

At \(0\ \text{K}\), Fermi function is a step function and chemical potential equals Fermi energy.

Answer 1

The Correct Option is A

Concept:
At absolute zero, electrons fill all states up to the Fermi energy and no states above it are occupied.

Step 1: Fermi function at \(0\ \text{K}\).
At: \[ T=0\ \text{K} \] Fermi function becomes a step function. \[ A \text{ is correct} \]

Step 2: Chemical potential at \(0\ \text{K}\).
At absolute zero: \[ \mu=E_F \] So, \[ B \text{ is correct} \]

Step 3: Check statement C.
Chemical potential is not equal to half of Fermi energy at \(0\ \text{K}\). \[ C \text{ is incorrect} \] Thus, correct statements are: \[ A,B \] \[ \therefore \text{Correct Answer is (A)} \]