# Quantum Statistics question

1. Dec 3, 2007

### neelakash

[SOLVED] Quantum Statistics question

1. The problem statement, all variables and given/known data

Electrons in a metal are considered as free electron gas where

(a) Fermi energy is (h^2/2m)[3N/8*pi*V]^(2/3)

(b)Average energy of the free electrons at absolute zero is E(0)=(3/5)E_f where E_f is the Fermi energy

(c)Pauli exclusion principle is obeyed.

(d) Total momentum at absolute zero is zero.

2. Relevant equations

3. The attempt at a solution

I think all but (d) are correct.i cannot visualize the electrons to have momentum zero yet having energy...at T=0

2. Dec 3, 2007

### Gokul43201

Staff Emeritus
Is energy proportional to momentum or momentum squared?

3. Dec 3, 2007

### neelakash

So total momentum may be zero?

Then,all four options are correct?

4. Dec 4, 2007

### Gokul43201

Staff Emeritus
I don't know if (a) has all the correct factors of 2 and pi and so on...but if it does, then yes.

5. Dec 4, 2007

I hope so...