Do Free Electrons Have Momentum Zero at Absolute Zero?

[neelakash]

[SOLVED] Quantum Statistics question

Homework Statement

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.

Homework Equations

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

 

[Gokul43201]

Is energy proportional to momentum or momentum squared?

 

[neelakash]

So total momentum may be zero?

Then,all four options are correct?

 

[Gokul43201]

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

 

[neelakash]

I hope so...