Do Free Electrons Have Momentum Zero at Absolute Zero?

In summary, the conversation discusses the properties of electrons in a metal as a free electron gas. The Fermi energy is calculated in option (a) and the average energy of the free electrons at absolute zero is given in option (b). The conversation also mentions the Pauli exclusion principle and the total momentum of the electrons at absolute zero, with the question of whether it is possible for both to be zero. The correctness of all four options is debated.
  • #1
neelakash
511
1
[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
 
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  • #2
Is energy proportional to momentum or momentum squared?
 
  • #3
So total momentum may be zero?

Then,all four options are correct?
 
  • #4
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
I hope so...
 

FAQ: Do Free Electrons Have Momentum Zero at Absolute Zero?

What is quantum statistics?

Quantum statistics is the branch of physics that deals with the statistical behavior of particles at the quantum level, taking into account their wave-like nature and the uncertainty principle.

What are the two main types of quantum statistics?

The two main types of quantum statistics are Bose-Einstein statistics and Fermi-Dirac statistics. These describe the behavior of particles with integer and half-integer spin, respectively.

What is the difference between Bose-Einstein and Fermi-Dirac statistics?

The main difference between these two types of statistics is that Bose-Einstein statistics allow for multiple particles to occupy the same quantum state, while Fermi-Dirac statistics do not. This leads to different behavior at low temperatures, with Bose-Einstein statistics predicting the formation of a Bose-Einstein condensate.

What is the significance of quantum statistics in understanding the behavior of matter?

Quantum statistics are crucial in understanding the behavior of matter at the microscopic level. They help explain phenomena such as superconductivity, superfluidity, and the structure of atoms and molecules.

How is quantum statistics related to the concept of entropy?

Quantum statistics play a fundamental role in the calculation of entropy, which is a measure of the disorder or randomness of a system. The different types of quantum statistics have different effects on the entropy of a system, and understanding this relationship is important in many areas of physics and chemistry.

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