Questions regarding the Fermi level of a metal

[heycoa]

Hello,

Are the electrons at the fermi level regarded as the "free electrons" of the metal?

Also, how does one go about calculating the Fermi level? Is there an equation or is it experimentally determined?

*Bonus question*
Electrons that undergo phonon exchange and pair up are called "Cooper pairs". Why do these Cooper pairs not experience resistance? I have been looking all over the place for this answer and cannot find out why this is the case.

 

[Simon Bridge]

Hello,

Are the electrons at the fermi level regarded as the "free electrons" of the metal?

Do you know about the band theory of solids?
Which band corresponds to the "free" electrons in the metal?
Where is the fermi-level with regard to this band?

Also, how does one go about calculating the Fermi level? Is there an equation or is it experimentally determined?

Both.
Do you know the definition of "Fermi level"?

*Bonus question*

For whom? Is this homework?

Electrons that undergo phonon exchange and pair up are called "Cooper pairs". Why do these Cooper pairs not experience resistance? I have been looking all over the place for this answer and cannot find out why this is the case.

electrons form cooper-pair at low temperature.
how does conduction normally happen?
what is special about a cooper pair?

 

[heycoa]

Hi, thanks for taking the time to read my post.

Yeah I know about band theory, and if I remember correctly there is a valence band and a conduction band and the Fermi level lies somewhere in between. I do not know where the free electrons are.

I also do know the definition of the Fermi level. Its where electrons reside at absolute zero... i.e. they obey the exchange principle so they don't condense, so there is this Fermi level which is the highest energy state that the electrons occupy.

as far as bonus question, I was making a joke because it doesn't really have anything to do with the title.

A cooper pair is a boson, that's what's special about it. I know how conduction normally happens. But I don't understand how at low temperature, cooper pairs don't feel any resistance.

 

[csmallw]

The answers to your questions are rather complicated, so I imagine it will be a little bit hard for anyone to answer adequately in a single paragraph or two ;)

Do you have access to any of the standard physics textbooks? I seem to remember that Chapter 5 of "Introduction to Quantum Mechanics" by Griffiths is pretty accessible in terms of explaining the role of the Fermi level with regard to metals and charge carriers. Ashcroft and Mermin is my favorite solid-state physics book, and will give a more complete explanation. You might check that out, also.

 

[Simon Bridge]

Hi, thanks for taking the time to read my post.

Yeah I know about band theory, and if I remember correctly there is a valence band and a conduction band and the Fermi level lies somewhere in between. I do not know where the free electrons are.

The free electrons are in the conduction band. Hence the name ;)

Since you know the band theory, you should know what is special about the valence and conduction bands in a conductor. This (and see below) tells you where the fermi level is.

JIC:
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/band.html

I also do know the definition of the Fermi level. Its where electrons reside at absolute zero... i.e. they obey the exchange principle so they don't condense, so there is this Fermi level which is the highest energy state that the electrons occupy.

Close - the Fermi-level is the highest energy level occupied by the electrons at absolute zero. It's a matter of counting the states. Not all electrons are at the Fermi level.

as far as bonus question, I was making a joke because it doesn't really have anything to do with the title.

Fair enough. The questions you ask can show up as part of assignments.

A cooper pair is a boson, that's what's special about it. I know how conduction normally happens. But I don't understand how at low temperature, cooper pairs don't feel any resistance.

Please describe how conduction normally happens and how resistance normally occurs.
The idea here is that it helps me know how to answer your questions effectively.

Under what conditions do Cooper pairs form?
Why is it special that a cooper-pair acts as a boson?

It looks to me like your reading is incomplete all right.
What education level do you need these replies at?

Note: the difficulty in providing potted answers is the reason I am, instead, trying to guide your reading and thoughts by asking questions back at you.