Fermi energy and ratio of the number of occupied levels at an energy

In summary, the conversation discusses calculating the Fermi energy for copper, the ratio of occupied levels at 8.5 eV to the Fermi energy, and the treatment of conduction electron gas as a quantum gas of indistinguishable particles at room temperature. The Fermi energy for copper is known to be 7.0 eV, but more information is needed to solve the problem. The Fermi function and density of states are needed to calculate the ratio of occupied levels, and to treat the conduction electron gas as a quantum gas.
  • #1
acusanelli
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0

Homework Statement



a) Calculate the Fermi energy for copper.

b) Calculate the ratio of the number of occupied levels at an energy of 8.5 eV to the number occupied levels at the Fermi energy at room temperature.

c) Based on your answer to a) and b) above, show that at room temperature, the conduction electron gas must be treated as a quantum gas of indistinguishable particles


The Attempt at a Solution



I know that the fermi energy for copper is 7.0ev but have no idea how it was set up. please help me set this problem up with equations or whatever i need to solve it
 
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  • #2
You will need to supply more info to solve (a). You will need to supply equations for the Fermi energy.
 
  • #3
that was all i was given to work with
 
  • #4
Well you will need more info to calculate the Fermi energy. Even if you assumed it to be a perfect fermi sea, you would need the density of carriers then.
 
  • #5
well if i know the fermi energy for copper is 7ev then how do i set up and solve for b?
 
  • #6
Look up the Fermi function. You will need that for (b) as well as the density of states.
 
Last edited:

1. What is Fermi energy?

Fermi energy is the maximum energy level that can be occupied by electrons at absolute zero temperature in a solid material. It is named after Italian physicist Enrico Fermi and is a crucial concept in understanding the electronic properties of solids.

2. How is Fermi energy related to the electron population in a solid material?

Fermi energy determines the highest energy level at which electrons can exist in a solid material at absolute zero temperature. This energy level also divides the energy levels into occupied and unoccupied states, with all energy levels below the Fermi energy being filled and those above being empty.

3. What is the ratio of the number of occupied levels at a certain energy to the total number of levels?

This ratio is known as the Fermi-Dirac distribution function and is represented by the symbol f(E). It gives the probability of finding an electron in an energy state E at absolute zero temperature.

4. How does the Fermi energy change with temperature?

At absolute zero temperature, the Fermi energy remains constant. However, as the temperature increases, some electrons gain enough energy to occupy higher energy levels, resulting in a slight increase in the Fermi energy.

5. How is the Fermi energy calculated?

The Fermi energy can be calculated using the formula EF = (h2/8m)(3π2n)2/3, where h is Planck's constant, m is the mass of an electron, and n is the number of electrons per unit volume. This formula is derived from the Fermi-Dirac distribution function and is valid for non-interacting electrons in a solid material.

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