Fermi energy in metals approximately doubling

In summary, the fermi energy in metal approximately doubles between Cs and Na. However, the carrier concentration does not double because in the free electron approximation, the Fermi energy is proportional to n^(2/3) where n is the free electron concentration. When taking the ratio of the concentrations and raising it to power 2/3, the result is 2, which is much better than expected.
  • #1
AIHUNTER
2
0
Between Cs and Na, the fermi energy in metal approximately doubles. why doesn't the carrier concentration also double?
 
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  • #2
Why would you expect to double?
The free electron concentration is not proportional to the Fermi level.
In the free electron approximation the Fermi energy goes like n^(2/3) where n is the free electron concentration.
n for sodium is about 2.65 and for Cs about 0.91 (from Ascroft and Mermin) . In same units, 10^22/cm^3, for example.
If you take the ratio of the concentrations and raise it to power 2/3 you get 2 Much better that I expected to work. :)
 
  • #3
nasu said:
Why would you expect to double?
The free electron concentration is not proportional to the Fermi level.
In the free electron approximation the Fermi energy goes like n^(2/3) where n is the free electron concentration.
n for sodium is about 2.65 and for Cs about 0.91 (from Ascroft and Mermin) . In same units, 10^22/cm^3, for example.
If you take the ratio of the concentrations and raise it to power 2/3 you get 2 Much better that I expected to work. :)

Thanks nasu :)
 

What is Fermi energy in metals?

Fermi energy in metals is the maximum energy that an electron can have at absolute zero temperature. It represents the energy level at which the highest occupied electron states are found in a metal.

How is Fermi energy related to the electronic structure of metals?

Fermi energy is closely related to the electronic structure of metals. It is determined by the number of electrons in a metal and the available energy levels for those electrons to occupy. This energy level also determines the electrical and thermal conductivity of a metal.

How does Fermi energy change in different metals?

Fermi energy varies for different metals depending on their electronic structures. Metals with a higher number of electrons and a more compact atomic structure will have a higher Fermi energy compared to metals with fewer electrons and a more spread out atomic structure.

Why does Fermi energy approximately double in metals?

Fermi energy in metals approximately doubles because of the Pauli exclusion principle. This principle states that no two electrons can have the same set of quantum numbers, which leads to an increase in energy levels as more electrons are added to a metal.

How is the doubling of Fermi energy in metals significant?

The doubling of Fermi energy in metals is significant as it affects the properties and behavior of the metal. It can impact the electrical and thermal conductivity, as well as the magnetic and optical properties of a metal. It also plays a crucial role in understanding and predicting the behavior of electrons in a metal.

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