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Between Cs and Na, the fermi energy in metal approximately doubles. why doesn't the carrier concentration also double?
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. :)
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.
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.
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.
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.
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.