Fermi energy in metals approximately doubling

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SUMMARY

The discussion centers on the relationship between Fermi energy and carrier concentration in metals, specifically between cesium (Cs) and sodium (Na). It is established that while the Fermi energy approximately doubles from sodium to cesium, the carrier concentration does not follow suit due to the non-proportionality of free electron concentration to the Fermi level. The free electron approximation indicates that Fermi energy is proportional to the free electron concentration raised to the power of 2/3, with sodium having a concentration of 2.65 x 10^22/cm^3 and cesium at 0.91 x 10^22/cm^3, confirming this relationship.

PREREQUISITES
  • Understanding of Fermi energy concepts in solid-state physics
  • Familiarity with free electron models in metals
  • Knowledge of carrier concentration calculations
  • Basic grasp of the Ascroft and Mermin reference for electron concentrations
NEXT STEPS
  • Study the free electron model in greater detail
  • Explore the implications of Fermi energy on electrical conductivity
  • Investigate the mathematical derivation of the relationship between Fermi energy and electron concentration
  • Review the Ascroft and Mermin text for additional insights on electron behavior in metals
USEFUL FOR

Physicists, materials scientists, and students studying solid-state physics who are interested in the properties of metals and the behavior of electrons within them.

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

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