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