Summarizing Free Electron Model of Metals

Summary

• Metals conduct electricity, and electricity is composed of large numbers of randomly colliding and approximately free electrons.
• The allowed energy states of an electron are quantized. This quantization appears in the form of very large electron energies, even at \(T=0\;\text{K}\).
• The allowed energies of free electrons in a metal depend on electron mass and on the electron number density of the metal.
• The density of states of an electron in a metal increases with energy, because there are more ways for an electron to fill a high-energy state than a low-energy state.
• Pauli’s exclusion principle states that only two electrons (spin up and spin down) can occupy the same energy level. Therefore, in filling these energy levels (lowest to highest at \(T=0\;\text{K}),\) the last and largest energy level to be occupied is called the Fermi energy.

Glossary

density of states

number of allowed quantum states per unit energy

electron number density

number of electrons per unit volume

Fermi energy

largest energy filled by electrons in a metal at \(T=0\;\text{K}\)

Fermi factor

number that expresses the probability that a state of given energy will be filled

Fermi temperature

effective temperature of electrons with energies equal to the Fermi energy

free electron model

model of a metal that views electrons as a gas