Physics » Condensed Matter Physics » Free Electron Model of Metals

# 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