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Modern Physics
Modern Physics

Fermi Energy

EF=ℏ22m(3π2n)2/3E_F = \frac{\hbar^2}{2m}(3\pi^2 n)^{2/3}

The highest occupied energy level at absolute zero for a system of fermions. Crucial for understanding metals, white dwarfs, and neutron stars.

Variables

E_F
Fermi energy
J
\hbar
Reduced Planck constant
J·s
m
Particle mass (e.g., electron)
kg
n
Number density of particles
m⁻³

Derivation

Derived from counting quantum states up to the Fermi level in a free electron gas.

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Common questions

What is the Fermi Energy formula?

Fermi Energy is written E_F = ℏ²/2m(3π² n)²/³. The highest occupied energy level at absolute zero for a system of fermions. Crucial for understanding metals, white dwarfs, and neutron stars. It belongs to Modern Physics, under Quantum Mechanics.

What are the units in E_F = ℏ²/2m(3π² n)²/³?

In SI units, E_F is fermi energy, measured in J; \hbar is reduced planck constant, measured in J·s; m is particle mass (e.g., electron), measured in kg; n is number density of particles, measured in m⁻³.

How is the Fermi Energy formula derived?

Derived from counting quantum states up to the Fermi level in a free electron gas. The result is E_F = ℏ²/2m(3π² n)²/³.