Fermi Energy
The highest occupied energy level at absolute zero for a system of fermions. Crucial for understanding metals, white dwarfs, and neutron stars.
Variables
Derivation
Derived from counting quantum states up to the Fermi level in a free electron gas.
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Constants in this formula
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- ℏ = 1.054 571 817… × 10⁻³⁴ J·s (Reduced Planck constant)
- m = 2 kg (Particle mass (e.g., electron))
- n = 3 m⁻³ (Number density of particles)
Result: EF = 5.535037 × 10⁻⁶⁸ J
Other modern physics formulas with the same quantities
- Heisenberg Uncertainty Principle (Quantum Mechanics) shares Reduced Planck constant
- Energy-Time Uncertainty (Quantum Mechanics) shares Reduced Planck constant
- Time-Dependent Schrödinger Equation (Quantum Mechanics) shares Reduced Planck constant
- Bohr Radius (Atomic Physics) shares Reduced Planck constant
Where this formula is listed
- Modern Physics formulas, under Quantum Mechanics, alongside Photon Energy (Planck), Photoelectric Effect, Stopping Potential, de Broglie Wavelength and Compton Scattering.
- In the modern physics list it comes after Photon Momentum and before Photoelectric Threshold Frequency.
- Modern Physics formula sheet, one of 41 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Fermi Energy formula?
Fermi Energy is written E_F = (ℏ²/(2m))(3π²n)^(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))(3π²n)^(2/3)?
In SI units, E_F is fermi energy, measured in J; ℏ 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))(3π²n)^(2/3).