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# Electron Degeneracy Pressure

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Electron degeneracy pressure is a consequence of the Pauli exclusion principle, which states that two fermions cannot occupy the same quantum state at the same time. The force provided by this pressure sets a limit on the extent to which matter can be squeezed together without it collapsing into a neutron star or black hole.
Solar Physics Series

Electron Degeneracy Pressure is an important factor in stellar physics because it is responsible for the existence of white dwarfs. When electrons are squeezed too close together, the exclusion principle requires them to have different energy levels. To add another electron to a given volume requires raising an electron's energy level to make room, and this requirement for energy to compress the material appears as a pressure.

A Black Hole Simulation

NASA

Electron degeneracy pressure will halt the gravitational collapse of a star if its mass is below the Chandrasekhar Limit (1.44 solar masses). This is the pressure that prevents a white dwarf star from collapsing. A star exceeding this limit and without usable nuclear fuel will continue to collapse to form either a neutron star or black hole because the degeneracy pressure provided by the electrons is weaker than the inward pull of gravity.

## Electron Degeneracy Pressure Calculations

The equation for calculating Electron Degeneracy Pressure is given by:

Equation 38 - Electron degeneracy pressure

Where h is Planck's constant, me is the mass of the electron, mp is the mass of the proton, ρ is the density, and μe = Ne / Np is the ratio of electron number to proton number.

This pressure is derived from the energy of each electron and every possible momentum state of an electron within this volume up to the Fermi energy being occupied. This degeneracy pressure is omnipresent and is in addition to the normal gas pressure.

Equation 49 - Normal gas pressure

At commonly encountered densities, this pressure is so low that it can be neglected. The matter is electron degenerate when the density (n/V) is high enough, and the temperature low enough, that the sum is dominated by the degeneracy pressure.

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