Everything about Electron Degeneracy Pressure totally explained
Electron degeneracy pressure is a consequence of the
Pauli exclusion principle, which states that two
fermions can't occupy the same
quantum state at the same time. The force provided by this pressure sets a limit on how much matter can be squeezed together without it collapsing into a
black hole. It is an important factor in
stellar physics because it's responsible for the existence of
white dwarfs.
Also relevant to the understanding of electron degeneracy pressure is the
Heisenberg uncertainty principle, which states that
»
where
is
Planck's constant (h) divided by 2
π, Δ
x is the uncertainty of the position measurements and Δ
p is the uncertainty in the
standard deviation of the
momentum measurements.
A material subjected to ever increasing pressure will become ever more compressed, and for electrons within it, the uncertainty in position measurements, Δ
x, becomes ever smaller. Thus, as dictated by the uncertainty principle, the uncertainty in the momenta of the electrons, Δ
p, becomes larger. Thus, no matter how low the temperature drops, the electrons must be traveling at this "
Heisenberg speed," contributing to the pressure. When the pressure due to the "Heisenberg speed" exceeds that of the pressure from the thermal motions of the electrons, the electrons are referred to as degenerate, and the material is termed
degenerate matter.
Electron degeneracy pressure will halt the gravitational collapse of a
star if its
mass is below the
Chandrasekhar Limit (1.38
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 a
neutron star or
black hole, because the degeneracy pressure provided by the electrons is weaker than the inward pull of
gravity.
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