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While degeneracy pressure usually dominates at extremely high densities, it is the ratio between degenerate pressure and thermal pressure which determines degeneracy. Given a sufficiently drastic increase in temperature (such as during a red giant star's helium flash ), matter can become non-degenerate without reducing its density.
Using the Fermi gas as a model, it is possible to calculate the Chandrasekhar limit, i.e. the maximum mass any star may acquire (without significant thermally generated pressure) before collapsing into a black hole or a neutron star. The latter, is a star mainly composed of neutrons, where the collapse is also avoided by neutron degeneracy ...
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In the nonrelativistic case, electron degeneracy pressure gives rise to an equation of state of the form P = K 1 ρ 5/3, where P is the pressure, ρ is the mass density, and K 1 is a constant. Solving the hydrostatic equation leads to a model white dwarf that is a polytrope of index 3 / 2 – and therefore has radius inversely ...
If k = 1, the chain reaction is critical and the neutron population will remain constant. In an infinite medium, neutrons cannot leak out of the system and the multiplication factor becomes the infinite multiplication factor, k = k ∞ {\displaystyle k=k_{\infty }} , which is approximated by the four-factor formula.
During the formation of neutron stars, or in radioactive isotopes capable of electron capture, neutrons are created by electron capture: p + e − → n + ν e. This is similar to the inverse beta reaction in that a proton is changed to a neutron, but is induced by the capture of an electron instead of an antineutrino.
This is the pressure that prevents a white dwarf star from collapsing. A star exceeding this limit and without significant thermally generated pressure 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.
The values of the neutron drip line are only known for the first ten elements, hydrogen to neon. [19] For oxygen (Z = 8), the maximal number of bound neutrons is 16, rendering 24 O the heaviest particle-bound oxygen isotope. [20] For neon (Z = 10), the maximal number of bound neutrons increases to 24 in the heaviest particle-stable isotope 34 ...