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what is relation between Chandrshekar limit & exclusion priceple?
Can any one explain correlation of exclusion princepal of quantum theroy & Chandrashekar limit, in connection to white dwarf and neutron star & black hole, as per this limit only masses more than chandrsheakar limit can become black holes lesser masses than chadrasheakar limit can only become either white dwarf or neutron stars which is becuase of exclsuion pricepal ( which says no particle of same mass & vilocity can not stay at single place at same time (as i understand)) so please any one explain this mechansisum how to understand this
4 Antworten
- Anonymvor 1 JahrzehntBeste Antwort
The limit to electron degeneracy pressure is called the Chandrasekhar limit (1.4 solar masses), but the limit to neutron degeneracy pressure is called the Schwarzschild limit (3.2 solar masses).
Normal stars are held suspended against their own gravitational pull by a combination of hydrostatic pressure and radiation pressure. When stars cool off, they collapse and temporarily heat up again, but when they've cooled off again they are held up by the degeneracy pressure between fermions caused by the Pauli exclusion principle.
An old star has thrown off all the mass that it's going to, and has less than 1.4 solar masses left in its core, will be a "white dwarf star" forever after (even after it has cooled to invisibility, we still call it that). The electrons in a white dwarf star aren't attached to individual atoms as in normal matter. Instead, the whole star is like a gravitationally bound molecule, with the component atoms bound by sharing all their electrons in common.
But an old star that has between 1.4 solar masses and 3.2 solar masses will pressure electrons into reverse beta-decay with the protons in the star, and this will transmute the degenerate matter into neutronium, or neutron matter. A neutron star is like one big atomic nucleus, except made of neutrons only. Theoretically, there are differences in neutron stars' internal strata, but the idea is that the quark Pauli exclusion principle is holding back the force of gravity.
If the old star had more than 3.2 solar masses left, then the electron degeneracy pressure would fail (by reverse beta-decay), and then the quark degeneracy pressure would fail as gravity smooshed the neutrons together into a singular quark state (with an event horizon around it).
- ?Lv 7vor 1 Jahrzehnt
The exclusion principle states that no two Fermion particles (such as electrons and protons) can occupy the same quantum state. Fermions are particles that have spin 1/2 or 3/2 or 5/2 etc. The reason for the exclusion principle is more than we can go into here, but basically it comes from the symmetry properties of the particles and what happens to a state when it is transformed by mirroring.
The exclusion principle is what makes most of the world around us the way it is---atoms are the way they are because no two electrons can occupy the same state. Once the lower energy states of an atom are filled, the electrons must then fill the higher energy states. This allows things to have a finite size, even at zero temperature---it allows there to be solid objects.
In a gas or plasma, however, the particles are so energetic that they get to lots of high energy states without filling all the low energy states first. A gas or plasma therefore obeys the gas laws, where PV=nRT, the pressure in a volume comes from the temperature of the gas.
Most stars are made of plasma, and therefore obey the gas laws. As a star gets old, however, and cools, there is a transition from the plasma state to a more "solid" state, where the particles are held up by the exclusion principle. For a small star (low mass), the star can exist even at zero temperature because the pressure to hold it up is provided by the exclusion principle. White dwarfs consist of ordinary atoms held up by the exclusion principle, and neutron stars consist of neutron matter held up by the exclusion principle.
The Chandrasekar limit comes from the realization that the pressure due only to the exclusion principle is not enough to hold up a really massive star (more than 1.4 solar masses). This is because the pressure "caused" by the exclusion principle adds to the gravity in General Relativity. As more and more mass is added to the star, the internal pressure continues to go up, and that pressure adds to the gravity. Eventually, the gravitiational field becomes so strong that the only solution is a black hole instead of a star. So any "starlike" object bigger than the Chandresekar limit must be a black hole.
This is not to say that you cannot have smaller black holes---black holes can be any size from a few kilograms to infinite. It just says that when you have more than 1.4 solar masses held up only by exclusion principle pressure, it won't work and the object must become a black hole.
Also, you can have stars more massive than 1.4 solar masses, but they must be lower density and held up by gas pressure instead of the exclusion principle.
- campbelp2002Lv 7vor 1 Jahrzehnt
The Pauli exclusion principle explains why matter occupies space exclusively for itself and does not allow other material objects to pass through it, at the same time allowing light and radiation to pass.
Electron degeneracy pressure is a force caused by the Pauli exclusion principle, which states that two electrons cannot occupy the same quantum state at the same time.
The Chandrasekhar limit is the maximum mass which can be supported against gravitational collapse by electron degeneracy pressure. Above that mass, electrons and protons in the atoms will be forced to combine into neutrons, making a neutron star. It doesn't really say how much more mass is needed to cause a neutron star to continue collapsing into a black hole.
Quelle(n): http://en.wikipedia.org/wiki/Pauli_exclusion_princ... http://en.wikipedia.org/wiki/Electron_degeneracy_p... http://en.wikipedia.org/wiki/Chandrasekhar_limit - Anonymvor 5 Jahren
Where do you think christianity got it's ideas of a soul and afterlife from for goodness sake? They stole it from the pagan tribes and peoples which existed hundreds and thousands of years before christianity!! From the stone age through vikings, Egyptians, Maoris, Aborigines, American Indians and especially the chinese, they all had elaborate funerals and grave goods to speed the soul into the next life with comfort!! So the relationship to god is that the idea of the soul was stolen by christianity just as the stole virtually everything in the religion from much earlier societies and religions!!