Did you know that stars die!When stars run out of hydrogen, the nuclear fusion reactions at their core stop and become unstable and collapse. It is important to note that not all stars collapse the same way. Massive stars explode into a supernova and then collapse into neutron stars, or black holes. We know this because of the work of astrophysicist Subrahmanyan Chandrasekhar. Chandrasekhar was an Indian-born scientist who spent 50 years at the University of Chicago. He is most famous for coming up with the theory that explains the death of the universe’s most massive stars. Before Chandrasekhar, scientists assumed that all stars collapsed into white dwarfs when they died.Chandrasekhar limit is the famous prediction done by Subrahmanyan Chandrasekhar.
What isChandrasekhar Limit?
The utmost mass that a white dwarf star that’s stable can have is known as the Chandrasekhar limit. E.C. Stoner and Willhelm Anderson pointed it out in their papers and termed it after Subrahmanyan Chandrasekhar, an Indian astrophysicist who made major independent discoveries on improving the preciseness of computation.
The scientific community ignored the limit at the start as it would legitimize the existence of black holes (technically unrealistic at this turn-off time). Due to the pressure of electron degeneration, the white dwarf stars oppose its gravitational collapse.
Chandrasekhar limit is established at a point when the mass at which the pressure from the degeneration of electrons is not able to balance the self-attraction of the gravitational field. The limit that has been established these days is 1.39 M☉.
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Explanation:
Pauli’s exclusion principle gives rise to a phenomenon of quantum mechanics termed as Electron degeneracy pressure. Electrons cannot have the same state or the minimum-energy level. This is because they are fermions.
A spectrum of energy levels exists, and electrons should be distributed throughout them. When the electron gas is compressed, the amount of electrons in a specific volume increases, and so does the energy level of the band that has been occupied. Thus, to produce the electron degeneracy pressure, pressure must be applied for the compression of the electron gas as their energy increases when compressed. Electron capture occurs when that pressure is so great that the electron goes into the nuclei.
Application of Chandrasekhar Limit
- When the nuclei of lighter elements fuse into the nuclei of a heavier one, the resultant heat is what keeps the core of the star from collapsing. The core will become condensed and hotter when collapsed as the exhaustion of the nuclei will take place.
- As getting energy through fusion is impossible in the case of iron ions, a dangerous circ*mstance occurs when iron amasses in the core. If the star is less than 8 solar masses, it will sooner or later reach a mass level lower than the Chandrasekhar limit.
- Stars that have more mass will be converted into a black holes as the pressure due to the electron degeneration will keep them from collapsing until the density is extremely high. Neutrinos are released when through electrons capturing electrons are captured by the protons. The released neutrinos take away the energy that was created due to the decreasing potential energy (collapse of the core). The energy is around 1046 joules.
What is Chandrasekhar Unit?
Chandrasekhar unit explains the maximum mass of a white dwarf star which is equivalent to 1.44 solar masses. The star turns into a neutron star or a black hole when the limit exceeds.
What is the Chandrasekhar limit for a neutron star?
The maximum Chandrasekhar limit for a neutron star is 3 Msun.
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Frequently Asked Questions – FAQs
Q1
What happens if a white dwarf exceeds the Chandrasekhar limit?
If a white dwarf exceeds the Chandrasekhar limit, they, under gravitational collapse, evolve as a stellar remnant similar to a neutron star or a black hole.
Q2
What is the significance of the Chandrasekhar limit?
The significance of the Chandrasekhar limit is that it is accepted to be 1.4 times the sun’s mass, such that if the white dwarf is within the limit, they stay as such forever. In contrast, the star that exceeds the limit will experience explosions, turning into a supernova.
Q3
State TRUE or FALSE: When a star exceeds the Chandrashekhar Limit, it turns into a neutron star or a black hole.
Q4
What would happen if a neutron star hit a black hole?
When a massive celestial body such as a neutron star hits a black hole, there is a production of gravitational waves that ripple through the fabric of space-time. Also, there will be the release of nuclear materials such as gold and platinum along with electromagnetic waves. These electromagnetic waves include light waves and gravitational waves.
Q5
Is there a limit to the size of a black hole?
The size of the black hole could be up to 50 billion times the mass of our sun.
FAQs
Chandrasekhar Limit Derivation
The Chandrasekhar limit is expressed in terms of Planck mass and proton mass. The upper limit is about 1.44 times the mass of the Sun. White dwarfs with masses greater than the limit cannot balance gravitational collapse through relativistic electron degeneracy.
What is the application of Chandrasekhar limit? ›
Application of Chandrasekhar Limit
As getting energy through fusion is impossible in the case of iron ions, a dangerous circ*mstance occurs when iron amasses in the core. If the star is less than 8 solar masses, it will sooner or later reach a mass level lower than the Chandrasekhar limit.
How do you calculate the Chandrasekhar limit? ›
For a fully relativistic treatment, the equation of state used interpolates between the equations P = K1ρ5/3 for small ρ and P = K2ρ4/3 for large ρ. When this is done, the model radius still decreases with mass, but becomes zero at Mlimit. This is the Chandrasekhar limit.
How many kg is a Chandrashekhar unit? ›
Chandrasekhar limit value- For a stable white dwarf star; it is the maximum mass. 1.4 M ☉ (2.765×1030 kg) is the currently accepted value for the Chandrasekhar limit.
What is the derivation of the Boltzmann constant dimension? ›
Boltzmann Constant(k) = energy/temperature. So, dimensions of Boltzmann Constant = dimension of energy/dimension of temperature. Dimension of energy = dimension of work done = dimension of force x dimension of displacement = [MLT-2] x [L]= [ML2T-2]. So, the dimension of Boltzmann Constant = [ML2T-2]/[K] = [ML2T-2K-1].
What is the formula for derivation of the laws of motion? ›
First Equation of motion : v = u + at. Second Equation of motion : s = ut + 1/2at. Third Equation of motion : v2 - u2 = 2as.
What happens after Chandrasekhar limit? ›
Beyond the Chandrasekhar limit
With no more fusion possible, the stellar core collapses for a final time. If the core has a mass under 3 times that of the sun, neutron pressure protects it from complete collapse leading to the creation of a neutron star.
What is the most important feature of a black hole? ›
A black hole is so dense that gravity just beneath its surface, the event horizon, is strong enough that nothing – not even light – can escape. The event horizon isn't a surface like Earth's or even the Sun's. It's a boundary that contains all the matter that makes up the black hole.
What is the limit for a star to become a black hole? ›
In general, stars with final masses in the range 2 to 3 solar masses are believed to ultimately collapse to a black hole.
How do you calculate maximum retardation? ›
- The correct answer is.
- a = v − u t.
- Therefore, the expression for the retardation is.
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.
What is the contribution of S Chandrasekhar to physics? ›
Chandrasekhar's most notable work is on the astrophysical Chandrasekhar limit. The limit gives the maximum mass of a white dwarf star, ~1.44 solar masses, or equivalently, the minimum mass that must be exceeded for a star to collapse into a neutron star or black hole (following a supernova).
What does the Chandrasekhar limit tell us? ›
Using Albert Einstein's special theory of relativity and the principles of quantum physics, Chandrasekhar showed that it is impossible for a white dwarf star, which is supported solely by a degenerate gas of electrons, to be stable if its mass is greater than 1.44 times the mass of the Sun.
What prevents the collapse of a neutron star? ›
The principle that prevents further collapse is known as neutron degeneracy pressure, where the neutrons are packed so tightly that the Pauli exclusion principle prevents them from occupying the same quantum state, providing the pressure needed to counteract gravity.
What is the limit of a neutron star? ›
If the remnant star has a mass exceeding the Tolman–Oppenheimer–Volkoff limit, which ranges from 2.2–2.9 M ☉, the combination of degeneracy pressure and nuclear forces is insufficient to support the neutron star, causing it to collapse and form a black hole.
What is the derivation of Einstein's equation of Brownian motion? ›
Einstein predicted that, just like a molecule in solution, such a Brownian particle would diffuse according to a simple equation: D = √[(kBT/6πηR)t], where D is the displacement (technically the root mean square displacement) of the particle, T is the temperature, η is the viscosity of the liquid, R is the size of the ...
What is the derivation of Helmholtz? ›
Derivation of Helmholtz Free Energy
Consider the following: A = U – TS .. eqn1. Final entropy is measured in Joules per Kelvin (JK1), where U represents the internal energy in Joules and T represents the absolute temperature in Kelvin.
What is the derivation of Wien's displacement law? ›
The Derivation of Wien's Displacement Law
According to Wien's distribution, the energy distribution varies in proportion to λ-5. For small values of λ, the exponential component becomes significant and contributes more than the other factor λ-5. This suggests that E grows as λ decreases at shorter wavelengths.
What is the derivation of law of conservation of energy? ›
Law of Conservation of Energy can be derived with the help of the following example, take a ball falling from the height H and the initial velocity is zero, also the potential energy at the surface of the earth is zero. Now at the height H from the ground, Etotal = Epotential + Ekinetic. ⇒ Etotal = 1/2mv2 + mgH.
