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#E = mc^2#


This is calculated using the famous equation of Einstein,

#E = m c^2#

In Fusion reaction like the ones taking place in the core of a Star, there is enough pressure to fuse hydrogen nuclei to form one helium nucleus.

So, 4 hydrogen nuclei are fused together to form one Helium nucleus. But, where does the energy come from that keeps the Sun from collapsing?.

When 4 Hydrogen nuclei are merged together they show a certain discrepancy in the mass when a Helium atom is formed, i.e the mass of 4 Hydrogen atoms before Fusion is less than the mass of the Helium atom after the reaction this mass defect is converted into energy by #E = mc^2#.

#"mass of a hydrogen atom " = " 1.00794 u"#

#"mass of one helium atom " = " 4.002602 u"#

Where #u = 1.6605 xx 10^(-27)"kg"#.

The mass defect, #Deltam#, will be

#Delta m = 4 xx m_H - m_(He)#

#= 4 xx "1.00794 u" - "4.002602 u"#

# = "0.029158 u "# or #" "4.8416859 * 10^(-29)"kg"#

In the equation #E = mc^2#, #c# is the speed of light in a vacuum, approximately equal to #3 * 10^8"m s"^(-1)#.

This means that you have

#E = 4.8416859 * 10^(-29)"kg" * (3 * 10^8)^2"m"^2"s"^(-2)#

#E = 4.35751731 * 10^(-12)" J per reaction"#


Black holes challenge the laws of physics as we know them.


Nothing should be able to defy the laws of physics. If something is inconsistent with the laws of physics then they need to be modified to accommodate the inconsistency.

Black holes are extreme objects. They were predicted from the Schwarzschild solution to Einstein's General Theory of Relativity. Many people didn't think that they existed until evidence was found. A black hole could explain the galactic X-ray source at Cygnus X-1. It is now believed that most large galaxies have a supermassive black hole at their centres.

One issue with black holes is that the theories suggest that there is a singularity inside them. A singularity is a point of infinite density and infinite curvature of spacetime. The physicist Kip Thorne described the singularity as the point where all laws of physics break down.

Another problem with black holes is the black hole information paradox. The issue is that if a particle falls into a black hole information about its state is lost. This is forbidden by the laws of physics as we know them. Stephen Hawking is working on a new theory by which the information is somehow retained at the event horizon.

Clearly we need new laws of physics if we are to completely understand black holes. As nothing which goes past the event horizon can ever escape. This makes it impossible to see inside a black hole.

So, yes, black holes defy the laws of physics as we know them. This means that our laws of physics are incomplete.




The layer chromosphere is #2000# km thick.

The radius of the sun is #0.7 * 10^6# km.

To calculate this you have to just do same as we do in calculation of our exam's marks percentage.

Just imagine,

Your exam is of total marks of #0.7 * 10^6#(not possible but you have #color(white)0000000000000000000000000000000#to just imagine this )
out of this you got #2000# marks.

To calculate the percentage you have to do something like this:

#=2000/(0.7 * 10^6) * 100#


Just do same calculation for this question,
Total radius of sun is #0.7 * 10^6# km.
out of this #2000# km is chromosphere.

#=2000/(0.7 * 10^6) * 100#



I have added image for your help by which you can know where is chromosphere of the sun.



#3380" N"#. Don't try this at home: you might get torn apart (see the explanation).


The amount of tension is given by the difference in gravitational force between the two masses. Let A and B be the masses, with A being closer to the black hole O. Then:



As the A and B masses are equal we substitute #M_A# for #M_B# and subtract to get the tension:


Now put in numbers and calculate:

#G=6.67xx10^{-11}" Nm"^2/"kg"^2# (same units in SI system as those given)

#M_A(=M_B)=1" kg"#, taken as exact values

#r_A=686,000-0.5=685,999.5" m"#

#r_B=686,000+0.5=686,000.5" m"#


#T=3380" N"#. This is over 170 times the gravity of Earth on the same amount of mass. A similar 100-g+ force acting on your mass would pull you apart, even though you are still relatively far from the hole's horizon.

It all started with Beta decay. An electron is emitted in the decay of a nucleus. There are no electrons in the nucleus, lepton number is not conserved unless another lepton is formed. Since electric charge is conserved, the particle needed to be neutral, it was called a neutrino. Associated with each lepton, we have one neutrino. One for the electron, one for the muon, and one for the Tau.

Neutrinos interact via gravity, weak interaction, but not electromagnetic interaction. Because they are neutral, their mean free path is larger than that of charged particles. Neutrinos are produced during Proton-Proton reactions. These reaction are fusion reactions, by which nuclei of increasingly large atomic number are produced. Starting with Hydrogen and moving up the Mendeleev ladder.

Fusion is the process that heats up the sun. It also prevents it from collapsing under its own weight. In the sun, conversion Hydrogen into Deuterium takes place through the chain PP I. P P III generates the most energetic neutrinos. It contains the reaction

#Be_5# gives #Be_4 + e + nu_e#.

These reactions were the ones for which John Bacall designed his experiment. When he observed about 1/3 of the expected number of neutrinos, the standard model had to be revised and a tiny mass was shown to give rise to neutrino oscillations. Electron neutrinos can turn into muon neutrinos. In general, all species of neutrinos can turn into each other. With a detector targeting only one species, the neutrino count was off by 2/3.
With this problem now solved, we can and we need to use neutrinos to probe the sun's interior.

Why we need neutrinos to know what is going on inside the sun is because the sun's core has 150 times the density of water. Assuming the path of a photon to be a random walk, the average size of each step was estimated to be 9/100 centimeters. Considering that the photon has almost 700000 kms to travel to reach the surface and that it does so through a diffusion process, one finds that it takes 1.7 10^5 years for photons to emerge out of the sun,

Photons are a poor way of probing the sun's interior. Neutrinos travel close to the speed of light and reach detectors much faster.


Spectroscopy is measuring light to find out what something is made of on an atomic scale.


Spectroscopy is measuring the light emitted by stars to tell what sort of atoms the star is making, or what a substance is made up of.

Each atom is a nucleus surrounded by a load of electrons. The electrons have specific energy levels, like stairs, and can move between the levels by absorbing or emitting photons of certain frequencies.

When an electron absorbs a photon, it gains energy and moves up the stairs. When it emits a photon, it loses energy and moves down the stairs again. Luckily for us, photons are also light, so we can see it when electrons lose energy in atoms.

Also, each atom has very specific energy levels that we can measure precisely here on Earth, so we know from the frequency of light emitted what energy is lost and so what atom it is in the star, or any other substance.


[The above image is an example of spectroscopy.]

Energy of a photon is given by:

#E=hf# or #E=hnu#

where #h# is called Planck's constant and is approximately #6.626*10^-34##J.s#, and #f# is the frequency of the light emitted in Hertz (oscillations per second).

We may not be able to directly measure the frequency, but we know that the speed of light is constant and that it is given by:

#c = flambda#

where #c# is the speed of light, #lambda# is wavelength, and #f# is, again, frequency. The speed of light is about #3*10^8m/s# approx. The real value is taken as #2.99792458*10^8m/s#. These values are speed of light in a vacuum.


#f=c/lambda#, so


This is great because the colour of light is how humans see wavelength, so just from the colour of something we can determine the energy of light emitted, and the energy of light emitted is specific to each atom.

We can also go the other way, rather than measuring the light that something emits, measure the light that it absorbs, which, although it is exactly the opposite, gives us exactly the same result. We can do this by shining white light on a gas in the lab and seeing what light comes through the other side. The light that doesn't come through is absorbed, and from this we can tell precisely what the gas is.

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