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| Einstein's Mass-Energy Equivalence Relation |
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| According to Newton's second law of motion, force acting on a body is defined as the rate of change of its momentum i.e., |
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| Now, if this force 'F' displaces the body through a distance dx, its energy increases by |
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| According to Einstein's relation of relativistic mass, |
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| or m2c2 - m2v2 = m02c2 |
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| Differentiating and noting that m0 and 'c' are constants, |
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| c2. 2m dm - m2. 2v dv - v2. 2m dm = 0 |
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 c2 dm = mv . dv + v2 dm = dK [from equation (i)] |
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 dK = dm . c2 |
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| If particle is accelerated from rest to a velocity v, let its mass m0 increase to m. |
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 K = (m - m0) c2 |
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| K + m0c2 = mc2 |
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| Here, the quantity m0c2 is the energy associated with the rest mass of the body. |
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| K is the kinetic energy of the body. Thus, the total energy of the body is given by E = mc2 |
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| This is Einstein's mass-energy equivalence relation. |
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| i) Kinetic energy of a body moving with a velocity v << c. |
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| We know that |
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| Here, mc2 is the total energy and m0c2 is the rest mass energy. Therefore, (mc2 - m0c2) represents the kinetic energy. |
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| This is the same result that we obtain by Newtonian mechanics. |
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| A positron has the same mass as an electron but an opposite charge of +e. When an electron and a positron come close to each other, they annihilate or destroy each other. Their masses are converted into energy according to Einstein's relation, and the energy thus obtained is released in the form of g- rays. Thus, matter is annihilated to give an equivalent amount of energy. |
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| This process is the reverse of annihilation of matter. A photon of energy 1.02 MeV nearing a massive nucleus, under its intense electric field, splits up into a pair of particles - an electron and a positron. Thus, energy has been materialised by converting it into matter. |
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| When protons and neutrons in the nucleus combine together to form the nucleus, the total mass of all the protons and neutrons (also called nucleons here, because these are the particles forming a nucleus) is just a little more than the mass of the nucleus itself. The deficiency in the mass, known as mass defect, is transformed into the binding energy of the nucleus. It is this energy which keeps the nucleus bound. If the nucleus is split up, as in an atomic bomb (strictly a nuclear bomb), this energy is released in the form of heat and g radiations. |
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