Nuclear energy Einstein equation

Nuclear energy in almost inconceivable quantities can be obtained from nuclear fission and fusion reactions according to Einstein s famous equation. 

This energy-equivalent of the calculated loss of mass is called the binding energy of the atom or nucleus. When m is expressed in kilograms and c in meters per second, E is in joules. A more convenient unit of energy for nuclear reactions is the MeV (see Chapter 8). The Einstein equation gives... 

The energy changes in nuclear reactions are much greater than those associated with chemical reactions. This is because there are mass changes in nuclear processes. Mass and energy are related by the Einstein equation... 

Energetics of Nuclear Reactions— The energy changes in nuclear reactions are a consequence of Einstein s discovery of a mass-energy equivalence (equation 25.19). 

STRATEGY If we know the mass loss, we can find the energy released by using Einstein s equation. Therefore, we must calculate the total mass of the particles on each side of the nuclear equation, take the difference, and substitute the mass difference into Eq. 6. Then we determine the number of nuclei in the sample from N = m(sample)/m(atom) and, finally, multiply the energy released from the fission of one nucleus bv that number to find the energy released by the sample. 

Nuclear fusion processes derive energy from the formation of low-mass nuclei, which have a different binding energy. Fusion of two nuclear particles produces a new nucleus that is lighter in mass than the masses of the two fusing particles. This mass defect is then interchangeable in energy via Einstein s equation E = me2. Specifically, the formation of an He nucleus from two protons and two neutrons would be expected to have mass ... 

You can use Einstein s equation to calculate the nuclear binding energy for carbon-12. 

As mentioned above, we assume that the molecular energy does not depend on the nuclear spin state For the initial rovibronic state nuclear spin functions available, for which the product function 4 i) in equation (2) is an allowed complete internal state for the molecule in question, because it obeys Fermi-Dirac statistics by permutations of identical fermion nuclei, and Bose-Einstein statistics by permutations of identical boson nuclei (see Chapter 8 in Ref. [3]). By necessity [3], the same nuclear spin functions can be combined with the final rovibronic state form allowed complete... 

Nuclear mass is always lower than the sum of proton and neutron masses because of mass-energy conversion, which transforms part of the mass into binding energy. For example, He has mass 4.002604, whereas the total mass of two protons and two neutrons is 4.032981. Based on Einstein s equation... 

It can be seen that the mass numbers on either side of the equation add up to the same number, 238, and that 92 protons are accounted for in the equation s product and reactant sides. This is a balanced nuclear equation. Actually, some mass is converted into energy, but the amount of mass is very small. From Albert Einstein s equation, E = me2, very little mass, m, is needed to produce a tremendous amount of energy, E, because c is the speed of light, 3 x 108 m/sec. This energy was evidenced when an atomic bomb was exploded over Hiroshima, Japan, during World War II. The fuel for that bomb was uranium-235. 

The mass of an atom is generally not equal to the sum of the masses of its component protons, neutrons, and electrons. If we could imagine a reaction in which free protons, neutrons, and electrons combine to form an atom, we would find that the mass of the atom is slightly less than the total mass of the component particles (an exception is H as there is only 1 nuclear part, the proton). Further, a tremendous amount of energy is released during the reaction which produces the atom. The loss in mass is exactly equivalent to the released energy, according to Einstein s famous equation,... 

Einstein is perhaps best known for his work on relativity, and his simple but elegant equation E = mf, which expresses an equivalence between energy and matter. It is this equation that describes the possibility of the transformation of mass into energy, and the phenomenon that is operational in a nuclear power plant or nuclear bomb. Very little matter can become an inordinate amount of energy, as the speed of light is a constant having an inordinately large value. 

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