Laws of Conservation
In analyzing nuclear reactions, we apply the many conservation laws. Nuclear reactions are subject to classical conservation laws for charge, momentum, angular momentum, and energy (including rest energies). Additional conservation laws, not anticipated by classical physics, are are electric charge, lepton number and baryon number. Certain of these laws are obeyed under all circumstances, others are not. We have accepted conservation of energy and momentum. In all the examples given we assume that the number of protons and the number of neutrons is separately conserved. We shall find circumstances and conditions in which this rule is not true. Where we are considering non-relativistic nuclear reactions, it is essentially true. However, where we are considering relativistic nuclear energies or those involving the weak interactions, we shall find that these principles must be extended.
Some conservation principles have arisen from theoretical considerations, others are just empirical relationships. Notwithstanding, any reaction not expressly forbidden by the conservation laws will generally occur, if perhaps at a slow rate. This expectation is based on quantum mechanics. Unless the barrier between the initial and final states is infinitely high, there is always a non-zero probability that a system will make the transition between them.
For purposes of this article it is sufficient to note four of the fundamental laws governing these reactions.
- Conservation of nucleons. The total number of nucleons before and after a reaction are the same.
- Conservation of charge. The sum of the charges on all the particles before and after a reaction are the same
- Conservation of momentum. The total momentum of the interacting particles before and after a reaction are the same.
- Conservation of energy. Energy, including rest mass energy, is conserved in nuclear reactions.
The Law of Conservation of Matter
The mass can neither be created nor destroyed.
The law requires that during any nuclear reaction, radioactive decay or chemical reaction in an isolated system, the total mass of the reactants or starting materials must be equal to the mass of the products.

- Why a piece of wood weighs less after burning?
- Can a matter or some of its part disappear?
In the case of burned wood the problem was the measurement of the weight of released gases. Measurements of the weight of released gases was complicated, because of the buoyancy effect of the Earth’s atmosphere on the weight of gases. Once understood, the conservation of matter was of crucial importance in the progress from alchemy to the modern natural science of chemistry.
Law of Conservation of Energy
The total energy of an isolated system remains constant over time.

Newton’s cradle. A device that demonstrates the Law of Conservation of Mechanical Energy and Momentum.
Energy can be defined as the capacity for doing work. It may exist in a variety of forms and may be transformed from one type of energy to another in hundreds of ways.
For example, burning gasoline to power cars is an energy conversion process we rely on. The chemical energy in gasoline is converted to thermal energy, which is then converted to mechanical energy that makes the car move. The mechanical energy has been converted to kinetic energy. When we use the brakes to stop a car, that kinetic energy is converted by friction back to heat, or thermal energy.
A consequence of the law of conservation of energy is that a perpetual motion machine of the first kind, which produces work without the input of energy, cannot exist.
The concept of energy conservation is widely used in many fields. In this article the following fields are discussed:
- Conservation of Mechanical Energy
- Conservation of Energy in Fluid Mechanics
- Conservation of Energy in Thermodynamics
- Conservation of Energy in Electrical Circuits
- Conservation of Energy in Chemical Reactions
- Conservation of Energy in Special Relativity Theory
- Conservation of Energy in Nuclear Reactions
Law of Conservation of Mass-Energy – Mass-Energy Equivalence

In special theory of relativity certain types of matter may be created or destroyed, but in all of these processes, the mass and energy associated with such matter remains unchanged in quantity. It was found the rest mass an atomic nucleus is measurably smaller than the sum of the rest masses of its constituent protons, neutrons and electrons. Mass was no longer considered unchangeable in the closed system. The difference is a measure of the nuclear binding energy which holds the nucleus together. According to the Einstein relationship (E = mc2) this binding energy is proportional to this mass difference and it is known as the mass defect.
63Cu nucleus has 29 protons and also has (63 – 29) 34 neutrons.
The mass of a proton is 1.00728 u and a neutron is 1.00867 u.
The combined mass is: 29 protons x (1.00728 u/proton) + 34 neutrons x (1.00867 u/neutron) = 63.50590 u
The mass defect is Δm = 63.50590 u – 62.91367 u = 0.59223 u
Convert the mass defect into energy (nuclear binding energy).
(0.59223 u/nucleus) x (1.6606 x 10-27 kg/u) = 9.8346 x 10-28 kg/nucleus
ΔE = (9.8346 x 10-28 kg/nucleus) x (2.9979 x 108 m/s)2 = 8.8387 x 10-11 J/nucleus
The energy calculated in the previous example is the nuclear binding energy. However, the nuclear binding energy may be expressed as kJ/mol (for better understanding).
Calculate the nuclear binding energy of 1 mole of 63Cu:
(8.8387 x 10-11 J/nucleus) x (1 kJ/1000 J) x (6.022 x 1023 nuclei/mol) = 5.3227 x 1010 kJ/mol of nuclei.
One mole of 63Cu (~63 grams) is bound by the nuclear binding energy (5.3227 x 1010 kJ/mol) which is equivalent to:
- 14.8 million kilowatt-hours (≈ 15 GW·h)
- 336,100 US gallons of automotive gasoline
It is known the average recoverable energy per fission is about 200 MeV, being the total energy minus the energy of the energy of antineutrinos that are radiated away.
The reaction rate per entire 3000MWth reactor core is about 9.33×1019 fissions / second.
The overall energy release in the units of joules is:
200×106 (eV) x 1.602×10-19 (J/eV) x 9.33×1019 (s-1) x 31.5×106 (seconds in year) = 9.4×1016 J/year
The mass defect is calculated as:
Δm = ΔE/c2
Δm = 9.4×1016 / (2.9979 x 108)2 = 1.046 kg
That means in a typical 3000MWth reactor core about 1 kilogram of matter is converted into pure energy.
Note that, a typical annual uranium load for a 3000MWth reactor core is about 20 tonnes of enriched uranium (i.e. about 22.7 tonnes of UO2). Entire reactor core may contain about 80 tonnes of enriched uranium.
Mass defect directly from E=mc2
The mass defect can be calculated directly from the Einstein relationship (E = mc2) as:
Δm = ΔE/c2
Δm = 3000×106 (W = J/s) x 31.5×106 (seconds in year) / (2.9979 x 108)2 = 1.051 kg
During the nuclear splitting or nuclear fusion, some of the mass of the nucleus gets converted into huge amounts of energy and thus this mass is removed from the total mass of the original particles, and the mass is missing in the resulting nucleus. The nuclear binding energies are enormous, they are of the order of a million times greater than the electron binding energies of atoms.
Generally, in both chemical and nuclear reactions, some conversion between rest mass and energy occurs, so that the products generally have smaller or greater mass than the reactants. Therefore the new conservation principle is the conservation of mass-energy.
See also: Energy Release from Fission
- J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
- J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
- W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
- Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
- W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
- G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
- Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
- U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
Advanced Reactor Physics:
- K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
- K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
- D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2.
- E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.
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