Binding energy, fission and reactor

A bound nucleus has less mass than the sum of the masses of the same protons and neutrons separately. No nucleon has vanished. Our comparison of the two states must therefore also account for interaction energy.

Separating a bound nucleus into free protons and neutrons requires an energy input: particles do not simply fly apart from a stable bound system. The required amount is called binding energy Eсв. Forming the same nucleus from free nucleons can release the corresponding energy. We compare the same particles in two states; a more strongly bound system needs more energy for complete separation.

Define Δm = sum of free nucleon masses − nuclear mass. This mass defect is positive for a nucleus bound relative to those separated particles. Nucleons do not disappear: the bound system's total rest energy decreases, and so does its mass. Imagine separating the particles and supplying the necessary energy: the separated system then has more mass. 'Defect' describes a comparison, not damaged matter.

The relation is Eсв = Δmc², where c is the vacuum speed of light. Doubling Δm doubles binding energy. To obtain joules, use kilograms for Δm and m/s for c; кг·м²/с² does give Дж. The very large c² explains why a small mass difference corresponds to appreciable energy. At Δm = 0, binding energy relative to the chosen free particles would be zero.

Individual nuclear masses are inconveniently small in kilograms. The atomic mass unit equals one twelfth of the mass of a free carbon-12 atom at rest in its ground state, approximately 1.66·10⁻²⁷ kg. It is a mass unit, not the nucleon count A. When comparing tabulated atomic and nuclear masses, remember electron masses: calculating a mass defect requires a consistent set of objects to compare.

Small energies also benefit from a convenient unit. An electronvolt, eV, is the energy gained by an electron accelerated in vacuum through a potential difference of 1 V, about 1.6·10⁻¹⁹ J. MeV means one million electronvolts. The particle merely helps define the unit: nuclear and photon energies can also be given in electronvolts. A volt and an electronvolt are not interchangeable: the former measures voltage, the latter energy.

To avoid converting mass to kilograms each time, use 1 а.е.м.·c² ≈ 931,5 МэВ. Multiply Δm in atomic mass units by 931.5 to obtain energy in MeV. This is still Eсв = Δmc², using different units. You cannot insert a mass in atomic mass units alongside c in m/s and call the result joules: units must remain consistent throughout.

A large nucleus usually has greater total binding energy simply because it contains more particles. To compare average binding, divide Eсв by A. In energy-releasing fission, the final particles have a smaller total mass, and the difference appears as kinetic energy and radiation. Average binding energy alone, however, cannot predict radioactive stability: the specific available transformations and their energy conditions matter.

Some heavy nuclei, such as uranium-235, can absorb a neutron and split into lighter fragments, emitting new neutrons and releasing energy. This is fission, not the emission of a single alpha or beta particle. Energy is released because the final particles have a smaller total mass. Breaking just any nucleus is not guaranteed to release energy: the direction of the energy balance must be checked.

Neutrons from one fission can cause further fissions. If each event leads on average to one next event, the chain is sustained; fewer than one makes it die out. Not every neutron continues the chain: some leave the material or are absorbed without the required fission. The balance matters, not merely the number of neutrons produced. This qualitative model explains self-sustaining behaviour without assuming every neutron must find another nucleus.

A state is critical when neutron production and losses sustain the chain. Critical mass is therefore not a universal number for any piece of material: composition, geometry and absorption also matter. Changing the surroundings changes neutron losses even at the same mass. The point is to understand how conditions depend on one another, rather than reduce a chain reaction to 'lots of material'.

A reactor controls the number of neutrons able to continue the chain. Control rods absorb some neutrons, while coolant removes the released heat. In thermal reactors, a moderator slows neutrons, a different function from absorption. One material may serve several functions, but the physical roles must be distinguished. Chain control and cooling are linked in operation, yet neither replaces the other.

Fission energy first becomes mainly kinetic energy of the products, then heats the material and coolant. A thermal cycle drives a turbine and a generator produces electricity. Even after the main chain stops, fission products continue to decay radioactively and release residual heat. Stopping the chain therefore does not stop heating instantly: cooling, shielding and radioactive-material management remain necessary.

A nucleus has a mass defect of 0.01 atomic mass units. Find its binding energy using 1 а.е.м.·c² = 931,5 МэВ.

Mass defect compares separated nucleons with the bound nucleus. Separating the nucleus requires an input Eсв = Δmc².

The given equivalence already converts а.е.м.·c² to МэВ: Eсв = 0,01 · 931,5 = 9,315 МэВ.

The positive result means energy must be supplied for separation. In the reverse binding of the same free nucleons, it corresponds to a decrease in the system's rest energy.

The binding energy is 9.315 MeV. This corresponds to the stated mass defect and is required to separate the nucleus into free nucleons.

A system's mass depends on its energy state: binding reduces rest energy without losing nucleons.

Eсв = Δmc² relates a measurable mass difference to energy; the chosen units must be consistent.

Fission can release energy and sustain a chain, while neutron control and heat removal serve different purposes.

Next, compare fission with fusion and examine how radiation interacts with matter.