Mass Defect

Nuclear processes are accompanied by energy changes, just as chemical reactions. Nuclear processes, on the other hand, have huge energy shifts compared to even the most energetic chemical reactions. In reality, the energy changes in a common nuclear reaction are large enough to cause a quantifiable mass change. The link between energy and mass in nuclear reactions is described in this part, and we explain how seemingly modest changes in mass precede nuclear processes, resulting in the release of vast amounts of energy. Fission and fusion are the most well-known exothermic nuclear transmutations. Atomic fission is the process of breaking apart heavy atomic nuclei (such as uranium and plutonium) into lighter nuclei, releasing nuclear energy. Fission energy is used to create electricity in numbers of locations across the world. Atomic fusion releases nuclear energy when light nuclei such as hydrogen fuse to generate heavier nuclei like helium. Nuclear fusion is used by the Sun and other stars to generate heat energy that is then radiated off the surface, a process known as stellar nucleosynthesis. Nuclear mass may be transformed to thermal energy and released as heat in any exothermic nuclear reaction.

Mass Defect

The discrepancy between the mass of an item and the summation of the masses of its constituent particles is known as mass defect (or “mass deficiency”). It can be explained using Albert Einstein’s formula E = mc2, which expresses the equivalence of energy and mass, which he discovered in 1905. The mass loss is equal to the energy released in the atom’s formation reaction divided by c2. Adding energy increases mass (both inertia and weight) according to this formula, but subtracting energy decreases mass. A helium atom with four nucleons, for example, has a mass that is around 0.8 percent less than the total mass of four hydrogen atoms (each comprising only one nucleon). Four nucleons are linked together in the helium nucleus, and the binding energy is holding them together in effect, the missing 0.8% of mass. 

Weighing a mixture of particles that includes extra energy, such as a molecule of the explosive TNT, exposes some excess mass as compared to the end products of an explosion. (However, the final products should be weighed after they have been stopped and cooled because, in theory, the excess mass should first disappear from the system as heat before its loss can be detected.) On the other hand, if energy is required to segregate a system of particles into its constituents, the beginning mass is smaller than the final mass of the constituents. The energy injected in this situation is usually “stored” as potential energy, which manifests as an increase in the mass of the components that store it. This is an illustration of the fact that energy of all types can be easily visible  in systems as mass, as mass and energy are equivalent, and each represents a “property” of the other.

Mass defect (Md) can be easily calculated as the difference between observed atomic mass (mo) and that expected from the combined masses of its protons (mp), each proton having a mass of 1.00728 amu and neutrons (mn, 1.00867 amu):

Md      =    (mn + mp) – mo

Example of Mass Defect

All particles, as you may recall, have wavelike behaviour, but the wavelength is inversely related to the particle’s mass (actually, to its momentum, the product of its mass and velocity). As a result, wavelike behaviour can only be detected in particles with extremely minuscule masses, including electrons. The chemical equation for graphite burning to produce carbon dioxide, for example, is as follows:

C(graphite) + 1/2 O₂(g) → CO₂(g)

ΔH° = −393.5 kJ/mol 

Combustion reactions are normally carried out under constant pressure, and the heat absorbed or released is equal to ∆H under these conditions. The heat released or absorbed when a reaction is carried out at constant volume is equal to ∆E. However, for the vast majority of chemical processes, E ≈ ∆H . We can rewrite Einstein’s equation as follows:

∆E = (∆m) c2

The following expression among the change in energy and the change in mass can be obtained by rearranging the equation:

Δm = ΔE/c2

As 1J = 1 (kg.m2)/s2, the change in mass is as follows                   

Δm = −393.5 kJ/mol/(2.998×108m/s)2

=−3.935×105(kg⋅m2)/(s2⋅mol)(2.998×108m/s)2

=−4.38×10−12 kg/mol 

This corresponds to a mass change of around 3.6 1010 g/g carbon consumed, or about 100 millionths of an electron’s mass per atom of carbon. In practise, the mass change is far too small to be measured experimentally and is therefore insignificant.

Conclusion

A nuclear reaction, besides a chemical reaction, results in a considerable shift in mass and energy, as stated by Einstein’s equation. Large increases in energy accompany nuclear processes, resulting in measurable mass changes. According to Einstein’s equation, E = (m)c2, the change in mass is proportional to the change in energy. The units of measurement for large energy shifts are commonly megaelectronvolts or kiloelectronvolts (thousands or millions of electronvolts). The empirically determined mass of an atom is always smaller than the sum of the masses of the component particles (protons, electrons, and neutrons) by an amount known as the mass defect of the nucleus, with the exception of 1H. The nuclear binding energy, or the energy dissipated when a nucleus is formed from its component particles, corresponds to the mass defect. Nuclei break into lighter nuclei in nuclear fission, releasing many neutrons and significant amounts of energy in the process. The critical mass is the smallest amount of matter required to maintain a nuclear chain reaction. Nuclear fusion refers to a process in which two light nuclei fuse together to form a heavier nucleus with a lot of energy.