Mass defect is the difference between the mass of an atom and the sum of the masses of its particles. The binding energy holding the atomic nucleus together accounts for the mass difference. In other words, some of the matter converts to energy when an atomic nucleus forms, but the sum of the mass and energy of the atom remains constant (conservation of mass and energy).
For example, the mass of a helium atom is 4.00260 amu, while the mass of the protons, neutrons, and electrons in the atom add up to 4.03298 amu. In other words, a helium atom is missing about 0.8% of the mass of its parts.
Mass deficit is another name for mass defect.
Mass Defect Formula
The mass defect is simply the difference between the sum of the masses of the protons (1.007825 amu), neutrons (1.008665 amu), and electrons (0.00054858 amu) and the actual mass of an atom. But, the electron mass is negligible compared to the mass of protons and neutrons, so they are omitted.
mass defect = (mass protons + mass neutrons) – atomic mass
For example, the isotope iron-56 contains 26 protons, 26 electrons, and 30 neutrons. The experimental atomic mass of iron-56 is 55.934938 amu. Find the mass defect.
mass defect = 26(mass protons) + 30(mass neutrons) – atomic mass
mass defect = (26)(1.007825 amu) + 30(1.008665 amu) – 55.934938 amu = 0.528462 amu
Now, let’s calculate the nuclear binding energy…
Nuclear Binding Energy
The nuclear binding energy is the energy needed to split an atomic nucleus into its component protons and neutrons. It is the energy equivalent to the mass defect. In 1905, Albert Einstein described mass defect and explained it using his famous formula relating energy, mass, and the speed of light:
E = mc2
So, the decrease in an atom’s mass equals the energy that is given off when the atom forms, divided by c2. This comes out to about 931 MeV/amu.
In the iron-56 example, the mass defect was 0.528462 amu. The nuclear binding energy of iron-56 is thus 0.528462 x 931 MeV/amu = 492 MeV. There are 56 nucleons in iron-56, so the binding energy per nucleon is 492 MeV/56 nucleons = 8.79 MeV/nucleon.
How Mass Defect Works
Mass and energy are like two sides of the same coin. In atoms and molecules, one converts into the other all the time. Conservation of mass and energy means that their sum remains unchanged.
Protons and neutrons stick together in an atomic nucleus because of the strong nuclear force. The strong force acts over a short distance, overcoming the electrostatic repulsion between the like charges of the protons in the nucleus. The mass defect is a lot of energy in small atoms, but it really adds up in large atoms. For example, the nuclear binding energy for uranium-238 is 1800 MeV or 7.57 MeV/nucleon.
The strong force only affects particles near each other. The nucleus of an atom like uranium, for example, is so big that electrostatic repulsion has a larger effect on nucleons near the edge of the nucleus. This leads to an unstable nucleus that is susceptible to fission or radioactive decay. When a uranium atom undergoes fission, some of the binding energy gets released. It’s a lot of energy.
Similarly, when atoms form chemical bonds and make molecules, energy is released. Molecules absorb energy to break chemical bonds. While there is a mass defect, the mass/energy difference is not as large because chemical reactions involve electrons rather than protons or neutrons. Electrons are much, much less massive than nucleons. It’s still a significant amount of energy. For example, breaking the nitrogen-nitrogen bonds in compounds releases a lot of heat and typically results in an explosion.
References
- Athanasopoulos, Stavros; Schauer, Franz; et al. (2019). “What is the Binding Energy of a Charge Transfer State in an Organic Solar Cell?”. Advanced Energy Materials. 9 (24): 1900814. doi:10.1002/aenm.201900814
- Lilley, J.S. (2006). Nuclear Physics: Principles and Applications (Repr. with corrections Jan. 2006. ed.). Chichester: J. Wiley. ISBN 0-471-97936-8.
- Pourshahian, Soheil (2017). “Mass Defect from Nuclear Physics to Mass Spectral Analysis.” Journal of The American Society for Mass Spectrometry. 28 (9): 1836–1843. doi:10.1007/s13361-017-1741-9