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The formula for mass defect is: Δm = (Z · m_p + N · m_n) − m_nucleus, where Z is the number of protons, N is the number of neutrons, m_p is the mass of a proton (1.007276 u), m_n is the mass of a neutron (1.008665 u), and m_nucleus is the experimentally measured nuclear mass. For helium-4, which has 2 protons and 2 neutrons, the sum of individual nucleon masses is (2 × 1.007276 + 2 × 1.008665) = 4.031882 u, while the actual mass of the helium-4 nucleus is 4.001505 u, giving a mass defect of approximately 0.030377 u.
This 'missing' mass of 0.030377 u for helium-4 corresponds to about 28.3 MeV of binding energy when converted using the factor 1 u = 931.5 MeV/c². This energy was released when the helium-4 nucleus formed from its constituent nucleons, and it is the exact amount of energy that would be required to completely disassemble the nucleus back into free protons and neutrons. The greater the mass defect per nucleon, the more tightly bound and stable the nucleus is. Iron-56 has one of the largest mass defects per nucleon, making it one of the most stable nuclei in existence.
Mass defect values are small fractions of atomic mass units, so high-precision measurements are required. Nuclear physicists use devices such as Penning traps and storage rings to measure nuclear masses with uncertainties as low as a few parts per billion. These precise measurements are compiled into nuclear mass tables such as the Atomic Mass Evaluation (AME), which is updated periodically and serves as the reference for all nuclear physics calculations. Mass defect calculations are crucial for predicting the energy released in nuclear reactions, designing nuclear reactors, and understanding stellar nucleosynthesis.
Isotopes, atomic mass, mass number, neutrons, and nuclear binding energy
Explore CategoryMass defect is the difference between the total mass of individual, unbound protons and neutrons and the actual mass of the assembled nucleus. It represents the mass that was converted into binding energy when the nucleus formed.
The mass defect of helium-4 is approximately 0.030377 u. This corresponds to a binding energy of about 28.3 MeV, calculated using the conversion 1 u = 931.5 MeV/c².
For a nucleus to be stable, energy must have been released when it formed, meaning the nucleus must be lighter than its constituent parts. A negative mass defect would imply the nucleus has more mass than its components, which is physically impossible for a bound state.
The proton rest mass is 1.007276 u (938.272 MeV/c²) and the neutron rest mass is 1.008665 u (939.565 MeV/c²). Note that neutrons are slightly heavier than protons.
A larger mass defect per nucleon indicates a more tightly bound, stable nucleus. Nuclei near iron-56 have the largest mass defect per nucleon, while very light nuclei (hydrogen-1 and hydrogen-2) and very heavy nuclei have smaller values, making them less stable.