16
16.13192
u
0.137005
u
2.275015e-28
kg
127.619
MeV
2.044681e-11
J
7.9762
MeV/nucleon
16
16.13192
u
0.137005
u
2.275015e-28
kg
127.619
MeV
2.044681e-11
J
7.9762
MeV/nucleon
The Mass Defect Calculator computes the mass defect of an atomic nucleus — the difference between the total mass of its constituent protons and neutrons (as free particles) and the actual measured atomic mass. This mass difference, multiplied by c^2 via Einstein's famous equation E = mc^2, gives the nuclear binding energy.
The mass defect delta_m = Z*m_p + N*m_n - M_nucleus (using atomic masses: delta_m = Z*m_H + N*m_n - M_atom, which automatically accounts for the Z electron masses). The energy equivalent in MeV is obtained by multiplying delta_m in atomic mass units by the conversion factor 931.494 MeV/u, which is derived from the definition 1 u = 1/12 of the mass of C-12 and E = mc^2.
The mass defect is not a unique property of nuclear physics — it is a general consequence of binding energy in any system governed by E = mc^2. However, it is most significant for nuclei because nuclear binding energies (millions of eV) are enormous compared to chemical binding energies (a few eV). A chemical reaction changes the mass by perhaps 10^-10 u per molecule — entirely undetectable. A nuclear reaction changes the mass by 10^-3 to 10^-2 u per nucleus — readily measurable by mass spectrometry.
The discovery of the mass defect in the 1920s, using Aston's mass spectrograph, was one of the first experimental confirmations of Einstein's mass-energy equivalence and revolutionized understanding of the energy source of stars (Eddington's 1920 proposal that stellar energy comes from nuclear mass conversion).
Using atomic masses: delta_m = Z*m_H + N*m_n - M_atom, where m_H = 1.00782503 u (hydrogen atom mass), m_n = 1.00866492 u (neutron mass). Energy: E = delta_m * 931.494 MeV = delta_m * 1.66054e-27 * c^2 J. Binding energy per nucleon: BE/A = E/(Z+N).
Positive delta_m means energy is released when the nucleus is formed (and required to break it apart). For any stable nucleus, delta_m > 0. Larger delta_m means more tightly bound nucleus. The conversion factor 931.494 MeV/u means even a tiny mass of 0.001 u corresponds to 0.931 MeV of energy.
Inputs
Results
Oxygen-16 has a mass defect of 0.137 u, corresponding to 127.6 MeV total binding energy (7.98 MeV/nucleon). This is one of the most abundant nuclei in the universe due to its double-magic (Z=8, N=8) stability.
Inputs
Results
The deuteron binding energy is 2.225 MeV — one of the smallest nuclear binding energies, explaining why deuterium can be broken apart by high-energy gamma rays (photodisintegration). The weak binding also makes deuterium reactions important in fusion reactors.
The difference between the total mass of free constituent nucleons (Z protons + N neutrons) and the actual measured nuclear mass. This missing mass has been converted to binding energy: BE = delta_m * c^2.
1 unified atomic mass unit = 1/12 of the mass of C-12 = 1.66054e-27 kg. Multiplying by c^2 = 8.9876e16 m^2/s^2 gives 1.4924e-10 J = 931.494 MeV. This exact conversion is fundamental to nuclear physics calculations.
Yes, but the effect is negligibly small. Forming a chemical bond releases a few eV, corresponding to a mass change of ~10^-35 kg per bond — far below any measurement capability. Only nuclear reactions have measurable mass defects.
Mass and energy are interconvertible. In endothermic nuclear reactions, kinetic energy is converted to mass (the products are heavier than reactants). In exothermic reactions (fission, fusion), mass is converted to kinetic energy of products.
Packing fraction = (M_atom - A)/A, where A is the mass number. It measures deviation of actual mass from integer atomic mass units. Maximum packing fraction (most mass converted to binding energy) occurs near Fe-56.
Mass defect gives the Q-value (energy released) in a decay. For alpha decay, Q = (M_parent - M_daughter - M_alpha) * 931.494 MeV. Higher Q means more energetic alpha particles and shorter half-life (Geiger-Nuttall law).
Q = (sum of initial masses - sum of final masses) * 931.494 MeV. Q > 0 means exothermic reaction (energy released). Q < 0 means endothermic reaction (energy must be supplied). The Q-value determines whether a reaction is energetically possible.
Modern Penning trap mass spectrometers (ISOLTRAP, TITAN) measure atomic masses with relative uncertainty of 10^-10 to 10^-11 — i.e., to 0.001 u for A=100 nuclei. This precision allows testing nuclear models and measuring masses of rare isotopes far from stability.
A comprehensive database of all known atomic nuclei (about 3,300), listing mass number, atomic number, atomic mass, half-life, decay mode, and spin/parity. The AME (Atomic Mass Evaluation) provides the most accurate atomic masses, updated periodically.
Some nuclei exist in excited states with measurable half-lives (nuclear isomers, metastable states). These have higher mass than the ground state by the excitation energy (in mass units, typically 10^-6 to 10^-3 u). Tc-99m (used in medical imaging) is a nuclear isomer of Tc-99.
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