0.044
u
40.9857
MeV
6.566639e-12
J
1
0.044
u
40.9857
MeV
6.566639e-12
J
1
Nuclear reactions involve the transformation of atomic nuclei, releasing or absorbing enormous amounts of energy due to changes in nuclear binding energy. The Q-value of a nuclear reaction quantifies this energy exchange, calculated from the mass difference between reactants and products using Einstein's mass-energy equivalence E = mc².
The fundamental principle underlying all nuclear energy calculations is the mass-energy equivalence: a small mass difference of just 1 atomic mass unit (u) corresponds to 931.494 MeV of energy. This is approximately 931 million electron volts, or about 1.49 × 10⁻¹⁰ joules — a tiny amount by everyday standards, but enormous on the atomic scale.
Nuclear reactions are classified by their Q-value: exothermic reactions (Q > 0) release energy and occur spontaneously once initiated, while endothermic reactions (Q < 0) require energy input to proceed. All nuclear fission and fusion reactions that are used for energy production have positive Q-values.
The Q-value formula is: Q = (M_reactants - M_products) × 931.494 MeV/u. This requires precise atomic mass values, typically taken from the Atomic Mass Evaluation (AME) tables maintained by the International Atomic Energy Agency (IAEA).
In nuclear physics research, Q-value calculations are essential for determining whether proposed reactions are energetically feasible, predicting the kinetic energies of reaction products, and designing experiments at particle accelerators. Understanding Q-values is also critical for nuclear reactor design, where engineers must account for the energy released in each fission event and the branching ratios of various reaction channels.
Medical physics applications include calculating the energy released in positron emission tomography (PET) tracers, where positron emission followed by annihilation produces two 511 keV gamma rays, and in targeted alpha therapy where the Q-value of alpha decay determines the radiation dose delivered to tumor cells.
Enter the total atomic mass of all reactants and all products in atomic mass units (u). The calculator computes the mass defect (Δm = M_reactants - M_products) and multiplies by 931.494 MeV/u to obtain the Q-value. A positive Q indicates an exothermic reaction that releases energy.
Positive Q-value: energy is released (exothermic reaction, such as fission or fusion). Negative Q-value: energy must be supplied (endothermic reaction, such as spallation or photodisintegration). The larger the positive Q, the more energy released per reaction event.
Inputs
Results
Approximate Q-value for U-235 fission (~200 MeV total including delayed energy from fission products).
Inputs
Results
Deuterium (2.014102 u) + Tritium (3.016049 u) → He-4 (4.002602 u) + neutron (1.008665 u). Q = 17.59 MeV.
The Q-value is the net energy released (positive) or absorbed (negative) in a nuclear reaction. It equals the mass difference between reactants and products multiplied by 931.494 MeV per atomic mass unit.
Precise atomic masses are tabulated in the Atomic Mass Evaluation (AME) published by the IAEA. The 2020 edition (AME2020) contains masses for thousands of nuclides. Online databases like the National Nuclear Data Center (NNDC) provide searchable access.
One atomic mass unit is defined as 1/12 the mass of a carbon-12 atom. Converting via E = mc²: (1.66054 × 10⁻²⁷ kg) × (2.998 × 10⁸ m/s)² ÷ (1.602 × 10⁻¹³ J/MeV) = 931.494 MeV.
Binding energy is the energy required to completely disassemble a nucleus into free protons and neutrons. Q-value is the energy difference for a specific reaction between two specific sets of nuclei. They are related but distinct concepts.
Theoretically yes, but it is extremely rare in practice. Such a reaction would be thermoneutral. Most reactions have measurable Q-values due to the differences in nuclear binding energies between reactants and products.
For endothermic reactions (Q < 0), there is a threshold kinetic energy below which the reaction cannot occur. The threshold energy in the lab frame is |Q| × (1 + m_projectile/m_target) due to conservation of momentum.
Nuclear binding energies are millions of times stronger than chemical bond energies. A single U-235 fission releases ~200 MeV, while burning one carbon atom releases only ~4 eV — a factor of 50 million difference.
The Q-value energy appears as kinetic energy of the reaction products (primarily), gamma radiation, and in some cases neutrino emission. For fission, about 80% becomes kinetic energy of fission fragments, which is converted to heat in reactor fuel.
The accuracy depends entirely on the precision of the atomic mass values you input. If you use AME2020 masses with 6+ significant figures, the Q-value will be accurate to the same precision. The conversion factor 931.494 MeV/u has an uncertainty of ±0.001 MeV/u.
For fission power: U-235 + n → fission fragments + 2-3n + ~200 MeV. For fusion power (future): D + T → He-4 + n + 17.59 MeV. The D-T reaction has the highest cross-section at achievable temperatures, making it the primary candidate for fusion reactors.
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