0.191
u
177.9154
MeV
2.850204e-11
J
1
0.191
u
177.9154
MeV
2.850204e-11
J
1
The Q-Value Calculator computes the energy released or absorbed in a nuclear reaction from the mass difference between reactants and products. The Q-value is the most fundamental quantity characterizing a nuclear reaction, determining whether it is energetically favorable (exothermic, Q > 0) or requires an energy input (endothermic, Q < 0).
For a nuclear reaction A + B -> C + D, the Q-value is Q = (M_A + M_B - M_C - M_D) * c^2 = delta_m * 931.494 MeV. When Q > 0, the products are less massive than the reactants — mass has been converted to kinetic energy of the products. When Q < 0, kinetic energy must be supplied to create the more massive products.
For radioactive decay, the Q-value equals the total kinetic energy released. For alpha decay: Q = (M_parent - M_daughter - M_alpha) * 931.494 MeV. This energy is distributed between the alpha particle and the daughter nucleus in inverse proportion to their masses (conservation of momentum). For fission of U-235 by a neutron: the total Q is about 200 MeV, of which approximately 168 MeV appears as kinetic energy of fission fragments, 5 MeV as prompt gamma rays, 7 MeV as prompt neutron kinetic energy, and the remainder as beta/gamma from fission products.
The threshold energy for an endothermic reaction (Q < 0) in a lab-frame collision is E_threshold = |Q| * (sum of all masses) / (2 * M_target), accounting for conservation of both energy and momentum. This is always greater than |Q| for a stationary target.
Q-values are tabulated for thousands of nuclear reactions and decays in nuclear data compilations. They are essential in nuclear engineering (reactor power calculations), nuclear medicine (dosimetry), particle physics (threshold calculations), and astrophysics (nucleosynthesis network calculations).
Q = (M_reactants - M_products) * 931.494 MeV, where masses are in atomic mass units (u). Positive Q means exothermic (energy released). Negative Q means endothermic (energy required). Q in Joules: multiply MeV by 1.602e-13. For practical use: sum all reactant masses, subtract sum of all product masses, multiply by 931.494.
Q > 0 (exothermic): reaction releases energy as kinetic energy of products. Q = 0 (thermonuclear): no net energy change. Q < 0 (endothermic): requires minimum input kinetic energy |Q| (more in lab frame due to threshold). For U-235 fission: Q ~ 177-200 MeV. For D-T fusion: Q = 17.6 MeV. For alpha decay of Ra-226: Q = 4.87 MeV.
Inputs
Results
D + T -> He-4 + n: reactant masses = 2.01410 + 3.01605 = 5.03015 u; product masses = 4.00260 + 1.00866 = 5.01126 u. Q = 0.01889 u * 931.494 = 17.59 MeV. This is the primary fusion reaction targeted by ITER and NIF.
Inputs
Results
Ra-226 -> Rn-222 + He-4. Q = 0.00524 u * 931.5 = 4.87 MeV (using exact masses). This energy is distributed mostly to the alpha particle (4.78 MeV) with a small fraction going to the Rn-222 recoil nucleus.
Q = (M_reactants - M_products) * 931.494 MeV — the energy released (Q > 0) or absorbed (Q < 0) in a nuclear reaction. It is the nuclear analog of reaction enthalpy in chemistry.
For Q < 0, the threshold kinetic energy needed in the lab frame is E_th = |Q| * (sum of all masses) / (2 * M_target), which exceeds |Q| because some kinetic energy must go into center-of-mass motion of the system.
About 177-200 MeV per fission event (depending on which fission fragment pair is produced). This breaks down as: ~168 MeV kinetic energy of fragments + ~5 MeV gamma + ~5 MeV neutron KE + ~12 MeV delayed beta/gamma from fission products.
The overall reaction 4p -> He-4 + 2e+ + 2nu_e has Q = 26.73 MeV. Of this, about 2 * 1.02 MeV = 2.04 MeV is carried away by neutrinos (poorly observable), leaving ~24.7 MeV as useful energy per He-4 produced.
The Q-value of a decay determines the energy of emitted particles, which determines the radiation range and dose. For example, the 0.511 MeV annihilation photons in PET scanning come from the Q = 1.022 MeV of positron emission + annihilation.
In nuclear physics, exoergic means Q > 0 (energy is released as kinetic energy). Exothermic in chemistry means enthalpy is negative (heat is released). They are analogous concepts in different contexts.
Yes: Q = BE_products - BE_reactants. If the products are more tightly bound than the reactants (higher total BE), energy is released. This is equivalent to the mass defect method since BE = delta_m * 931.5 MeV.
For electron capture (p + e- -> n + nu), Q = (M_parent_atom - M_daughter_atom) * 931.494 MeV (using atomic masses). Since no positron is emitted, electron capture is energetically possible whenever Q > 0 (unlike positron emission which requires Q > 1.022 MeV).
A nucleus is stable against a particular decay mode if the Q-value for that mode is negative (or borderline zero). For example, a nucleus decays by alpha emission only if Q_alpha > 0, i.e., if (M_parent - M_daughter - M_alpha) > 0.
At stellar temperatures, reactions occur through Gamow window tunneling. The reaction rate depends on Q (threshold), nuclear masses, and quantum tunneling probability. Reaction networks with hundreds of Q-values determine element abundances in stars and supernovae.
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