Nuclear Reaction Q-Value Calculator

The Q-value is the net energy released (Q > 0) or absorbed (Q < 0) in a nuclear reaction. It comes from the mass difference between reactants and products via E = mc^2.

☢️ Nuclear Physics📐 Q = Δmc²⚛️ Particle Physics
Reactant total mass (AMU)
Product total mass (AMU)
Please enter valid values.

Formula & Reference

VariableSymbolFormulaUnits
Q-ValueQ(∑mreactants − ∑mproducts)c²MeV
Mass-EnergyEE = mc²J or MeV
1 AMUu931.494 MeV/c²MeV/c²
ExothermicQ > 0Energy releasedMeV
EndothermicQ < 0Energy requiredMeV

Step-by-Step Examples

Example 1
D-D Fusion

D+D -> He-4. Reactants: 2*2.01410 = 4.02820 AMU. He-4: 4.00260 AMU.

  • dm = 4.02820 - 4.00260 = 0.02560 AMU
  • Q = 0.02560 * 931.494 = 23.85 MeV
✓ 23.85 MeV released per D-D fusion
Example 2
Alpha Decay Q-value

Ra-226 -> Rn-222 + alpha. Ra: 226.02541, Rn+He4: 222.01758+4.00260=226.02018 AMU.

  • dm = 226.02541 - 226.02018 = 0.00523 AMU
  • Q = 0.00523 * 931.494 = 4.87 MeV
✓ 4.87 MeV Q-value for Ra-226 alpha decay
Example 3
Endothermic Reaction

Gamma + O-16 -> N-15 + p. dm < 0 -> Q < 0.

  • If products heavier than reactants by 0.01 AMU
  • Q = -0.01 * 931.494 = -9.31 MeV
✓ 9.31 MeV must be supplied by photon

Real-World Applications

☢️
Nuclear Reactors
Fission Q-values (~200 MeV per U-235 fission) determine reactor energy output per fuel mass.
💥
Fusion Research
D-T fusion (Q=17.6 MeV) is the main target for fusion power reactors.
⚕️
Medical Isotope Production
Q-values determine feasibility of producing medical isotopes by proton bombardment of targets.
🔬
Particle Physics
Q-values identify whether particle reactions are energetically allowed.

Common Mistakes to Avoid

⚠️
Must use AMU for the 931.494 factor

1 AMU = 931.494 MeV/c^2. If using kg, use E = dm*c^2 with c = 3e8 m/s and convert joules to MeV (1 MeV = 1.602e-13 J).

⚠️
Include ALL particles

Account for every reactant and product, including emitted electrons, positrons, or photons if they have rest mass.

⚠️
Electron mass matters in beta decay

Electron mass = 0.000549 AMU = 0.511 MeV. Must include in products for beta decay Q-value.

Frequently Asked Questions

What does Q-value mean physically? ▾
Q > 0 (exothermic): reaction releases energy. Q < 0 (endothermic): reaction requires energy input. The magnitude gives how much.
Why does mass decrease in fusion? ▾
The strong nuclear force binds nucleons. Bound nucleons have lower mass than free ones (mass defect). Fusion to more tightly bound nuclei releases this energy.
What is the largest nuclear Q-value? ▾
Fission of U-235 releases ~200 MeV, but per nucleon, fusion of hydrogen to iron gives most energy. Fission releases ~0.9 MeV/nucleon, D-T fusion ~3.5 MeV/nucleon.
Can Q-value be calculated from binding energies? ▾
Yes: Q = BE(products) - BE(reactants). Higher binding energy products release energy.
What is the threshold energy for endothermic reactions? ▾
E_threshold = |Q|*(1 + m_projectile/m_target) in the lab frame. Slightly more than |Q| due to recoil.

Related Physics Calculators

⛛ Mass-Energy☢️ Binding Energy/Nucleon☢️ Radioactive Decay☢️ Half-Life☢️ Nuclear Binding Energy

Formula Explorer connections

Interpretation: This relationship connects quantized energy, wavelength, probability, nuclear mass or radioactive change. Assumption: Use the correct particle, quantum state, nuclide and energy units. Idealized potentials, nonrelativistic motion or single decay channels may be assumed.

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