Nuclear Reaction Q-Value Calculator
Calculate the Q-value (energy released or absorbed) of nuclear reactions using mass defect.
Supports alpha decay, beta decay, proton capture, and custom reactions.
What Is the Q-Value? The Q-value of a nuclear reaction is the energy released (Q > 0) or absorbed (Q < 0) during the reaction. It is calculated from the mass difference between reactants and products, using Einstein’s mass-energy equivalence: E = mc². Q > 0 (exothermic/exoergic): the reaction releases energy. Q < 0 (endothermic/endoergic): energy must be supplied. Every nuclear decay, fusion, and fission reaction has a characteristic Q-value.
The Q-Value Formula Q = (Σm_reactants − Σm_products) × c² Where masses are in atomic mass units (u) and c² = 931.494 MeV/u. One atomic mass unit (u) = 1.66054 × 10⁻²⁷ kg = 931.494 MeV/c². A mass defect of just 0.001 u releases 931 keV — far more than chemical reactions (eV range).
Common Nuclear Reaction Types Alpha decay: ᴬZ → ᴬ⁻⁴(Z−2) + ⁴He (alpha particle). Q = M_parent − M_daughter − M_alpha. Beta⁻ decay: n → p + e⁻ + ν̄_e. Q = M_parent − M_daughter (electron masses cancel in atomic masses). Beta⁺ decay: p → n + e⁺ + ν_e. Q = M_parent − M_daughter − 2m_e. Proton capture: ᴬZ + p → ᴬ⁺¹(Z+1) + γ (gamma). Q = M1 + M2 − M_product. Fission: heavy nucleus splits into two medium nuclei + neutrons. Q ~ 200 MeV for U-235. Fusion: D + T → He-4 + n. Q = +17.59 MeV (tokamak fuel reaction).
Famous Q-Values in Physics Deuterium-Tritium fusion: Q = 17.59 MeV — the energy basis of experimental fusion reactors (ITER). U-235 fission: Q ≈ 202 MeV per fission — basis of nuclear power and weapons. Solar pp chain: 4p → He-4 + 2e⁺ + 2ν. Total Q ≈ 26.7 MeV per helium nucleus formed. Carbon-14 beta decay: Q = 0.156 MeV — used to calibrate radiocarbon dating instruments.
Energy Units in Nuclear Physics 1 MeV = 10⁶ eV = 1.602 × 10⁻¹³ joules. Nuclear Q-values are typically 0.1–200 MeV. Chemical reactions: 1–10 eV range. Nuclear reactions: 10³–10⁸ times more energetic. 1 gram of matter = 9×10¹³ J if fully converted (E = mc²) — equivalent to ~21 kilotons TNT.
Threshold Energy For endothermic reactions (Q < 0), a minimum kinetic energy (threshold) must be supplied. Threshold energy = −Q × (1 + m_projectile/m_target) in the lab frame. This accounts for the need to conserve both energy AND momentum.