Q-Value Calculator (Nuclear Reactions)
Compute the Q-value of any nuclear reaction or radioactive decay from atomic masses.
💥 What is the Q-Value Calculator?
The Q-value of a nuclear reaction is the net energy released or absorbed when reactant nuclei are transformed into product nuclei. A positive Q-value means the reaction is exothermic: the products are lighter than the reactants, and the mass deficit appears as kinetic energy of the products. A negative Q-value means the reaction is endothermic: the products are heavier than the reactants, and the projectile must provide a minimum kinetic energy (the threshold energy) to initiate the reaction.
This calculator supports two modes. In General Reaction mode, you enter atomic masses for up to two reactants and three products. The Q-value formula Q = (Σm_reactants - Σm_products) × 931.494 MeV/u converts the mass difference into energy using Einstein's mass-energy equivalence (E = mc²), where 1 atomic mass unit equals 931.494 MeV/c². In Nuclear Decay mode, you select the decay type (alpha, beta-minus, beta-plus, or electron capture) and enter the parent and daughter atomic masses. The calculator automatically applies the correct formula for each decay type, accounting for the different bookkeeping of electron masses between atomic mass tables and nuclear decay equations.
The Q-value concept was foundational in early nuclear physics. When James Chadwick discovered the neutron in 1932, he used Q-value calculations from atomic mass measurements to prove that beryllium was emitting a neutral particle (the neutron) rather than gamma rays. Today, Q-values are used in reactor physics to calculate power output per fission, in astrophysics to model nucleosynthesis in stellar cores, in nuclear medicine to assess the energy available from positron emitters in PET scanning, and in accelerator physics to determine the projectile energy needed to produce radioactive isotopes by threshold reactions.
The General Reaction mode is designed for reactions of the form A + a to B + b + c, where the third product c (often multiple neutrons) can be entered as the combined mass of all third-group products. The Decay mode handles the four main types of radioactive decay. For fission reactions, enter the two fission fragment masses and the mass of all neutrons emitted as the three product masses.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 - U-235 Fission (Exothermic)
U-235 + n to Ba-141 + Kr-92 + 3n: prompt fission Q-value
Example 2 - Ra-226 Alpha Decay
Ra-226 to Rn-222 + alpha: Q-value of radium alpha decay
Example 3 - Be-9(p,n)B-9: Endothermic Threshold Reaction
p + Be-9 to n + B-9: what minimum proton energy is needed?
❓ Frequently Asked Questions
🔗 Related Calculators
What is the Q-value in nuclear physics?
The Q-value is the energy released (Q > 0) or absorbed (Q < 0) in a nuclear reaction. It equals the mass difference between reactants and products multiplied by c²: Q = (Σm_reactants - Σm_products) × 931.494 MeV/u. A positive Q means the reaction is exothermic; a negative Q means the reaction is endothermic and requires a minimum projectile kinetic energy called the threshold energy.
How do you calculate the Q-value of a nuclear reaction?
Obtain the atomic masses of all reactants and products from a standard table (such as AME2020). Sum the reactant masses and subtract the sum of the product masses to get the mass difference Δm in atomic mass units (u). Multiply Δm by 931.494 MeV/u to convert to energy. For example, U-235(n,fission) with Ba-141 + Kr-92 + 3n: Q = (235.043929 + 1.008665 - 140.914400 - 91.926156 - 3.025995) × 931.494 = 173.3 MeV.
What is the Q-value of U-235 fission?
The prompt Q-value for U-235(n,f) producing Ba-141 + Kr-92 + 3n is approximately 173 MeV. The total Q-value, including the energy from subsequent beta decays of the fission products, is about 200 MeV per fission event. The difference of about 27 MeV is released over time as fission product radioactive decay, not as prompt fission energy.
What is the threshold energy for an endothermic nuclear reaction?
The threshold kinetic energy T_th is the minimum kinetic energy of the projectile (in the lab frame, with target at rest) needed to initiate an endothermic reaction. The formula is T_th = |Q| × (sum of all particle masses) / (2 × target mass). It is always greater than |Q| because some energy goes into the kinetic energy of the recoiling center-of-mass system.
How does the Q-value differ for alpha versus beta decay?
For alpha decay: Q = (M_parent - M_daughter - M_alpha) × 931.494 MeV/u, using atomic masses (He-4 mass = 4.002602 u). For beta-minus decay: Q = (M_parent - M_daughter) × 931.494, because atomic masses implicitly include the emitted electron. For beta-plus decay: Q = (M_parent - M_daughter - 2m_e) × 931.494, where m_e = 0.000549 u, because the positron creates an extra electron-positron pair relative to the atomic mass bookkeeping.
Why is the Q-value formula different for beta-plus and electron capture?
In beta-plus decay, the daughter's atomic mass already includes one extra electron compared to the parent (the nucleus has one fewer proton), but the positron is an additional particle that must be created. This requires subtracting 2m_e from the Q formula. In electron capture, an orbital electron is consumed instead of creating a positron, so the formula becomes Q = (M_parent - M_daughter) × 931.494, which is identical to the beta-minus formula using atomic masses.
What atomic mass table should I use for Q-value calculations?
The standard reference is the Atomic Mass Evaluation (AME2020), published by Wang et al. in Chinese Physics C 45 (2021). It is freely available at the National Nuclear Data Center (NNDC) at Brookhaven National Laboratory. Masses are tabulated in atomic mass units (u) and as mass excess in keV. For a quick reference, the NIST Physical Reference Data also provides selected atomic masses.
Can the Q-value be negative for radioactive decay?
A radioactive decay with a negative Q-value would violate energy conservation and cannot occur spontaneously. All observed spontaneous radioactive decays have positive Q-values. If you calculate a negative Q for a proposed decay, the decay mode is energetically forbidden. This is why oxygen-16 does not alpha-decay even though it is technically two alpha particles plus helium-8: the Q-value is negative.
What is the difference between Q-value and binding energy?
The Q-value measures the energy change in a specific nuclear reaction (positive for exothermic). Binding energy measures how much energy holds a nucleus together - it is the energy required to completely disassemble a nucleus into free protons and neutrons. For a nuclear reaction, Q = (sum of binding energies of products) - (sum of binding energies of reactants). Reactions with products that are more tightly bound release energy, giving a positive Q.
How is Q-value used in reactor physics?
In reactor physics, the Q-value per fission event (approximately 200 MeV for U-235 or Pu-239) determines the fuel's energy content. Knowing Q, engineers calculate how many fissions per second are needed to produce a given thermal power: P (watts) = Q (joules) × fission rate (per second). For U-235, Q = 3.204 × 10^-11 J, so a 3000 MW thermal reactor undergoes about 9.4 × 10^19 fissions per second.
What is the Q-value for the proton-proton chain in the Sun?
The overall proton-proton chain (4p → He-4 + 2e+ + 2ν) has a Q-value of 26.73 MeV, but about 2% is carried away by the neutrinos and is not available as heat. The first step, p + p → D + e+ + ν, has Q = 0.42 MeV. The overall process converts 0.7% of the hydrogen mass to energy, consistent with Einstein's E = mc².
How accurate is the Q-value formula using atomic masses?
Using tabulated atomic masses from AME2020, the Q-value formula Q = Δm × 931.494 MeV/u is accurate to better than 1 keV for most nuclear reactions. The main source of error is the precision of the atomic masses themselves (typically 1-100 eV uncertainty). The formula is exact in principle; the electron binding energies cancel for all reactions involving neutral atoms, introducing an error of at most a few eV, which is negligible for nuclear energy calculations in MeV.