Write the reaction with “?” for the unknown particle — the calculator finds it from conservation of mass number and charge and computes the reaction energy from isotope masses. The “Binding energy” tab gives the mass defect, binding energy and energy per nucleon.
Conservation laws
Every nuclear reaction conserves the mass number A and the charge Z, so the unknown particle follows by subtraction: in ¹⁴₇N + ⁴₂He → ? + ¹₁p, A = 17 and Z = 8 — oxygen-17.
- Alpha decay: A − 4, Z − 2.
- Beta-minus decay: A unchanged, Z + 1 (electron and antineutrino emitted).
- Beta-plus decay: Z − 1 (positron and neutrino).
- Gamma emission: A and Z unchanged.
Reaction energy
Q = (Σm before − Σm after)·c² = Δm · 931.5 MeV for masses in u. Q > 0 — energy is released, Q < 0 — absorbed. 1 MeV = 1.602·10⁻¹³ J. The calculator uses nuclear masses (atomic mass minus electrons), so beta decays need no extra corrections. Isotope masses: AME2020.
Mass defect and binding energy
Δm = Z·mₚ + N·mₙ − M_nuc, E_b = Δm·c². The binding energy per nucleon peaks (~8.8 MeV) near iron and nickel — that is why both fusion of light nuclei and fission of heavy ones release energy.
FAQ
How do I find the missing particle?
By conservation: the sums of mass numbers and charges on both sides are equal. Put “?” in place of the particle.
How is the Q value calculated?
Add the masses before and after, take the difference Δm in u and multiply by 931.5 MeV. Positive means energy is released.
What is the mass defect?
The difference between the mass of free protons and neutrons and the nuclear mass: Δm = Z·mₚ + N·mₙ − M_nuc.
How much energy does U-235 fission release?
About 200 MeV per nucleus on average; the channel U-235 + n → Ba-141 + Kr-92 + 3n gives ≈ 173 MeV directly.
How do I enter a nucleus?
Element symbol and mass number: U-235, U235 or 235U, or with indices ²³⁵₉₂U. Particles: n, p, d, t, α, e-, e+, γ, ν.