Alpha Decay Energy Calculator

Alpha decay is a type of radioactive decay in which an unstable atomic nucleus emits an alpha particle — a helium-4 nucleus consisting of 2 protons and 2 neutrons. This occurs in heavy nuclei (typically with atomic number Z > 82) where the strong nuclear force can no longer fully overcome the electrostatic repulsion among protons. Emitting an alpha particle lowers the nuclear binding energy, resulting in a more stable daughter nucleus.

The Q-value represents the total energy released during alpha decay. It is calculated using Einstein's mass-energy equivalence: Q = (m_parent − m_daughter − m_alpha) × c². A positive Q-value means the decay is energetically favorable and will occur spontaneously. The energy is shared as kinetic energy between the alpha particle and the recoiling daughter nucleus.

You need three values: (1) the atomic mass of the parent nucleus, (2) the atomic mass of the daughter nucleus, and (3) the mass of the alpha particle (4.002602 u). The difference in total mass before and after decay — the mass defect — is converted to energy in MeV using the conversion factor 931.494 MeV/u.

By conservation of momentum, the alpha particle and daughter nucleus move in opposite directions with equal and opposite momenta. The alpha particle receives the larger share of kinetic energy because it has a much smaller mass. The alpha particle's kinetic energy is T_alpha = Q × (A_daughter / A_parent), and the daughter's recoil energy is T_daughter = Q × (4 / A_parent), where A is the mass number.

Use unified atomic mass units (u), where 1 u = 1.66054 × 10⁻²⁷ kg. Precise atomic masses are published in nuclear data tables such as the AME (Atomic Mass Evaluation). For example, Ra-226 has a mass of 226.025403 u, Rn-222 is 221.970915 u, and the alpha particle is 4.002602 u. Using at least 6 decimal places gives accurate MeV results.

The accuracy depends almost entirely on the precision of the input masses. Using tabulated nuclear masses from AME2020 or NUBASE data gives results accurate to within a few keV. The formula itself (Q = Δm × c²) is exact within the framework of special relativity. For practical nuclear physics and dosimetry applications, this level of precision is generally sufficient.

Yes. This calculator is an excellent teaching tool for nuclear physics students learning about radioactive decay, mass-energy equivalence, and conservation laws. By entering different parent nuclei, students can explore why heavier elements tend to be alpha emitters, how Q-values relate to decay probability, and how energy is partitioned between decay products.

This calculator assumes a two-body decay (parent → daughter + alpha) and uses non-relativistic momentum conservation for energy partitioning, which is valid for typical alpha energies (4–9 MeV). It does not account for nuclear excited states, gamma emission, or tunneling probability (decay rate). For full decay chain analysis or activity calculations, a dedicated decay chain tool is needed.