When an unstable atomic nucleus undergoes alpha decay, it ejects an alpha particle (a helium nucleus comprising two protons and two neutrons). In accordance with the principle of conservation of momentum, the newly formed daughter nucleus recoils in the opposite direction to the emitted alpha particle. This backward movement, known as alpha recoil, imparts significant kinetic energy to the daughter atom, often dislodging it from its original chemical and physical matrix.
Alpha decay is a two-body disintegration process where a parent nucleus (P) transforms into a daughter nucleus (D) and an alpha particle (). If the parent nucleus is initially at rest, the total momentum before decay is zero. For momentum to be conserved, the momenta of the daughter nucleus and the alpha particle must be equal in magnitude and opposite in direction:
If , then , implying that . Representing momentum as , where is mass and is velocity, we have:
Where and are the mass and velocity of the daughter nucleus, and and are those of the alpha particle.
The kinetic energy () of the recoiling daughter nucleus can be determined relative to the alpha particle's kinetic energy. From the momentum conservation equation, . Substituting this into the kinetic energy expression for the daughter nucleus:
Knowing that , we can express in terms of :
Given that the mass of an alpha particle () is significantly smaller than that of a typical daughter nucleus (), the daughter nucleus receives a smaller fraction of the total decay energy. However, even this smaller fraction typically amounts to tens to hundreds of kiloelectronvolts (keV). For instance, in the alpha decay of Uranium-238 to Thorium-234, where the alpha particle carries approximately 4.2 MeV, the Thorium-234 nucleus recoils with an energy of about 71 keV (). This energy is vastly greater than the few electronvolts (eV) required to break chemical bonds or displace atoms within a crystal lattice.
The considerable kinetic energy imparted by alpha recoil allows the recoiling daughter nucleus to escape its original position within a mineral matrix or material. This phenomenon is particularly relevant for the release of noble gases like radon from solid materials. When a uranium atom embedded in a mineral decays to thorium, and subsequently to radium and then radon, each alpha decay event can cause the recoiling atom to be ejected from the host crystal lattice into pore spaces or the surrounding environment. This mechanism is a primary contributor to environmental radon exposure and plays a crucial role in understanding the long-term behaviour and migration of radionuclides in geological repositories and contaminated sites. The range of recoil in solids is typically short, usually tens of nanometres, but this is often sufficient to breach the immediate atomic bonds.