Contribution of Recoil Nucleus Energy to Total Absorbed Dose from Alpha and Beta Decay of Radionuclides Radium, Radon and Their Radioactive Progeny

When conducting nuclear medical procedures like brachytherapy or performing repairs at industrial nuclear facilities, the energy of an alpha or beta particle released from a nucleus is calculated. Nonetheless, the energy deposited by the nucleus recoil is not included. The contribution of recoil nucleus energy may provide radiation risk at high exposure rates. The study thus calculates the contribution of recoil nucleus energy to the total absorbed radiation dose to tissues from alpha and beta decay of all naturally occurring radon isotopes (Rn-222, Rn-220, and $\mathrm{Rn}-219)$ and their radioactive progenies. Nucleus recoil energy is computed via the law of equality of momenta of the released particle or photon and the recoiling atom. All characteristic energies with a combined emission probability over $99 \%$ are considered for alpha decays. The highest beta particle energy determines the maximum nucleus recoil energy for beta decay. Alpha particles from Rn-222, Rn-220, and Rn219 and their progenies emit energies ranging from 4.60 to 8.79 MeV, while beta particles have much smaller energies (0.06-3.28 MeV). Recoil nucleus energies from alpha decay range from 0.08 to 0.17 MeV, while beta decay energies are much lower (0.1818.67 eV). Emitted alpha particles carry about 55 times more energy than recoiling nuclei, while beta particles have maximum energies five orders of magnitude higher than the nucleus recoil. Recoil nuclei contribute around $2 \%$ of the total absorbed dose to tissues from alpha decay and only $0.0001 \%$ from beta decay. In alpha-emitting radionuclides like Rn-222, Rn-220, and Rn-219 and their progenies, this recoil nucleus energy can be significant at high exposure rates, whereas it is negligible in beta decay.