In a \({\rm{3 \times 1}}{{\rm{0}}^{\rm{9}}}\)-year-old rock that originally contained some\(^{{\rm{238}}}{\rm{U}}\)which has a half-life of \({\rm{4}}{\rm{.5 \times 1}}{{\rm{0}}^{\rm{9}}}\) years, we expect to find some \(^{{\rm{238}}}{\rm{U}}\)remaining in it. Why are \(^{{\rm{226}}}{\rm{Ra}}{{\rm{,}}^{{\rm{222}}}}{\rm{Rn, and}}{{\rm{ }}^{{\rm{210}}}}{\rm{Po}}\) also found in such a rock, even though they have much shorter half-lives (1600 years, 3.8 days, and 138 days, respectively)?

The process of radioactive decay known as "alpha decay," in which an atomic nucleus produces an alpha particle and changes into a separate atomic nucleus with a mass number that is reduced by four and an atomic number that is reduced by two, is known as radioactive decay.

Beta decay is a type of radioactive decay in nuclear physics in which a beta particle is emitted from an atomic nucleus, converting the original nuclide to an isobar of that nuclide.

The time required for the original number of nuclei to decay to half is defined as the half-life. Some nuclides are stable and live indefinitely. Unstable nuclides decay and produce stable nuclides after various decays. The products of decay are referred to as daughters, while the original nuclide is referred to as the parent nuclide. \(^{238}U\) Decay into another unstable nuclide, resulting in decay where each nuclide decays to form a stable nuclide.

The decay series begins with\(^{238}U\)and ends with\(^{226}Ra\)and\(^{210}{\rm{Po}}\)both of which are radioactive isotopes.\(^{222}Rn\)is also generated. As a result, radioactive isotopes with shorter half-lives are found in such rock.