A nucleus of uranium-238 embedded in a mineral lattice is observed to undergo two successive radioactive emissions before the lattice can respond mechanically. In the first step it emits one particle R1, forming an intermediate nuclide. That intermediate nuclide immediately emits a particle R2, forming the final daughter.
Initial nucleus: 92238U
Final daughter: unknown
The identities of R1 and R2 are not given.
(a) Assuming R1 is an α particle, write the nuclear equation for the first decay step and identify the intermediate nuclide.
(b) The second emission R2 is known to be a β− particle. Write the nuclear equation for the second step starting with the intermediate nuclide obtained in part (a).
(c) Combine your results from parts (a) and (b) to give a single overall nuclear equation relating 92238U to its final daughter nucleus, explicitly listing all emitted particles.
(d) Demonstrate, using explicit calculations, that both nucleon number and electric charge are unchanged between the initial nucleus and the collection of final products in part (c).