Final answer:
The daughter nucleus will have an atomic number of 82 and a mass number of 208 after the parent isotope undergoes the emission of 4 beta particles and 6 alpha particles. This is because each alpha emission decreases the atomic number by 2 and mass by 4, while beta emission increases the atomic number by 1 without changing the mass.
Step-by-step explanation:
The question asks for the atomic number and mass number of the daughter nucleus after a parent isotope with an atomic number of 90 and a mass number of 232 has undergone radioactive decay, emitting 4 beta particles (β-) and 6 alpha particles (α).
An alpha particle (α) emission reduces the atomic number by 2 and the mass number by 4. Therefore, after 6 alpha particles are emitted, the atomic number decreases by 6 x 2 = 12, and the mass number decreases by 6 x 4 = 24.
A beta particle (β-) emission increases the atomic number by 1 but does not affect the mass number. After emitting 4 beta particles, the atomic number increases by 4 x 1 = 4.
Starting with an atomic number of 90 and mass number of 232, we subtract 12 and add 4 to the atomic number, resulting in 90 - 12 + 4 = 82. For the mass number, we subtract 24 to get 232 - 24 = 208. The atomic number and mass number of the daughter nucleus are therefore 82 and 208, respectively.
Answer: (A) Atomic number = 82, mass number = 208.