Nucleus A decays in to nucleus C in a two-step process. $$A \rightarrow B + {}^4_2\text{He}$$ and $$B \rightarrow C + 2e^-$$. Then

Solution

Alpha emission lowers the atomic number by 2 and the mass number by 4, so B has $$Z - 2$$ and $$M - 4$$. Emitting two electrons (beta particles) raises the atomic number by 2 without changing the mass number, so C has $$Z$$ and $$M - 4$$. A and C have the same atomic number but different mass numbers, so they are isotopes.

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