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A radioactive nucleus decays through the sequence A --α--> A1 --β--> A2 --α--> A3 --γ--> A4. If nucleus A has mass number 180 and atomic number 72, what are the mass number and atomic number of A4?

1. 172 and 69
2. 174 and 70
3. 176 and 69
4. 176 and 70

Correct answer: 174 and 70

Solution

The decay sequence involves two alpha decays and one beta decay. Each alpha decay decreases the mass number by 4 and the atomic number by 2, while the beta decay increases the atomic number by 1. Starting from A (mass 180, atomic 72), after two alpha decays, the mass becomes 172 and the atomic number 68, then the beta decay increases the atomic number to 69, resulting in A4 having a mass number of 174 and an atomic number of 70.

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