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A radioactive nucleus (initial mass number A and atomic number Z) emits 3 α-particles and 2 positrons. The ratio of the number of neutrons to that of protons in the final nucleus will be

1. (A - Z - 8)/(Z - 4)
2. (A - Z - 4)/(Z - 8)
3. (A - Z - 12)/(Z - 4)
4. (A - Z - 4)/(Z - 2)

Correct answer: (A - Z - 4)/(Z - 8)

Solution

The emission of 3 α-particles decreases the mass number by 12 (3x4) and the atomic number by 6 (3x2), while the emission of 2 positrons decreases the atomic number by an additional 2. Therefore, the final mass number is A - 12 and the final atomic number is Z - 8, leading to the ratio of neutrons to protons being (A - Z - 4)/(Z - 8).

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