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If species ᵇₐX emits firstly a positron, then two α and two β and in last one α and finally converted to species ᶜₐY, so correct relation is:

1. c = a - 5, d = b - 12
2. c = a - 6, d = b - 8
3. c = a - 4, d = b - 12
4. c = a - 5, d = b - 8

Correct answer: c = a - 5, d = b - 8

Solution

The positron emission decreases the atomic number by 1, each α-particle emission decreases the atomic number by 2 and mass number by 4, and β-particle emission does not affect the mass number but increases the atomic number by 1. After applying these changes step-by-step, the final relation is c = a - 5 and d = b - 8.

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