Physics - Modern Physics Question with Solution | TestHub

After emitting three$\alpha$- particles, the radioactive nucleus (initial mass number$A$and atomic number$Z$) will be rendered into a nucleus having mass number$(A-12)$and atomic number$(Z-6)$. Further, after emitting two positrons, the mass number will remain unchanged i.e.,$(A-12)$but atomic number will become$(Z-6-2)$i.e.,$(Z-8)$.

Therefore, number of protons in the final nucleus$=\left(A-12\right)-\left(Z-8\right)=\left(A-Z-4\right)$

Therefore, the ratio of number of neutrons to that of protons in the final nucleus

$=\frac{A-Z-4}{Z-8}$