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  4. In a radioactive decay, an element ZXA emits four α-particles, three β-particles and eight gamma photons. The atomic number and mass number of the resulting final nucleus are

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Q. In a radioactive decay, an element $_ZX^{A}$ emits four $\alpha$-particles, three $\beta$-particles and eight gamma photons. The atomic number and mass number of the resulting final nucleus are

KCETKCET 2012Nuclei

Solution:

After $n_{\alpha} $ $\alpha$ -decays and $n_{\beta}$ $\beta$-decays, the respective atomic number and mass number of resulting nucleus are given by
$Z'=Z-2 n_{\alpha}+n_{0}=Z-8+3=Z-5$
and $A'=A-4 n_{\alpha}=A-16$