In the nuclear decay given below _ Z ^ A X _ Z+1 ^ A Y _ Z-1 ^ A-4...

Key Idea In a nuclear reaction conservation of charge number and mass number must hold good. Alpha particles are positively charged particles with charge $+2 e$ and mass $4 \mathrm{~m}$. Emission of an $\alpha$-particle reduces the mass of the radionuclide by 4 and its atomic number by 2. $\beta$-particles are negatively charged particles with rest mass as well as charge same as that of electrons. $\gamma$-particles carry no charge and mass. Radioactive transition will be as follows$$\begin{aligned}& { }_{\mathrm{Z}}^{\mathrm{A}} \mathrm{X} \longrightarrow{ }_{\mathrm{Z}+1}{ }^{\mathrm{A}} \mathrm{Y}+\beta_{-1}^0 \\ & { }_{\mathrm{Z}+1}^{\mathrm{A}} \mathrm{Y} \longrightarrow{ }_{\mathrm{Z}-1}^{\mathrm{A}-4} \beta+\alpha_2^4 \\ & { }_{\mathrm{Z}+1}^{\mathrm{A}-4} \beta \longrightarrow{ }_{\mathrm{Z}-1}^{\mathrm{A}-4} \mathrm{\beta}+\gamma_0^0 \\ & \end{aligned}$$