WBJEE 2025 Physics and Chemistry Papers

Let's analyze the decay chain step-by-step. We start with a nucleus $X$ having atomic number $Z$ and mass number $A$. The decay chain is as follows:$X \xrightarrow{\alpha} X_1$In alpha decay, an alpha particle (helium nucleus) is emitted, which has a mass number of 4 and an atomic number of 2 .Therefore: $X_1:$ atomic number $=Z-2,\;\;$ mass number $=A-4$$X_1 \xrightarrow{\beta} X_2$In beta decay, a neutron is converted into a proton, increasing the atomic number by 1 while the mass number remains unchanged.Therefore: $\;X_2:$ atomic number $=(Z-2)+1=Z-1,$ mass number $=A-4$$\;X_2 \xrightarrow{\alpha} X_3$Again, alpha decay reduces the atomic number by 2 and the mass number by 4 .Therefore: $X_3:$ atomic number $=(Z-1)-2=Z-3,\;\;$ mass number $=(A-4)-4=A-8$$X_3 \xrightarrow{\gamma} X_4$Gamma decay does not change either the atomic number or the mass number.Therefore: $X_4:$ atomic number $=Z-3,$ mass number $=A-8$We are given that $X_4$ has a mass number of 172 and an atomic number of 69 . This gives us two equations:$\;Z-3=69$$\;A-8=172$ Now, solve these equations:From the first equation:$Z=69+3=72.$From the second equation:$A=172+8=180.$ Thus, the original nucleus $X$ has an atomic number of 72 and a mass number of 180 .