WBJEE 2024 Physics & Chemistry Paper

To determine the number of neutrons in the atom after the emission of a $\beta$-particle and an $\alpha$-particle from ${}_{83}^{214}\mathrm{Bi}$, we need to understand how these emissions affect the atomic and mass numbers.1. Emission of a $\beta$-particle:$A\beta$-particle is essentially an electron, and its emission converts a neutron into a proton. Therefore, the atomic number increases by 1 , but the mass number remains the same. For ${}_{83}^{214}\mathrm{Bi}$ (bismuth), after the emission of a $\beta$-particle, the atomic number becomes 84 :${}_{83}^{214}\mathrm{Bi}\rightarrow {}_{84}^{214}\mathrm{Po}+\beta$2. Emission of an $\alpha$-particle:An $\alpha$-particle consists of 2 protons and 2 neutrons, so its emission decreases the atomic number by 2 and the mass number by 4 . Therefore, for ${}_{84}^{214}\mathrm{Po}$ (polonium), after the emission of an $\alpha$-particle, the atomic number becomes 82 and the mass number becomes 210:${}_{84}^{214}\mathrm{Po}\rightarrow {}_{82}^{210}\mathrm{Pb}+\alpha$ Now, we need to find the number of neutrons in the resulting atom, ${}_{82}^{210}\mathrm{Pb}$ (lead). The number of neutrons is given by the difference between the mass number and the atomic number:Number of neutrons $=$ Mass number - Atomic numberNumber of neutrons $=210-82=128$Therefore, the correct answer is:Option B$128$