To solve this problem, we need to apply the principle of conservation of nucleons and charge in a nuclear reaction.$\\$The given reaction is:$\\ {}^{235}_{92}$U$+ {}^{1}_{0}$n$\rightarrow {}^{89}_{36}$Kr$+ 3 \times {}^{1}_{0}$n$+ X \\$We need to find the unknown nucleus $X. \\$Step 1: Conservation of Mass Number$\\$The total mass number on the left side is:$\\ 235 + 1 = 236 \\$The total mass number on the right side is:$\\ 89 + 3 \times 1 + A_X = 89 + 3 + A_X = 92 + A_X \\$Equating both sides for mass number conservation:$\\ 236 = 92 + A_X \\ A_X = 236 - 92 \\ A_X = 144 \\$Step 2: Conservation of Atomic Number$\\$The total atomic number on the left side is:$\\ 92 + 0 = 92 \\$The total atomic number on the right side is:$\\ 36 + 0 + Z_X = 36 + Z_X \\$Equating both sides for atomic number conservation:$\\ 92 = 36 + Z_X \\ Z_X = 92 - 36 \\ Z_X = 56 \\$Therefore, the unknown nucleus $X$ is ${}^{144}_{56}$Ba$. \\$This corresponds to Option 4.