Which of the following nuclear fragments corresponding to nuclear fission between neutron $$\binom{1}{0}n$$ and uranium isotope $$\left(_{92}^{235}U\right) $$ is correct:

We need to identify the correct nuclear fission products when a neutron hits uranium-235.

Write the nuclear reaction.

$$ {}^{235}_{92}U + {}^{1}_{0}n \rightarrow \text{products} $$

Apply conservation laws.

Total mass number on the left: $$235 + 1 = 236$$

Total atomic number on the left: $$92 + 0 = 92$$

The products must conserve both mass number and atomic number.

Check each option.

Option 1: $${}^{144}_{56}Ba + {}^{89}_{36}Kr + 4{}^{1}_{0}n$$

Mass: $$144 + 89 + 4 = 237 \neq 236$$. Rejected.

Option 2: $${}^{144}_{56}Ba + {}^{89}_{36}Kr + 3{}^{1}_{0}n$$

Mass: $$144 + 89 + 3 = 236$$ $$\checkmark$$

Atomic number: $$56 + 36 + 0 = 92$$ $$\checkmark$$

Both conservation laws are satisfied. Correct.

Option 3: $${}^{140}_{56}Xe + {}^{94}_{38}Sr + 3{}^{1}_{0}n$$

Atomic number: $$56 + 38 + 0 = 94 \neq 92$$. Rejected.

Option 4: $${}^{153}_{51}Sb + {}^{99}_{41}Nb + 3{}^{1}_{0}n$$

Mass: $$153 + 99 + 3 = 255 \neq 236$$. Rejected.

The correct answer is Option (2): $${}^{144}_{56}Ba + {}^{89}_{36}Kr + 3{}^{1}_{0}n$$.