In a nuclear fission reaction given below, the three neutrons are released. The value of \( x \) and \( y \) are
\( {}^{1}_{0}\mathrm{n} + {}^{235}_{92}\mathrm{U} \rightarrow {}^{x}_{56}\mathrm{Ba} + {}^{89}_{y}\mathrm{Kr} + 3\,{}^{1}_{0}\mathrm{n} \)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( x = 144,\ y = 36 \)
In a nuclear reaction the mass number (total number of nucleons) and the atomic number (total charge) are both conserved. Balance each one separately.
Mass number: the left side has \( 1 + 235 = 236 \), the right side has \( x + 89 + 3 \times 1 \).
\( \displaystyle 236 = x + 89 + 3 \;\Rightarrow\; x = 144 \)
Atomic number: the left side has \( 0 + 92 = 92 \), the right side has \( 56 + y + 0 \).
\( \displaystyle 92 = 56 + y \;\Rightarrow\; y = 36 \)
So \( x = 144 \) and \( y = 36 \).
Note: This question is from NCERT (2026-27). NTA sets numerical questions from NCERT too, so do not ignore NCERT while practising numericals.
NCERT (2026-27):
Fission – “… A most important neutron-induced nuclear reaction is fission. An example of fission is when a uranium isotope \( {}^{235}_{92}\mathrm{U} \) bombarded with a neutron breaks into two intermediate mass nuclear fragments
\( \displaystyle {}^{1}_{0}\mathrm{n} + {}^{235}_{92}\mathrm{U} \rightarrow {}^{236}_{92}\mathrm{U} \rightarrow {}^{144}_{56}\mathrm{Ba} + {}^{89}_{36}\mathrm{Kr} + 3\,{}^{1}_{0}\mathrm{n} \qquad (13.10) \)”