Which of the following is the correctly balanced equation for the nuclear fission of uranium-235 when it is bombarded with a neutron?

• A. n + ^{235}U \rightarrow ^{236}U + n
• B. ^{235}U \rightarrow ^{140}Xe + ^{94}Sr + 2n
• C. ^{235}U + ^{92}Kr \rightarrow ^{141}Ba + 3n
• D. n + ^{235}U \rightarrow ^{141}Ba + ^{92}Kr + 3n

Answer: (D)

Verified step by step guidance

1. Step 1: Understand that in a nuclear fission reaction, the sum of the mass numbers (top numbers) and the sum of the atomic numbers (bottom numbers) must be equal on both sides of the equation to satisfy conservation of nucleons and charge.
2. Step 2: Write down the reactants and products with their mass numbers and atomic numbers. For example, neutron (n) has mass number 1 and atomic number 0, uranium-235 is written as \(^{235}_{92}U\), and so on.
3. Step 3: Check the given balanced equation: \(n + ^{235}_{92}U \rightarrow ^{141}_{56}Ba + ^{92}_{36}Kr + 3n\). Sum the mass numbers on the left side: 1 (neutron) + 235 (uranium) = 236. On the right side, sum the mass numbers: 141 (barium) + 92 (krypton) + 3 \times 1 (neutrons) = 236. This confirms mass number conservation.
4. Step 4: Similarly, sum the atomic numbers on the left: 0 (neutron) + 92 (uranium) = 92. On the right: 56 (barium) + 36 (krypton) + 3 \times 0 (neutrons) = 92. This confirms atomic number conservation.
5. Step 5: Conclude that the equation \(n + ^{235}_{92}U \rightarrow ^{141}_{56}Ba + ^{92}_{36}Kr + 3n\) is correctly balanced because it satisfies both mass number and atomic number conservation, which are essential for nuclear reactions.