Fission fragment accounting: when a slow neutron is absorbed by 92U235 to form a compound nucleus that fissions into 54Xe139 and 38Sr94, how many neutrons are emitted along with the fission fragments?

Introduction / Context:
Balancing nuclear reactions is a core competency in reactor physics and nuclear chemistry. It ensures conservation of nucleon number and charge, and it helps estimate neutron economy—vital for sustaining a chain reaction and for calculating reactivity and breeding ratios.

Given Data / Assumptions:

• Incident: a slow neutron captured by 92U235.
• Fission products: 54Xe139 and 38Sr94.
• We must find the number of emitted neutrons, n_emitted.

Concept / Approach:
Use conservation of mass number (A) and atomic number (Z). On capture, 92U235 + 0n1 → 92U236* (compound). After fission, the sum of product mass numbers plus emitted neutrons must equal 236. Similarly, the sum of product atomic numbers must equal 92, which is satisfied by Z = 54 + 38 = 92 for xenon and strontium.

Step-by-Step Solution:
Compute compound mass number: 235 + 1 = 236.Sum fragment mass numbers: 139 + 94 = 233.Conservation of A: 236 = 233 + n_emitted ⇒ n_emitted = 3.Verify Z: 54 + 38 = 92; atomic number is conserved.

Verification / Alternative check:
This result matches common averages for U-235 thermal fission, where approximately 2–3 neutrons per fission are emitted, depending on fragment split and excitation energy; the exact integer here follows from the specified split.

Why Other Options Are Wrong:
1 or 2: Would undercount mass number relative to 236.4 or 5: Would overcount relative to the specified fragment masses.

Common Pitfalls:
Forgetting to include the incident neutron in the compound nucleus mass number, or misadding the fragment masses and then forcing charge balance incorrectly.

Final Answer:
3