To initiate nuclear fission, the critical (excitation) energy of the compound nucleus should be how large relative to the neutron binding energy of the target nucleus?

Introduction / Context:
Nuclear fission by neutron absorption forms a compound nucleus in an excited state. Whether fission occurs depends on whether the excitation energy exceeds the fission barrier. The relation between this critical (threshold) energy and neutron binding energy determines the need for fast neutrons or whether thermal neutrons suffice for certain nuclides.

Given Data / Assumptions:

• Compound nucleus model (neutron capture followed by de-excitation paths).
• Fission barrier exists and must be overcome.
• Binding energy refers to the energy required to remove the captured neutron.

Concept / Approach:
When a neutron is captured, the released binding energy plus the neutron’s kinetic energy sets the excitation energy of the compound nucleus. For fission to be energetically possible, this excitation must exceed the fission barrier (critical energy). In nuclides that fission with thermal neutrons, the binding energy alone is typically sufficient; in others, additional kinetic energy from a faster neutron is required, implying that the critical energy must be above the binding energy level.

Step-by-Step Solution:
Capture neutron: target + n → compound nucleus + excitation energy.Excitation energy = binding energy + kinetic energy of neutron.Fission condition: excitation > fission barrier (critical energy).Therefore, critical energy must exceed binding energy to ensure threshold behavior.

Verification / Alternative check:
Fast-fission thresholds observed in U-238 illustrate cases where thermal neutrons lack sufficient energy, requiring higher kinetic energy to push excitation above the barrier, consistent with “more than binding energy.”

Why Other Options Are Wrong:
Equal / less than: would imply no threshold for nuclides that clearly have one.Either more or less: contradicts the known threshold behavior in non-thermal-fissioning isotopes.Exactly half: arbitrary and unphysical.

Common Pitfalls:
Confusing binding energy with fission barrier; they are distinct energies.Assuming all actinides fission with thermal neutrons; many require fast neutrons.

Final Answer:
More than the neutron binding energy