Control rods in nuclear reactors: which statements correctly describe their material choice and neutron-interaction requirement?

Introduction / Context:
Control rods regulate reactor power by absorbing thermal (and sometimes epithermal) neutrons. Effective reactivity control requires materials with high absorption probabilities so that small rod motions produce measurable changes in neutron population.

Given Data / Assumptions:

• Thermal reactor context (PWR/BWR/HWR).
• Standard rod materials and claddings.
• Goal: reliable shutdown and fine control during operation.

Concept / Approach:
Good control-rod materials combine a large microscopic absorption cross-section with acceptable mechanical, thermal, and radiation resistance. Boron (in B4C), silver–indium–cadmium (Ag–In–Cd), hafnium, and cadmium are classic choices because they remove neutrons efficiently, lowering reactivity (negative reactivity insertion).

Step-by-Step Solution:
Identify material requirement: high absorption cross-section desired.List common materials: B4C, Hf, Cd, Ag–In–Cd, dysprosium-titanate in some designs.Relate to function: inserting rods increases neutron captures, reducing k_eff.Thus, statements about boron/hafnium/cadmium and “large cross-section” are both correct.

Verification / Alternative check:
Shutdown margin and rod-worth calculations depend on these high capture cross-sections; licensing documents and vendor specs emphasize these materials for reactivity control.

Why Other Options Are Wrong:
Small cross-section (A): would make rods ineffective.Structural-only role (E): incorrect; nuclear absorption is their primary function.

Common Pitfalls:
Confusing control rods with burnable absorbers or soluble boron; all are absorbers but used differently.Ignoring temperature and radiation effects on rod materials over lifetime.

Final Answer:
Both (b) and (c)