How does k_eff differ from k_infty, and why does leakage matter in finite reactors?

• A. k_infty ignores neutron leakage, while k_eff includes leakage; leakage reduces k_eff in real reactors.
• B. k_infty accounts for leakage, while k_eff does not.
• C. k_infty is defined for subcritical systems only.
• D. k_eff equals k_infty in all reactors.

Answer: (A)

The key idea is how boundary losses change neutron reproduction. k_infty is the multiplication factor for an infinite, boundary-free medium, so there is no neutron leakage and every generation’s neutrons stay in the system to cause further fission. In a real, finite reactor, neutrons can reach the boundary and escape, which reduces the number of neutrons available to sustain fission. The actual, observable multiplication factor that accounts for this leakage is k_eff. Because leakage removes neutrons, k_eff is smaller than k_infty in real reactors. In very large systems where leakage is negligible, k_eff can approach k_infty.

So the correct statement reflects that k_infty ignores leakage, while k_eff includes leakage, and leakage lowers k_eff in real reactors.