Physics
Physics
Problem
A sub-critical assembly of plutonium is rapidly compressed so that its radius is reduced to half while its mass remains the same. Predict qualitatively whether the assembly will become supercritical, and support your answer with one geometric argument related to neutron escape.Intuitive explanation
The key is understanding how neutron leakage depends on geometry. When you compress the sphere to half its radius, its volume drops by a factor of 8—but the surface area (where neutrons escape) only drops by a factor of 4. This means the ratio of surface area to volume increases, so neutrons have a shorter average distance to travel before hitting the boundary and escaping. Fewer neutrons survive to cause fission, making the assembly less likely to go supercritical, not more.
Intuitive explanation
The key is understanding how neutron leakage depends on geometry. When you compress the sphere to half its radius, its volume drops by a factor of 8—but the surface area (where neutrons escape) only drops by a factor of 4. This means the ratio of surface area to volume increases, so neutrons have a shorter average distance to travel before hitting the boundary and escaping. Fewer neutrons survive to cause fission, making the assembly less likely to go supercritical, not more.