E.4 · IB Physics
Fission chain reaction
Fire a neutron into a lattice of fuel nuclei. Each fission releases two or three more neutrons, so the chain can grow, hold steady or die away. Push the control rods in to absorb neutrons and tame it.
Predict first
Start from the defaults (control rods 0 %, 3 neutrons per fission). If you move the Control rods slider to 50 %, what happens to the 'Neutrons per hit' value?
Each hit is absorbed with probability 0.50, otherwise it causes a fission that releases 3 neutrons. The average is ν(1 − p) = 3 × 0.50 = 1.5.
Check it in the model: Move the Control rods, absorption slider from 0 % to 50 % and read the Neutrons per hit, ν(1 − p) value.
unused fuel neutron used nucleus control rod
fission → ν new neutrons
neutrons per hit = ν(1 − p) (above 1 = growing)
energy per fission ≈ 200 MeV = 3.2×10⁻¹¹ J
Peak so far:
Fissions:
Fuel left:
Neutrons per hit, ν(1 − p):
Energy released:
Status:
Try this
- Set the rods to 0 % with 3 neutrons per fission and fire one neutron. Watch the graph: does the neutron count grow, and what happens when the fuel runs low?
- Raise the rods to 55 % and fire again. Compare the "neutrons per hit" value with 1, and look at whether the chain survives. Repeat a few times, since each run is random.
- Set 2 neutrons per fission with the rods at 30 %, then find the rod setting where the chain just stops being able to grow.
Common error: mixing up the moderator and the control rods. Control rods absorb neutrons to hold the chain at exactly critical (on average one new fission per fission); a moderator slows neutrons so that they are more likely to cause fission.