E.4 Fission

Model fission

A heavy nucleus can split into two lighter nuclei after absorbing a neutron, or spontaneously in an unstable state. The products have a greater binding energy per nucleon than the original heavy nucleus.

Track the release

The increase in total binding energy appears as kinetic energy of the fission products, neutron energy and radiation. The mass of the products is slightly smaller, with the mass difference converted to energy.

Worked example — use binding energy per nucleon

For $^{235}\mathrm{U}$ splitting into $^{89}\mathrm{Kr}$ and $^{144}\mathrm{Ba}$, use $B=A(B/A)$. With values $7.59$, $8.72$ and $8.27\,\mathrm{MeV}$ per nucleon, $E=[89(8.72)+144(8.27)]-235(7.59)=1.83\times10^2\,\mathrm{MeV}$. The products are more tightly bound, so this positive difference is released.

Understand fissile material

Enrichment increases the fraction of uranium-235 relative to uranium-238, making a sustained fission process more feasible.

Common trap

Do not say energy is created from nothing. It comes from the mass defect and the change in nuclear binding energy.

Start the chain

A fission event can emit neutrons. If one of them causes another fission, the process becomes a chain reaction.

Control the multiplication

A self-sustaining reactor requires, on average, one effective neutron from each fission to cause the next fission. Neutrons can instead escape, be absorbed by control rods, or be absorbed without causing fission.

Explain moderation

Fast neutrons are slowed by collisions with a moderator because low-energy neutrons have a higher probability of causing the relevant fission in this reactor model.

Common trap

Do not say every emitted neutron continues the chain. Losses and absorption determine whether the reaction dies out, stays critical or grows.

Track the energy path

Nuclear energy becomes kinetic energy of fission products, then internal energy of coolant, kinetic energy of steam and turbine, and finally electrical energy from the generator. The heat exchanger transfers energy; it does not create or regulate the fission reaction.

Common trap

Both moderator and control rods interact with neutrons, but their jobs differ: the moderator slows them, whereas control rods remove some by absorption.

Judge the management problem

A long half-life does not automatically mean a greater activity: for the same number of nuclei, a longer half-life means a smaller decay constant. Waste decisions must consider amount, radiation type, activity, heat, containment and timescale together.

Common trap

Do not assume shutting down the chain reaction makes spent fuel immediately safe. Unstable fission products continue to decay after neutron-induced fission has stopped.