43-1 Nuclear Fission

43-1 Nuclear Fission#

Prompts

  • Why does fission of a heavy nucleus (e.g., \(^{235}\text{U}\)) release energy? Connect your answer to the binding-energy-per-nucleon curve (section 42-2).

  • What is a fissile nuclide? Why does \(^{235}\text{U}\) fission with slow (thermal) neutrons but \(^{238}\text{U}\) typically does not? What is the difference between fissile and fertile?

  • A single fission of \(^{235}\text{U}\) releases ~200 MeV and produces ~2.5 neutrons on average. Explain how this leads to a chain reaction. What is critical mass?

  • Why must neutrons be moderated (slowed) in a reactor? What happens if they are too fast?

  • Compare subcritical, critical, and supercritical — what does each mean for the chain reaction?

Lecture Notes#

Overview#

  • Nuclear fission is the splitting of a heavy nucleus into lighter fragments. It releases energy because the binding energy per nucleon is higher for medium-mass nuclei than for heavy ones (section 42-2).

  • Fissile nuclides (\(^{235}\text{U}\), \(^{239}\text{Pu}\)) undergo fission when struck by slow (thermal) neutrons. The fission cross section is large at low neutron energies.

  • A chain reaction occurs when neutrons from one fission trigger further fissions. The critical mass is the minimum amount of fissile material needed for a sustained chain reaction.

Why Fission Releases Energy#

The binding energy per nucleon \(E_b/A\) peaks near iron (\(A \approx 56\)) and decreases for heavier nuclei (section 42-2). A heavy nucleus (e.g., \(A \approx 235\)) has less binding per nucleon than two medium-mass fragments (e.g., \(A \approx 90\) and \(A \approx 140\)).

Splitting the heavy nucleus into lighter ones therefore increases the total binding energy — energy is released. Typical fission of \(^{235}\text{U}\) releases ~200 MeV, mostly as kinetic energy of the fragments and neutrons.

(463)#\[ ^{235}\text{U} + n \to \text{fragment}_1 + \text{fragment}_2 + 2\text{--}3\ \text{neutrons} + \text{energy} \]

The fragments are typically unstable and decay by beta emission; the neutrons can induce further fissions.

Fissile vs. Fertile#

Fissile nuclides undergo fission when struck by slow neutrons. Examples: \(^{235}\text{U}\), \(^{239}\text{Pu}\), \(^{233}\text{U}\).

Fertile nuclides do not fission readily with thermal neutrons but can be converted into fissile material by neutron capture. Example: \(^{238}\text{U}\) captures a neutron to form \(^{239}\text{U}\), which beta-decays to \(^{239}\text{Pu}\) (fissile).

Nuclide

Fissile?

Note

\(^{235}\text{U}\)

Yes

~0.7% of natural uranium; large fission cross section for thermal neutrons

\(^{238}\text{U}\)

No (fertile)

~99.3% of natural uranium; fission requires fast neutrons

\(^{239}\text{Pu}\)

Yes

Produced in reactors from \(^{238}\text{U}\)

Why thermal neutrons?

For \(^{235}\text{U}\), the fission cross section is much larger at thermal energies (~0.025 eV) than at fast energies. Slow neutrons spend more time near the nucleus, increasing the capture probability. \(^{238}\text{U}\) has a fission threshold — fast neutrons are needed to overcome it.

The Chain Reaction#

Each fission produces ~2–3 neutrons on average. If at least one of these triggers another fission, the reaction can sustain itself — a chain reaction.

  • Subcritical: On average, fewer than one neutron per fission causes another fission. The reaction dies out.

  • Critical: Exactly one neutron per fission, on average, causes another fission. Steady power.

  • Supercritical: More than one neutron per fission causes further fissions. The reaction grows (explosively in a bomb; controlled in a reactor).

Neutrons can be lost by escaping the material or by non-fission capture (e.g., \(^{238}\text{U}\) absorbs without fissioning). The critical mass is the minimum mass of fissile material needed so that enough neutrons produce fissions before escaping — geometry and purity matter.

Summary#

  • Fission: heavy nucleus splits; energy released because \(E_b/A\) is higher for medium-mass nuclei.

  • Fissile (\(^{235}\text{U}\), \(^{239}\text{Pu}\)): fission with thermal neutrons; fertile (\(^{238}\text{U}\)): converts to fissile.

  • Chain reaction: neutrons from fission trigger more fissions; critical mass for sustained reaction.

  • Subcritical / critical / supercritical: <1, =1, >1 neutron per fission causing further fission.