Sections#

Review & Summary#

Nuclear Fission#

A heavy nucleus can split into lighter fragments (fission), releasing energy because the binding energy per nucleon is greater for medium-mass nuclei. Fissile nuclides such as \(^{235}\mathrm{U}\) and \(^{239}\mathrm{Pu}\) undergo fission when struck by slow (thermal) neutrons. 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.

The Nuclear Reactor#

A nuclear reactor uses controlled fission to produce heat, which is converted to electricity. A moderator (e.g., water, graphite) slows neutrons to thermal energies where the fission cross section is large. Control rods (e.g., boron, cadmium) absorb neutrons to regulate the power level. A coolant removes heat from the core. Breeder reactors convert fertile material (e.g., \(^{238}\mathrm{U}\)) into fissile material (\(^{239}\mathrm{Pu}\)), producing more fuel than they consume.

A Natural Nuclear Reactor#

The Oklo deposit in Gabon: about 2 billion years ago, when \(^{235}\mathrm{U}\) was more abundant (~3% vs ~0.7% today), geological conditions allowed a natural chain reaction. Evidence includes anomalous isotope ratios of fission products.

Thermonuclear Fusion: The Basic Process#

Light nuclei can fuse to form heavier ones, releasing energy when the product lies below iron on the binding-energy-per-nucleon curve. The deuterium-tritium reaction has the largest cross section at achievable temperatures:

(462)#\[ d + t \to {}^4\mathrm{He} + n + 17.6\,\mathrm{MeV} \]

where the energy is shared as kinetic energy of the products.

Thermonuclear Fusion in the Sun and Other Stars#

The proton-proton chain and CNO cycle fuse hydrogen to helium in stars. Gravitational confinement compresses and heats the plasma, sustaining the high temperature (\(\sim 10^7\) K) and density needed for fusion.

Controlled Thermonuclear Fusion#

Tokamaks (magnetic confinement) and inertial confinement (laser or particle-beam compression) aim to achieve fusion on Earth. Ignition requires the Lawson criterion: \(n\tau T\) above a threshold, where \(n\) is the particle density, \(\tau\) is the confinement time, and \(T\) is the temperature. Fusion offers abundant fuel (deuterium from seawater) and produces less long-lived radioactive waste than fission.