14.2 Nuclear Reactions and Energy

Nuclear reactions involve changes in atomic nuclei that release massive amounts of energy through fission (splitting atoms) or fusion (combining atoms). These processes drive everything from nuclear power plants to the cores of stars, making them central to both modern energy production and astrophysics.

Nuclear Fission and Fusion

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Fundamental Nuclear Processes

Nuclear fission splits a heavy atomic nucleus into two lighter nuclei, releasing energy and neutrons in the process. The most common example is uranium-235, which is used in nuclear reactors. When a neutron strikes a U-235 nucleus, it splits into smaller elements like barium and krypton, plus additional free neutrons and a large burst of energy.

Nuclear fusion is the opposite: light atomic nuclei combine to form a heavier nucleus, releasing even more energy than fission. Fusion is what powers the sun and other stars, where hydrogen nuclei fuse into helium under extreme temperatures (around 15 million °C) and pressures.

Both processes convert a tiny amount of mass into energy, described by Einstein's mass-energy equivalence equation:

$E = mc^2$

• E = energy produced
• m = mass lost during the reaction
• c = speed of light ($3 \times 10^8$ m/s)

Because $c^2$ is such a huge number, even a very small loss of mass produces an enormous amount of energy. For example, the fission of just 1 kg of U-235 releases roughly the same energy as burning 2,700 metric tons of coal.

Nuclear Binding Energy

Binding energy is the energy required to break an atomic nucleus apart into its individual protons and neutrons. The higher the binding energy per nucleon, the more stable the nucleus.

You can calculate binding energy with this equation:

$BE = [Zm_p + (A - Z)m_n - m_{nucleus}]c^2$

• Z = atomic number (number of protons)
• A = mass number (protons + neutrons)
• $m_p$ = mass of a proton
• $m_n$ = mass of a neutron
• $m_{nucleus}$ = measured mass of the nucleus

The key idea: the nucleus always weighs slightly less than the sum of its individual parts. That "missing" mass (called the mass defect) has been converted into binding energy holding the nucleus together.

Iron-56 has the highest binding energy per nucleon of any element, making it the most stable nucleus. This is why fission works best with elements heavier than iron (splitting them moves toward iron's stability), and fusion works best with elements lighter than iron (combining them also moves toward iron's stability).

Nuclear Chain Reaction

Self-Sustaining Fission Process

A chain reaction happens when the neutrons released by one fission event go on to trigger additional fission events, which release more neutrons, and so on. Here's how it works step by step:

1. A neutron strikes a U-235 nucleus, causing it to split.
2. The fission releases energy plus 2-3 new neutrons.
3. Those neutrons hit other U-235 nuclei, causing more fission events.
4. Each new fission releases another 2-3 neutrons, and the process repeats.

Without any control, this leads to an exponential increase in reactions (the principle behind nuclear weapons). In a nuclear reactor, two tools keep the reaction steady:

• Neutron moderators (water, graphite) slow neutrons down. Slower neutrons are actually more likely to cause fission in U-235 than fast ones.
• Control rods (made of neutron-absorbing materials like boron or cadmium) soak up excess neutrons. Pushing the rods further into the reactor slows the reaction; pulling them out speeds it up.

Critical Mass and Reaction Control

Critical mass is the minimum amount of fissile material needed to sustain a chain reaction. If too many neutrons escape the material without hitting another nucleus, the reaction fizzles out.

• Subcritical mass: Not enough fissile material. Neutrons escape faster than new ones are produced, and the chain reaction dies.
• Critical mass: Exactly enough material to keep the reaction self-sustaining at a steady rate. This is how reactors operate.
• Supercritical mass: More than enough material. The number of fission events increases exponentially.

Critical mass depends on several factors: the purity of the fissile material, its shape and geometry (a sphere minimizes surface area, reducing neutron escape), and whether neutron reflectors surround the material to bounce escaping neutrons back in. Weapons-grade uranium requires much higher enrichment (90%+ U-235) compared to reactor-grade fuel (3-5% U-235).

Nuclear Power and Waste

Nuclear Reactor Design and Operation

Nuclear reactors generate electricity by harnessing heat from controlled fission reactions. The basic process works like this:

1. Fuel rods containing enriched uranium (typically uranium dioxide) undergo fission in the reactor core, producing intense heat.
2. A coolant (usually water, sometimes liquid metal) circulates through the core and absorbs that heat.
3. The heated coolant transfers its energy to water in a steam generator, producing high-pressure steam.
4. The steam spins turbines connected to electrical generators, producing electricity.
5. Control rods are raised or lowered to regulate the fission rate and adjust power output.

Common reactor types include pressurized water reactors (PWRs), boiling water reactors (BWRs), and fast neutron reactors. They differ mainly in what fuel, moderator, and coolant they use, but the core principle is the same: controlled fission produces heat, and that heat ultimately drives a turbine.

Nuclear Waste Management and Disposal

Nuclear waste consists of spent fuel rods and other radioactive materials produced during reactor operation. It's classified by how radioactive it is and how long it remains hazardous:

• Low-level waste: Lightly contaminated items like clothing and tools. Radioactivity fades within years to decades.
• Intermediate-level waste: Reactor components and chemical residues. Requires shielding but less intensive long-term management.
• High-level waste: Spent fuel rods and reprocessing byproducts. Extremely radioactive and generates significant heat. Remains dangerous for thousands of years.

Spent fuel rods are first stored in water-filled cooling pools for several years to reduce their heat and radioactivity. After cooling, they can be moved to dry cask storage (sealed steel and concrete containers) for longer-term holding. The ultimate goal is permanent disposal in deep geological repositories, stable rock formations hundreds of meters underground.

Reprocessing is another option: extracting usable uranium and plutonium from spent fuel to be recycled into new fuel rods. This reduces waste volume but raises concerns about nuclear proliferation, since the separated plutonium could potentially be used in weapons.

The major challenges of nuclear waste remain its extremely long hazard period, the risk of environmental contamination, and the difficulty of ensuring secure storage over thousands of years. Research into advanced reactor designs (like thorium reactors and Generation IV concepts) aims to produce less waste and improve overall safety.