Lecture 34: Physics of Nuclear Fission and Fusion

Introduction to Nuclear Fission and Fusion

Lecture 34 explores the energy harnessed by the atomic nucleus through the processes of nuclear fission and fusion.
Key concepts discussed include:
- Nuclear fission mechanisms.
- Chain reactions and criticality.
- Nuclear power generation and its implications.
- Nuclear fusion and its occurrence in nature versus laboratory settings.

The Mechanism and History of Nuclear Fission

Radioactive Decay Recap: As established in previous lectures, decay occurs when a nucleus is unstable. This instability arises when the electromagnetic repulsion between protons becomes stronger than the strong nuclear force that binds the nucleus together.
Definition of Fission: Nuclear fission is the process where an atomic nucleus is split into two smaller nuclei. This occurs if an atom is artificially elongated, allowing electromagnetic repulsion to overcome the strong nuclear force.
Provocation Requirement: Fission is not typically a spontaneous process; it must be provoked by an external stimulus.
Historical Context:
- The observation of nuclear fission occurred in 1938.
- It was observed by scientists Otto Hahn, Fritz Strassmann, and Lise Meitner.
- The theoretical explanation for these observations was provided by Lise Meitner and her nephew Otto Frisch.

Mass-Energy Equivalence and the Origin of Energy

Mass Discrepancy: When an atom undergoes fission, the mass of the starting atom plus the bombarding particle is measured. After the split, the total mass of the byproducts is slightly smaller than the original mass.
Conservation of Mass-Energy: While mass and energy are often discussed as separate conserved quantities, they are intrinsically related. It is more accurate to speak of the "conservation of mass-energy."
Energy Generation: The energy released in fission comes directly from the mass that is lost during the process.
The Einstein Equation: The amount of energy created is quantified using the formula: $E = mc^2$
- $E$ represents the energy generated.
- $m$ represents the mass of the particles at rest (the "missing" mass).
- $c$ represents the speed of light ( $c \approx 3 \times 10^8\,m/s$ ).
Impact of the Speed of Light: Because the value of $c^2$ is an extremely large number, even a very small amount of mass can be converted into an enormous quantity of energy.

Atomic Weight and the Energy Potential of Elements

Susceptibility to Fission: Not all atoms are suitable for energy generation via fission.
The Iron Threshold:
- A graph of mass per nucleon shows that Hydrogen atoms have a high mass per nucleon.
- Uranium atoms also have a high mass per nucleon.
- Iron ( $Fe$ ) possesses the least mass per nucleon of any element.
Energy Release Directionality:
- Atoms heavier than Iron (like Uranium) release energy when they undergo nuclear fission (splitting toward the Iron state).
- Atoms lighter than Iron release energy when they undergo nuclear fusion (joining toward the Iron state).
Uranium-235 ( $^{235}U$ ):
- This is the primary source of nuclear power in the United States.
- It is a fissionable isotope of uranium.
- The Reaction: When a neutron is shot at ${}^{235}U$ , it splits into:
  - Krypton-92 ( ${}^{92}Kr$ ).
  - Barium-141 ( ${}^{141}Ba$ ).
  - Three additional neutrons.
- Conservation in Reaction: In this process, the total number of nucleons and the total charge are conserved, even though rest mass is converted to energy.
Use of Neutrons: Neutrons are used to provoke fission rather than protons because they are electrically neutral. This allows them to approach the nucleus without being deflected by electromagnetic repulsion forces.

Chain Reactions and Criticality

Definition of Chain Reaction: A self-sustaining fission process that does not require further external intervention once started.
Mechanism: In a reaction like that of ${}^{235}U$ , the three neutrons generated by the first fission event can strike neighboring atoms, causing them to undergo fission and release even more neutrons.
Critical Mass: The minimum amount of fissionable material required to sustain a chain reaction. If a critical mass is present in a specific configuration, an explosion resulting in a massive energy release can occur, which is the principle behind nuclear weapons.
Levels of Criticality:
1. Subcritical: On average, less than one new fission reaction is generated per single fission event. The reaction is not self-sustaining and will eventually stop.
2. Critical: On average, exactly one new fission reaction is generated per event. The reaction is self-sustaining and continues at a steady rate until the fuel is consumed. This is compared to a line of falling dominoes.
3. Supercritical: On average, more than one new fission event is generated per event. This leads to exponential growth.
Exponential Growth Data: Assuming one initial fission event starts the process, after 10 generations:
- Critical Reaction: 1 event occurring.
- Supercritical (2 neutrons/event): $512$ events occurring.
- Supercritical (3 neutrons/event): nearly $20000$ events occurring.
Control Rods: In nuclear power generation, supercritical reactions are avoided using control rods made of neutron-absorbing materials to maintain the reaction at the critical stage.

Nuclear Power Plants and Electricity Generation

Uranium Composition: Most natural uranium is Uranium-238 ( ${}^{238}U$ ), which is non-fissionable. It contains small amounts of ${}^{235}U$ .
Enrichment: The technical process of increasing the proportion of ${}^{235}U$ in a sample to make it suitable for fuel.
Reactor Components:
- Moderator: A substance used to slow down neutrons so they travel at the optimal speed to cause fission in ${}^{235}U$ .
- Control Rods: Absorbers that prevent the reaction from becoming supercritical.
Electricity Generation Process:
1. Water flows through the reactor, absorbing heat from the fission.
2. Heated water enters a heat exchanger to create steam.
3. Steam spins a turbine.
4. The turbine causes the relative rotation of a magnetic field and a coil of wire, generating electricity (as per the principles of electromagnetic induction).

Benefits and Drawbacks of Nuclear Energy

Benefits:
- Lack of Combustion: No fossil fuels are burned, resulting in zero greenhouse gas emissions during the fission process.
- Energy Density: Uranium is extremely energy-dense; one kilogram of uranium produces significantly more energy than an equivalent kilogram of coal, oil, or gas.
Drawbacks:
- Radioactivity: Small amounts of radioactivity can be released into the environment during processing.
- Proliferation: The enrichment process required for power can be diverted to create nuclear weapons.
- Waste Management: Fission byproducts are themselves radioactive and have extremely long half-lives, making safe storage a significant ongoing challenge.
- Disaster Risk: Potential for catastrophic failure in plant systems.
Historical Nuclear Accidents:
- Three Mile Island (United States).
- Chernobyl (Soviet Union/Ukraine).
- Fukushima (Japan).

Nuclear Fusion

Definition: The process of smashing light atomic nuclei together to form a heavier nucleus.
Mechanism: Crushing two hydrogen atoms together results in Helium. Because Helium has less mass per nucleon than Hydrogen, the "leftover" mass is converted into energy.
Primary Source: Fusion is the most prevalent energy source in the universe. Our Sun has been converting hydrogen to helium via fusion for 4.6 billion years and has enough fuel to continue for at least another 5 billion years.
Challenges on Earth:
- Electromagnetic Repulsion: Hydrogen nuclei (protons) strongly repel each other.
- High Speed/High Temperature: To overcome repulsion, atoms must move at extraordinarily high speeds, requiring intense heat and pressure.
- Current Status: While preliminary evidence suggests it may be possible to reach a "break-even" point (where energy produced equals energy required to start the reaction), we are far from creating a sustained fusion reaction capable of powering homes.