Nuclear Fission and Fusion

Cheatsheet Content

Nuclear Fission Nuclear fission is a nuclear reaction in which a heavy nucleus splits into two or more smaller nuclei, along with a few neutrons and a large amount of energy. This process is typically initiated by bombarding a heavy nucleus with a neutron. Process Overview Neutron Absorption: A heavy, unstable nucleus (e.g., Uranium-235) absorbs a neutron. Nucleus Instability: The absorption makes the nucleus highly unstable and excited. Fission: The unstable nucleus splits into two or more smaller "daughter" nuclei, typically releasing 2-3 new neutrons. Energy Release: A significant amount of energy is released due to the mass defect (mass of products is less than mass of reactants). This energy is primarily kinetic energy of the fission products and gamma rays. Chain Reaction: The released neutrons can then strike other heavy nuclei, causing further fission events, leading to a chain reaction. Example: Uranium-235 Fission A common fission reaction involves Uranium-235: $$ ^{235}_{92}\text{U} + ^1_0\text{n} \rightarrow ^{236}_{92}\text{U}^* \rightarrow ^{141}_{56}\text{Ba} + ^{92}_{36}\text{Kr} + 3^1_0\text{n} + \text{Energy} $$ Other fission products are possible, such as Xenon and Strontium. Energy Release Sequence Initial binding energy of $^{235}\text{U}$ is lower per nucleon compared to the fission products ($^{141}\text{Ba}$, $^{92}\text{Kr}$). The difference in binding energy is released as kinetic energy of the fission products and gamma rays. Approximately 200 MeV of energy is released per fission event. Diagram: Nuclear Fission U-235 Neutron Fission Ba-141 Kr-92 Energy Nuclear Fusion Nuclear fusion is a nuclear reaction in which two or more light atomic nuclei combine to form a heavier nucleus, releasing a tremendous amount of energy. This process powers stars, including our Sun. Process Overview Extreme Conditions: Requires extremely high temperatures (millions of Kelvin) and pressures to overcome the electrostatic repulsion between positively charged nuclei. Collision and Fusion: Under these conditions, light nuclei (e.g., isotopes of hydrogen) collide with sufficient kinetic energy to fuse. Formation of Heavier Nucleus: The nuclei combine to form a heavier nucleus. Particle Emission: Often, a neutron or other light particle is emitted. Energy Release: A colossal amount of energy is released due to the mass defect. The binding energy per nucleon of the product nucleus is significantly higher than that of the reactants. Example: Deuterium-Tritium (D-T) Fusion One of the most promising fusion reactions for energy generation on Earth: $$ ^2_1\text{H} + ^3_1\text{H} \rightarrow ^4_2\text{He} + ^1_0\text{n} + \text{Energy} $$ Where $^2_1\text{H}$ is Deuterium and $^3_1\text{H}$ is Tritium. Energy Release Sequence The binding energy per nucleon for Helium-4 ($^4_2\text{He}$) is much higher than for Deuterium and Tritium. This difference in binding energy is released as kinetic energy of the products (primarily the neutron) and gamma rays. Approximately 17.6 MeV of energy is released per D-T fusion event. While less per reaction than fission, fusion reactions are more energy-dense per unit mass of fuel. Diagram: Nuclear Fusion D ($^2_1$H) T ($^3_1$H) High T/P He-4 Neutron Energy Comparison Feature Fission Fusion Process Heavy nucleus splits Light nuclei combine Fuel Uranium, Plutonium Deuterium, Tritium Conditions Neutron bombardment Extremely high T & P Energy Release $\sim 200$ MeV per event $\sim 17.6$ MeV per D-T event (more energy-dense) Byproducts Radioactive waste, neutrons Helium, neutrons (less radioactive waste) Applications Nuclear power plants, atomic bombs Stars, hydrogen bombs (potential future energy source)