8.3 Nuclear Transmutation, Fission, and Fusion Study Notes

Transmutation is defined as the process of converting one nuclide into a different nuclide.
This conversion occurs through two primary mechanisms:
- Spontaneous Transmutation: Natural radioactive decay where unstable isotopes transform into more stable forms via five specific decay types.
- Induced Transmutation: Artificial processes conducted in laboratory environments, typically involving the bombardment of nuclei.
Induced transmutation often utilizes particle accelerators, which are sophisticated devices designed to increase the kinetic energy of particles. These devices employ electromagnetic fields within a vacuum to accelerate particles to high velocities before colliding them with target nuclei to produce new elements or particles.
A prominent modern example is the Large Hadron Collider (LHC) located near Geneva, Switzerland, which is used for the discovery of new subatomic particles and elements.

The first recorded instance of artificial transmutation was achieved by Ernest Rutherford in the year 1919.
Rutherford observed the transformation of nitrogen into oxygen by bombarding a nitrogen-14 nucleus with an alpha particle.
The reaction released a proton and resulted in a more stable isotope of oxygen, specifically oxygen-17.
Reactants and products of early experimental transmutation:
- Initial Target: Nitrogen ( $14$ mass number, $7$ atomic number).
- Projectile: Alpha particle ( $4$ mass number, $2$ atomic number).
- Resulting Nucleus: Oxygen ( $17$ mass number, $8$ atomic number).
- Ejected Particle: Proton ( $1$ mass number, $1$ atomic number).

Nuclear fission involves the fragmentation of a heavy, large nucleus into smaller pieces, accompanied by the release of substantial energy.
This process was the foundational principle behind the first nuclear weapons and continues to power modern nuclear reactors.
A standard fission example involves bombarding Uranium-235 ( $^{235}_{92}\text{U}$ ) with a neutron:
- The collision makes the uranium nucleus unstable, causing it to split.
- Common fission products include Barium-141 ( $^{141}_{56}\text{Ba}$ ) and Krypton-92 ( $^{92}_{36}\text{Kr}$ ).
Energy Statistics for Fission:
- The energy produced per mole of uranium fission is roughly $1.8 \times 10^{10}\,kJ\,mol^{-1}$ .
- In comparison to chemical reactions, the energy from fission is orders of magnitude higher. For instance, the fission of one kilogram of Uranium-235 generates approximately $2,500,000$ times more energy than the combustion of one kilogram of octane or coal.

A nuclear chain reaction occurs when the neutrons released during a single fission event proceed to strike and split adjacent nuclei, creating a self-sustaining cycle.
This process is exponential; a single neutron can trigger the release of multiple neutrons (e.g., three), which in turn trigger multiple subsequent fission events.
Fissile/Fissionable Material: Substances capable of maintaining a nuclear chain reaction (e.g., Uranium-235).
Critical Mass: The minimum quantity of fissionable material required to sustain a chain reaction. This threshold is influenced by factors such as:
- Material purity.
- Temperature.
- Nuclear geometry/shape.
Classification of mass thresholds:
- Subcritical Mass: A quantity of material where the rate of fission cannot be sustained; the reaction eventually dies out.
- Critical Mass: The exact amount needed to sustain the reaction at a constant rate.
- Supercritical Mass: A quantity where the fission rate increases rapidly and uncontrollably, characteristic of atomic explosions.

Nuclear fusion is the process of combining light nuclei to form a heavier, more stable nucleus.
Fusion generates even greater energy density than fission. For example, a fusion reaction can produce approximately $3,000,000$ times the energy of octane combustion.
Fusion in the Sun:
- The Sun functions via the fusion of four hydrogen nuclei to create a single helium nucleus.
- This process also produces two positrons ( $0, +1$ particles).
- The energy yield is approximately $3.6 \times 10^{11}\,kJ\,mol^{-1}$ of helium produced.
Advantages of Fusion over Fission:
- Minimal radioactive waste production compared to fission byproducts.
- Lower risk of catastrophic nuclear accidents (referencing historical events like Three Mile Island and Fukushima).
- Potential for a nearly inexhaustible source of clean energy.
Current limitations: Achieving the high-temperature and high-pressure conditions necessary for sustained fusion remains a significant technological challenge on Earth.