Fission Knowledge-Based Study

Study notes

1. What is Nuclear Fission?

   Nuclear fission is a nuclear reaction in which a heavy, unstable atomic nucleus absorbs a neutron and splits into two or more smaller, more stable nuclei (called fission fragments), accompanied by the release of additional neutrons and a large quantity of energy.

   Unlike ordinary chemical reactions, which involve the rearrangement of valence electrons and conserve atomic identities, fission alters the composition of the atomic nucleus itself, transforming one chemical element into others.

   • Parent Nucleus: A heavy nuclide with a high mass number, such as uranium-235 ($^{235}_{92}\text{U}$) or plutonium-239 ($^{239}_{94}\text{Pu}$).
   • Inducing Particle: Typically a low-energy thermal neutron that destabilizes the target nucleus.
   • Fission Products: Medium-mass daughter nuclei, which are usually radioactive and neutron-rich.
   • Prompt Neutrons: Two to three fast-moving free neutrons emitted during the splitting event.

   How Fission Occurs

   Nuclear fission is often induced when a fissile nucleus captures a thermal (slow) neutron. Upon capture, the nucleus enters an excited compound state. The electrostatic repulsive forces between the large number of protons overcome the short-range strong nuclear force holding the nucleons together, causing the nucleus to elongate and ultimately sever into two lighter fragments.

   Balancing Nuclear Fission Equations

   In every nuclear equation, two fundamental conservation laws must be obeyed:

   1. Conservation of Mass Number ($A$): The sum of mass numbers of the reactants equals the sum of mass numbers of the products.
   2. Conservation of Atomic Number ($Z$): The sum of atomic numbers (nuclear charges) of the reactants equals the sum of atomic numbers of the products.

   A representative fission pathway for uranium-235 is:

   $$^{235}_{92}\text{U} + \,^{1}_{0}\text{n} \longrightarrow \,^{236}_{92}\text{U}^* \longrightarrow \,^{141}_{56}\text{Ba} + \,^{92}_{36}\text{Kr} + 3\,^{1}_{0}\text{n} + \text{energy}$$

   Checking conservation:

   • Mass numbers: $235 + 1 = 141 + 92 + (3 \times 1) = 236$
   • Atomic numbers: $92 + 0 = 56 + 36 + (3 \times 0) = 92$

   Nuclear Chain Reactions

   Each fission event of $^{235}_{92}\text{U}$ releases an average of 2 to 3 free neutrons. If at least one of these secondary neutrons is captured by another fissile nucleus, a self-sustaining sequence called a nuclear chain reaction is established.

   Stages of Criticality

   The progression of a chain reaction depends on the effective neutron multiplication factor ($k$), defined as the ratio of neutrons produced by fission in one generation to the number of neutrons absorbed or lost in the preceding generation:

   • Subcritical ($k < 1$): Neutron loss exceeds neutron production. The rate of fission decreases over time, and the chain reaction eventually dies out.
   • Critical ($k = 1$): The rate of neutron production exactly balances the rate of neutron absorption and leakage. The reaction proceeds at a constant, steady rate (the operational state of commercial nuclear power reactors).
   • Supercritical ($k > 1$): Each fission generation produces more inducing neutrons than the last, causing an exponential increase in fission rate and energy output.

   Critical Mass: The minimum mass of fissile material required to maintain a continuous, self-sustaining nuclear chain reaction under specific geometric and physical conditions.

   Origin of Fission Energy

   The enormous amount of energy liberated during nuclear fission originates from the conversion of nuclear mass into energy, governed by Albert Einstein's mass-energy equivalence principle:

   $$E = \Delta m c^2$$

   Where:

   • $E$ is the released energy in joules ($\text{J}$),
   • $\Delta m$ is the mass defect in kilograms ($\text{kg}$),
   • $c$ is the speed of light in a vacuum ($\approx 3.00 \times 10^8\text{ m/s}$).

   Why Mass is Lost

   The total rest mass of the resulting fission fragments and emitted neutrons is slightly less than the combined mass of the initial target nucleus and the incident neutron. This difference ($\Delta m$) corresponds to an increase in nuclear binding energy per nucleon: the medium-mass daughter nuclei have higher binding energy per nucleon than the heavy parent nucleus, making them more tightly bound and energetically stable.

   A single fission of uranium-235 yields approximately $200\text{ MeV}$ of energy, primarily in the form of kinetic energy of the fission fragments, which is transferred as thermal energy (heat) to the surrounding medium.

   Controlled Fission in Nuclear Power

   Nuclear reactors harness the heat produced by controlled fission chain reactions to produce steam, drive turbines, and generate electricity without direct greenhouse gas emissions.

   Key Reactor Components

   • Fuel Elements: Enriched uranium (typically containing 3% to 5% $^{235}_{92}\text{U}$) fabricated into ceramic pellets and sealed in metal fuel rods.
   • Moderator: A substance composed of light atoms (such as light water, heavy water, or graphite) that slows down fast fission neutrons into thermal neutrons through elastic collisions, significantly increasing the probability of further fission events.
   • Control Rods: Materials with high neutron-absorption cross-sections (such as cadmium, boron, or hafnium). Inserting control rods absorbs excess neutrons and reduces the reaction rate; withdrawing them increases $k$.
   • Coolant: A circulating fluid (commonly pressurized water or liquid sodium) that removes heat from the reactor core and transfers it to a steam generator.
   • Containment Structure: Thick steel and reinforced concrete shielding designed to prevent radioactive materials from escaping into the environment.