Nuclear Fission

Nuclear fission is a nuclear reaction or a radioactive decay process in which the nucleus of an atom splits into two or more smaller, lighter nuclei. This process often releases a significant amount of energy, along with photons (in the form of gamma rays) and free neutrons. Nuclear fission of heavy elements was discovered on December 17, 1938, by German chemist Otto Hahn and his assistant Fritz Strassmann, and interpreted theoretically in early 1939 by Lise Meitner and her nephew Otto Robert Frisch.

Short Definition

Nuclear fission is the process by which a heavy atomic nucleus, such as Uranium-235 or Plutonium-239, absorbs a neutron or undergoes spontaneous instability, causing it to divide into two smaller nuclei of roughly equal mass. This division is accompanied by the release of a large amount of energy, typically around 200 MeV per fission event, due to the difference in binding energy between the parent nucleus and the resulting fission fragments.

Detailed Explanation

The mechanism of nuclear fission is best understood through the Liquid Drop Model of the nucleus. In this model, the nucleus is treated as a drop of incompressible nuclear fluid held together by the strong nuclear force, which competes against the electrostatic repulsion of the protons.

The Fission Process

When a heavy nucleus captures a low-energy (thermal) neutron, it enters an excited state. This excitation energy causes the nucleus to vibrate and deform. If the deformation is severe enough, the nucleus reaches a "saddle point" where the strong nuclear force can no longer overcome the Coulomb repulsion between the two bulging halves. At this stage, the nucleus elongates into a "scission" shape and eventually snaps into two distinct fission fragments.

Energy Release and Mass Defect

The energy released during fission arises from the fact that the total mass of the resulting fission products and neutrons is less than the original mass of the heavy nucleus and the initiating neutron. This "missing mass" is known as the mass defect (##\Delta m##). According to Einstein’s mass-energy equivalence principle, this mass is converted into kinetic energy and electromagnetic radiation.

The distribution of the 200 MeV released in a typical U-235 fission event is approximately:

• Kinetic energy of fission fragments: ~165 MeV
• Kinetic energy of prompt neutrons: ~5 MeV
• Energy of prompt gamma rays: ~7 MeV
• Energy from beta decay of fragments: ~7 MeV
• Energy from delayed gamma rays: ~6 MeV
• Energy carried away by neutrinos: ~10 MeV (this energy is usually lost as neutrinos rarely interact with matter)

Chain Reactions and Criticality

A single fission event produces multiple neutrons (on average 2.4 to 3.0 depending on the isotope). If these neutrons go on to induce fission in neighboring nuclei, a self-sustaining sequence called a chain reaction occurs.

The state of a chain reaction is described by the multiplication factor (##k##):

• Subcritical (k < 1): The number of fissions decreases over time; the reaction dies out.
• Critical (k = 1): The number of fissions remains constant; this is the steady state required for nuclear power plants.
• Supercritical (k > 1): The number of fissions increases exponentially; this is the state utilized in nuclear weapons or during the startup of a reactor.

Fission Product Distribution

Fission does not usually split the nucleus into two equal halves. Instead, it typically results in a "double-humped" distribution of mass numbers. For Uranium-235, the most common mass numbers for fragments are around 95 (e.g., Strontium, Krypton) and 137 (e.g., Barium, Cesium).

Key Formula / Principle

The fundamental principle governing the energy release in nuclear fission is Einstein's mass-energy equivalence formula:

Where:

• ##E## is the energy released (Joules).
• ##\Delta m## is the mass defect (kg), calculated as ##m_{initial} - m_{final}##.
• ##c## is the speed of light in a vacuum (approximately ##3 \times 10^8## m/s).

In the context of a specific reaction, such as the fission of Uranium-235 by a neutron:

Where ##Q## represents the disintegration energy (Q-value). To calculate ##Q##, one sums the atomic masses of the reactants and subtracts the atomic masses of the products:

Important Characteristics

1. Cross-Section

The probability that a fission reaction will occur is measured by the "nuclear cross-section," denoted by ##\sigma##. It is measured in units called barns (##1 \text{ barn} = 10^{-28} \text{ m}^2##). For U-235, the cross-section for fission is significantly higher for slow-moving "thermal" neutrons than for fast neutrons.

2. Prompt vs. Delayed Neutrons

Most neutrons (over 99%) are released almost instantaneously (within ##10^{-14}## seconds) and are called prompt neutrons. However, a small fraction (less than 1%) are emitted by the fission fragments after a delay ranging from milliseconds to minutes. These delayed neutrons are critical for the control of nuclear reactors, as they provide a time buffer for mechanical control systems to adjust the reaction rate.

3. Fissile vs. Fertile Materials

Not all heavy isotopes can undergo fission with thermal neutrons.

• Fissile materials: Can sustain a chain reaction with thermal neutrons (e.g., U-235, Pu-239, U-233).
• Fertile materials: Cannot easily undergo fission themselves but can be converted into fissile materials via neutron capture (e.g., U-238 becomes Pu-239; Th-232 becomes U-233).

Practical Example

In a Pressurized Water Reactor (PWR), the most common type of nuclear power plant, nuclear fission is used to generate heat.

Common Confusions or Misconceptions

• Fission vs. Fusion: Fission is the splitting of a heavy nucleus into lighter ones, whereas fusion is the joining of light nuclei (like Hydrogen) to form a heavier one (like Helium). Both release energy, but fusion requires extreme temperatures and pressures.
• Radioactivity vs. Fission: While fission is a form of nuclear reaction, it is not the same as simple alpha or beta decay. Fission involves a massive structural failure of the nucleus, whereas standard radioactive decay involves the emission of small particles to reach a more stable state.
• "Atomic" vs. "Nuclear": Though often used interchangeably (e.g., "atomic bomb"), the term "nuclear" is more scientifically accurate because the energy originates from the nucleus, not the electron shells of the atom.
• Reactor Explosions: A commercial nuclear reactor cannot explode like a nuclear bomb. The enrichment levels of U-235 in a reactor (3-5%) are far too low to support the uncontrolled, lightning-fast supercriticality required for a nuclear explosion (which requires >90% enrichment).

Related Terms

• Isotope: Atoms of the same element with the same number of protons but different numbers of neutrons.
• Binding Energy: The energy required to disassemble a nucleus into its constituent protons and neutrons.
• Half-life: The time required for half of a sample of radioactive material to decay.
• Enrichment: The process of increasing the percentage of a specific isotope (usually U-235) in a sample of uranium.
• Neutron Poison: A material with a high neutron absorption cross-section that "poisons" the chain reaction (e.g., Xenon-135).

Why It Matters

Nuclear fission is a cornerstone of modern energy production and science for several reasons: