Nuclear Fission
Nuclear fission is a nuclear reaction in which a heavy atomic nucleus (such as uranium-235 or plutonium-239) splits into two or more lighter nuclei, releasing a large amount of energy and typically two or three neutrons. The energy released comes from the binding energy difference between the original nucleus and the products, as described by Einstein's mass-energy equivalence (E = mc²). Controlled fission is the basis of nuclear power plants, while uncontrolled rapid fission is the mechanism of nuclear (fission) bombs.
Key Formula
ΔE = Δm × c²
LaTeX: \Delta E = \Delta m \cdot c^2
| Symbol | Meaning | Unit |
|---|---|---|
| ΔE | Energy released in the reaction | Joule (J) or MeV |
| Δm | Mass defect (mass of reactants minus products) | kilogram (kg) or u |
| c | Speed of light (3 × 10⁸ m/s) | m/s |
Worked Example
Problem
A U-235 nucleus absorbs a neutron and undergoes fission: ²³⁵U + n → ¹⁴¹Ba + ⁹²Kr + 3n. Given masses: U-235 = 235.0439 u, n = 1.0087 u, Ba-141 = 140.9144 u, Kr-92 = 91.9262 u. Calculate the energy released. (1 u = 931.5 MeV/c²)
Solution
Step 1: Mass of reactants = 235.0439 + 1.0087 = 236.0526 u. Step 2: Mass of products = 140.9144 + 91.9262 + 3(1.0087) = 140.9144 + 91.9262 + 3.0261 = 235.8667 u. Step 3: Mass defect Δm = 236.0526 − 235.8667 = 0.1859 u. Step 4: Energy released ΔE = 0.1859 u × 931.5 MeV/u = 173.2 MeV. Step 5: Convert to joules: 173.2 MeV × 1.602 × 10⁻¹³ J/MeV = 2.77 × 10⁻¹¹ J per fission event.
Answer
ΔE ≈ 173 MeV (2.77 × 10⁻¹¹ J) per fission event; for 1 kg of U-235 fully fissioned this is ~8.2 × 10¹³ J
Comparison of Fission Fuel Characteristics
| Fuel Isotope | Natural Abundance | Critical Mass (sphere) | Energy per Fission | Main Use |
|---|---|---|---|---|
| Uranium-235 | 0.72% | ~52 kg (bare) | ~202 MeV | Power reactors, weapons |
| Uranium-238 | 99.3% | Not fissile (fertile) | ~5 MeV (fast only) | Breeder reactors |
| Plutonium-239 | Artificial | ~10 kg (bare) | ~207 MeV | Power reactors, weapons |
| Thorium-232 | 100% | Not fissile (fertile) | Breeds U-233 | Thorium reactors (R&D) |
| Uranium-233 | Artificial (from Th) | ~16 kg (bare) | ~200 MeV | Experimental reactors |
| Californium-252 | Artificial | ~2.73 kg | ~220 MeV | Neutron source |
Interactive Tools
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Related Terms
Mass-Energy Equivalence
Mass-energy equivalence is the principle, derived from Einstein's special theory of relativity, stating that mass and energy are two forms of the same physical quantity and can be converted into each other. Expressed by the famous equation E = mc², it reveals that even a small amount of mass corresponds to an enormous amount of energy, since c² (the square of the speed of light) is approximately 9 × 10¹⁶ m²/s². This principle underlies the energy released in nuclear fission and fusion reactions, and explains the origin of stars' energy output.
Nuclear Fusion
Nuclear fusion is a nuclear reaction in which two light atomic nuclei (typically isotopes of hydrogen — deuterium and tritium) combine to form a heavier nucleus, releasing an enormous amount of energy. The energy released greatly exceeds that of fission per unit mass, and the fuel (hydrogen isotopes) is abundant, making fusion the energy source of stars including the Sun. Fusion requires extremely high temperatures (tens of millions of kelvin) to overcome the Coulomb repulsion between positively charged nuclei, which is why sustaining controlled fusion on Earth for power generation remains a major technological challenge being pursued by projects such as ITER and NIF.
Special Relativity
Special relativity is a physical theory proposed by Albert Einstein in 1905 that describes the relationship between space and time for objects moving at constant velocities, particularly near the speed of light. It is founded on two postulates: the laws of physics are identical in all inertial frames of reference, and the speed of light in a vacuum is constant for all observers regardless of their motion. The theory reveals that time, length, and mass are not absolute but depend on the relative motion between observer and object, unifying space and time into a single four-dimensional continuum called spacetime.
From Latin "fissio" (splitting, cleaving), from "findere" (to split). The term was introduced by physicists Otto Frisch and Lise Meitner in their January 1939 paper in Nature, by analogy with binary fission in biology. Frisch chose the word after consulting a biologist about the closest equivalent term.