Visualize exponential radioactive decay N(t) = N₀e^(−λt) in real time. Plot half-life, decay constant, and activity change on graphs. Supports uranium series, Bateman decay chains, and radiocarbon dating calculations.
Alpha decay emits a helium nucleus (⁴He) and has low penetration, stopped by paper. Beta decay emits an electron or positron and has moderate penetration, stopped by a few millimeters of metal. Gamma decay emits high-energy photons and has high penetration, requiring lead shielding.
A decay chain is a sequence in which the daughter nuclide produced by one decay is also radioactive and decays again. Uranium-238 becomes stable lead-206 after 14 decay steps in the uranium series. Because each step has a different half-life, long-term activity prediction requires solving coupled differential equations.
PET imaging uses fluorine-18, with a half-life of about 110 minutes, in glucose-like tracers to image metabolically active regions such as tumors. Short half-lives help reduce exposure while preserving diagnostic usefulness. Iodine-131, with an 8-day half-life, is used in thyroid therapy because it concentrates selectively in thyroid tissue.
Becquerel (Bq) counts decays per second, while sievert (Sv) estimates biological dose effect in the human body. The same Bq value can have different biological impact depending on radiation type; alpha radiation has a much larger weighting factor than beta or gamma radiation.
| Nuclide | Half-life | Decay Type | Main Uses / Issues |
|---|---|---|---|
| Hydrogen-3 (tritium) | 12.3 yr | β⁻ | Fusion research, water contamination tracing |
| Carbon-14 | 5,730 yr | β⁻ | Radiocarbon dating |
| Iodine-131 | 8.02 days | β⁻+γ | Thyroid cancer therapy, nuclear accident monitoring |
| Cesium-137 | 30.17 yr | β⁻+γ | Nuclear accident contamination |
| Radium-226 | 1,600 yr | α | Historical radium therapy, luminous paint |
| Plutonium-239 | 24,110 yr | α | Nuclear weapons, reactor fuel |
| Uranium-235 | 704 million yr | α | Fission fuel, nuclear weapons |
| Uranium-238 | 4.47 billion yr | α | Uranium-lead dating in geology |
Half-life means the time for half of this nuclide to remain, right? But all the atoms do not decay at the same time, do they?
Exactly. Individual atoms decay randomly, and half-life is a statistical average. With about $10^{23}$ atoms, the law of large numbers makes the sample follow $N(t)=N_0 e^{-\lambda t}$ very closely. For a single atom, it means there is a 50% chance it has decayed after one half-life.
How does carbon-14 dating tell us the age of something from the past?
Living organisms continuously exchange carbon with the atmosphere through respiration and food, so their ${}^{14}C/{}^{12}C$ ratio stays close to the atmospheric value. After death, intake stops and ${}^{14}C$ decays with a 5,730-year half-life. Measuring the current ratio gives the age from $t = \frac{t_{1/2}}{\ln 2} \ln\!\left(\frac{N_0}{N}\right)$.
Cesium-137 became a problem after nuclear accidents because its half-life is about 30 years, right?
Right. Iodine-131 has an 8-day half-life, so it mostly disappears within a few months. Cesium-137 lasts about 30 years, roughly a human generation. It can bind to soil, enter food chains, and keep internal-exposure risk relevant for a long time. Tritium and plutonium-239 pose different problems because their half-lives are very different.
What is a decay chain? Uranium-238 does not become stable lead in one step, does it?
Correct. Uranium-238 reaches lead-206 through 14 decay steps. Intermediate nuclides include radon-222, a gas with a 3.8-day half-life, and polonium-210. Radon can enter buildings from soil and is a major natural radiation source linked to lung cancer risk. In a decay chain, the number of atoms of each intermediate nuclide is found by solving coupled differential equations.
| Decay Type | Emitted Particle | Penetration | Atomic Number Change | Example |
|---|---|---|---|---|
| Alpha decay | Helium nucleus (He-4) | Stopped by paper | Z: -2, A: -4 | U-238 → Th-234 |
| Beta-minus decay | Electron + antineutrino | A few mm of aluminum | Z: +1, A: unchanged | Cs-137 → Ba-137 |
| Beta-plus decay | Positron + neutrino | Low, followed by annihilation radiation | Z: -1, A: unchanged | F-18 → O-18 (PET) |
| Gamma decay | High-energy photon | Requires lead or concrete | No change; excited state relaxes | Co-60 → Ni-60 + γ |
| Electron capture | Characteristic X-ray + neutrino | Low | Z: -1, A: unchanged | I-125 → Te-125 |
Radioactive Decay Chain is a fundamental topic in engineering and applied physics. This interactive simulator lets you explore the key behaviors and relationships by directly manipulating parameters and observing real-time results.
By combining numerical computation with visual feedback, the simulator bridges the gap between abstract theory and physical intuition — making it an effective learning tool for students and a rapid-verification tool for practicing engineers.
The simulator is based on the governing equations behind Radioactive Decay Chain Simulator. Understanding these equations is key to interpreting the results correctly.
Each parameter in the equations corresponds to a slider in the control panel. Moving a slider changes the equation's solution in real time, helping you build a direct connection between mathematical expressions and physical behavior.
Engineering Design: The concepts behind Radioactive Decay Chain Simulator are applied across mechanical, structural, electrical, and fluid engineering disciplines. This tool provides a quick way to estimate design parameters and sensitivity before committing to full CAE analysis.
Education & Research: Widely used in engineering curricula to connect theory with numerical computation. Also serves as a first-pass validation tool in research settings.
CAE Workflow Integration: Before running finite element (FEM) or computational fluid dynamics (CFD) simulations, engineers use simplified models like this to establish physical scale, identify dominant parameters, and define realistic boundary conditions.
Model assumptions: The mathematical model used here relies on simplifying assumptions such as linearity, homogeneity, and isotropy. Always verify that your real system satisfies these assumptions before applying results directly to design decisions.
Units and scale: Many calculation errors arise from unit conversion mistakes or order-of-magnitude errors. Pay close attention to the units shown next to each parameter input.
Validating results: Always sanity-check simulator output against physical intuition or hand calculations. If a result seems unexpected, review your input parameters or verify with an independent method.