Radioactive Decay Simulation
Radioactive decay is one of the most elegant examples of randomness in nature. Although we can never predict exactly when a single unstable nucleus will decay, large groups of atoms follow beautifully consistent mathematical patterns. Use our interactive radioactive decay simulation to watch individual isotopes decay in real time and compare their behaviour to the ideal exponential decay curve. Adjust the initial population and half‑life to see how these factors shape the process.
Unfortunately the simulation is not compatible with mobile devices. For the best experience please view this page on a desktop.
Quick Guide to using the Nuclear Chain Reaction Simulation
INITIAL ISOTOPE POPULATION – Determines how many radioactive particles the simulation starts with.
HALF-LIFE – Controls how quickly the isotopes decay over time.
START – Sets the simulation going with the selected parameters. The simulation animates individual decays and plots the results. Press Pause to temporarily stop it. Press Resume to continue.
PARTICLE FIELD – Each dot represents one isotope, updating in real time. Green dots are still undecayed. Grey dots have decayed. The pattern becomes more sparse as time passes.
GRAPH – The graph shows how the simulation matches the theoretical model. The blue line tracks the random decay from the simulation. The orange line represents ideal exponential decay. Watch how randomness averages out over time.
RESET – Clears the graph and particle field. Choose new slider values and start again.
What Is Radioactive Decay?
Radioactive decay is a natural process in which unstable atomic nuclei transform into more stable forms by releasing energy or particles. This happens because some nuclei have an imbalance of forces inside them, making them energetically unstable. Over time, they spontaneously change into different elements or isotopes.
A key feature of radioactive decay is that it is random at the level of individual atoms. There is no way to predict exactly when a specific nucleus will decay. However, when you observe large numbers of atoms, their behaviour becomes highly predictable and follows smooth mathematical patterns.
The Role of Probability
Each unstable nucleus has a constant probability of decaying in any given moment. This probability does not change over time. A nucleus that has existed for one second or one million years is no more or less likely to decay in the next moment. This constant probability leads to an exponential decay pattern when many atoms are observed together.
Because each nucleus decays independently and with the same probability per unit time, the rate of decay is always proportional to the number of nuclei still present. This creates a smooth exponential curve when plotted, even though the underlying process is random.
What Is Half‑Life?
The half‑life of a radioactive substance is the time it takes for half of the original nuclei in a sample to decay. After one half‑life, 50% remain; after two half‑lives, 25% remain; after three, 12.5%, and so on. The amount never reaches zero, but it becomes smaller and smaller in a predictable way.
Half‑life is extremely useful because it is a fixed property of each radioactive isotope. It does not depend on temperature, pressure, chemical bonding, or the amount of material present. Some isotopes decay almost instantly, with half‑lives measured in microseconds, while others decay so slowly that their half‑lives stretch into millions or billions of years. This wide range makes half‑life a powerful tool in fields such as archaeology, geology, medicine, and nuclear science.