Radioactive Decay and Half-Life Simulation

About this experiment

You can never say when one radioactive nucleus will decay. It might be in the next second or in a thousand years. But in a large sample, the same share of the nuclei decays in every equal stretch of time, so the number left halves again and again at a steady rate. That time is the half-life. Watch a sample of nuclei decay at random, listen to the Geiger counter, compare the result with the smooth prediction, and see why bigger samples follow the curve more closely.

Learning goals

Describe radioactive decay as a random process
Define half-life and read it from a decay curve
Calculate the amount left after a whole number of half-lives
Explain why activity falls in the same way as the number of nuclei
Explain why small samples follow the prediction less closely than large ones

How to use it

1Press Start and watch. Can you predict which nucleus will decay next?
2Use Next half-life three times. Record the number left each time and compare with 400, 200, 100, 50.
3Press New sample a few times with 100 nuclei. How much does the measured half-life change? Repeat with 1600 nuclei.
4Switch the graph to Activity. How does the activity change after each half-life?
5Change the isotope. Does the shape of the graph change, or only the time scale?
6Switch on Geiger counter clicks and listen to the count rate fall as the sample decays.

The model

N = N_{0} (\frac{1}{2})^{t / t_{1/2}}

Number of undecayed nuclei after time t

N = N_{0} e^{- λ t}, λ = \frac{ln 2}{t _{1/2}}

The same law written with the decay constant λ

A = λ N

Activity: decays per second, proportional to the nuclei left

t = t_{1/2} lo g_{2} \frac{N _{0}}{N}

Age of a sample from the fraction still undecayed, as used in carbon dating

Assumptions

Each nucleus decays independently with the same probability per unit time. Decay times are drawn from a seeded random generator, so each sample number always gives the same result.
Time is measured in half-lives and converted to seconds, days or years for the chosen isotope. The playback speed only changes how fast the clock runs on screen.
The products of the decay are not radioactive here. Real decay chains, such as that of uranium-238, contain many radioactive daughters.
There is no background radiation, and the Geiger counter detects every decay.

Try this in class

Q1A sample of iodine-131 has an activity of 800 Bq. What will its activity be after 24 days?
Q2After how many half-lives is less than 1 % of the sample left?
Q3A piece of wood has 25 % of the carbon-14 of living wood. How old is it?
Q4Why is it impossible to say exactly when a single nucleus will decay, even though the half-life is known precisely?
Q5Why are isotopes with short half-lives used for medical tracers instead of isotopes with long half-lives?

Frequently asked questions

Does a nucleus get more likely to decay as it gets older?

No. A nucleus does not age. The chance that it decays in the next second is the same whether it was made a moment ago or a billion years ago. That is why the same share decays in every half-life.

Why is the measured half-life not exactly 1?

Because decay is random. In a sample of 100 nuclei, the time for 50 to decay varies from one sample to the next. With more nuclei the variation shrinks; real samples contain billions of billions of nuclei, so they follow the curve almost exactly.

Can heating or pressure change the half-life?

Practically no. Radioactive decay happens inside the nucleus, and ordinary temperatures, pressures and chemical reactions hardly affect it. This is what makes radioactive dating reliable.