Radioactive half-life lab

Radioactive decay is random for each atom but beautifully predictable for a crowd. This simulation lets you decay thousands of virtual atoms and watch the classic half-life curve emerge. Learning goals: define half-life and use it to predict remaining amounts; explain why decay follows an exponential curve; compare isotopes by half-life and describe practical uses like carbon dating.

Half-lives elapsed: 0

100.0% of the original sample remains

After each half-life, half of what remains decays. The half-life never changes, no matter how much you start with.

Controls

Isotope selector: Chooses the isotope, each with its real half-life.
Initial atoms: Sets the starting number of radioactive atoms.
Time step: Advances the clock in steps of the chosen half-life.
Graph view: Toggles the decay curve and the remaining-fraction readout.

The chemistry

N = N_0\left(\tfrac{1}{2}\right)^{t/t_{1/2}}

Fraction remaining after time t

\lambda = \frac{\ln 2}{t_{1/2}}

Decay constant from half-life

A = \lambda N

Activity of a sample

Assumptions

Each atom decays randomly and independently.
The sample is large enough that the curve looks smooth.
Daughter products are not tracked in this model.

Guided activity

Start with 1000 atoms and advance one half-life at a time.
Plot remaining atoms versus time and identify the curve shape.
Compare a short half-life isotope with a long one over the same time span.
Show that the fraction remaining after n half-lives is always (1/2)^n.

Challenge questions

Predict how many atoms remain after three half-lives before simulating.
Explain why half-life stays constant even as the sample shrinks.
Decide whether a 10 g or 1 g sample of the same isotope decays faster per gram.