Modern Physics
Carbon-14 decay
Press Play — N(t) halves every compressed half-life; graph N or activity vs time.
Carbon-14 decay — interactive Modern Physics simulation. Press Play — N(t) halves every compressed half-life; graph N or activity vs time. Free browser-based virtual physics lab with live SI measurements and a guided tutorial.
Radioactive decay
Press Play — N(t) halves every compressed half-life; graph N or activity vs time.
Carbon-14 beta-decays to nitrogen-14 with T½ ≈ 5,730 years. Press Play: the atom grid turns from blue ¹⁴C to orange ¹⁴N as N(t) falls. Playback compresses time so one half-life fits a few seconds, but the fraction follows N/N₀ = (½)^(t/T½) = e^(−λt) with λ = ln2/T½. Use the decay graph to read activity A = λN.
- N(t) = N₀ e^(−λt)
- T½ = ln2/λ
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
Carbon-14 has a half-life of 5,730 years. If you start with a fixed number of C-14 atoms, how much remains after exactly 2 half-lives have passed?
Predictions to weigh
- 1/2 remains, the same as after one half-life.
- 1/4 remains — each half-life cuts the amount in half, so two half-lives means (1/2)×(1/2) = 1/4.
- Essentially none remains after 2 half-lives.
Variable roles
What you set:
- Half-lives elapsed
What you measure:
- Remaining fraction N/N₀
How the investigation runs
- Open the carbon-14 preset and press Reset. The half-life is fixed at 5,730 years; the sample starts with N₀ = 10¹² atoms.
- Enable the remaining-nuclei-count readout.
- Set the elapsed time for each trial (in units of half-lives) and record the fraction of nuclei remaining.
Governing equation
Exponential Decay Law — N(t) = N₀ e^(−λt)
The number of undecayed radioactive nuclei falls exponentially with time: N(t) = N₀·(1/2)^(t/T½), where T½ is the half-life — the time for exactly half of any remaining sample to decay.
What the printable worksheet asks students to work out
- For one trial, compute N/N₀ = (1/2)^(t/T½) using T½ = 5,730 years. Compare to the table.
- Explain why radioactive decay is exponential, not linear — each half-life halves whatever amount remains at that point, so equal time intervals always remove the same FRACTION, not the same absolute amount.
Where this shows up beyond the lab
- Carbon dating measures the remaining fraction of C-14 in an organic sample (compared to the atmospheric ratio when the organism was alive) to estimate its age. Using N/N₀ = (1/2)^(t/T½), explain why carbon dating becomes unreliable for samples much older than about 50,000 years (roughly 8-9 half-lives).
- Radioactive decay is fundamentally random at the level of a single atom — you can never predict exactly when one specific C-14 nucleus will decay. Explain why the half-life law still works precisely for a large sample, even though individual decays are unpredictable.
- AP Physics 2 — Unit 15: Modern Physics
- IB Physics — E.3 Radioactive decay
- General High School Physics — Modern physics intro
- NGSS High School Physics — Wave-particle duality of light
- Welcome to Carbon 14
- Select the nuclide
- Press Play
- Exponential decay curve
- Open the Properties panel
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.