Radioactive Decay: Carbon-14 Dating

1 · Predict

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?

• 1/4 remains — each half-life cuts the amount in half, so two half-lives means (1/2)×(1/2) = 1/4.
• 1/2 remains, the same as after one half-life.
• Essentially none remains after 2 half-lives.

2 · Set Up

1. Open the carbon-14 preset and press Reset. The half-life is fixed at 5,730 years; the sample starts with N₀ = 10¹² atoms.
2. Enable the remaining-nuclei-count readout.
3. Set the elapsed time for each trial (in units of half-lives) and record the fraction of nuclei remaining.

3 · Collect Data

Plot remaining fraction N/N₀ (y-axis) against half-lives elapsed (x-axis) for your three trials. Is the curve a straight line or a curve?

4 · Analyze

1. For one trial, compute N/N₀ = (1/2)^(t/T½) using T½ = 5,730 years. Compare to the table.
2. 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.

5 · Extend

1. 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).
2. 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.

The Physics Behind This Experiment

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