About this experiment
Radioactive atoms decay at a fixed rate that heat, pressure and chemistry cannot change, so a mineral that locks in a parent isotope when it forms carries a clock. Measure how much daughter has built up for each parent atom left and the age follows from one equation. Watch a sample of atoms decay in four real dating systems, see why counting a small sample gives a scattered answer, and then use the isochron method, which works even when you do not know how much daughter the rock started with.
Learning goals
- Relate half-life, decay constant and the fraction of parent remaining
- Derive the age equation t = ln(1 + D/P)/λ and use it with measured ratios
- Choose a suitable isotope system for the age range of a sample
- Explain how a branched decay such as K-40 changes the age equation
- Construct an Rb-Sr isochron and read both the age and the initial ratio from it
How to use it
- 1In the decay clock, choose U-Pb and press Let time pass. After one half-life, what is the D/P ratio? After two?
- 2Switch to C-14. Why can radiocarbon not date a dinosaur bone? Find the age at which less than 1 % of the C-14 is left.
- 3Choose K-Ar and compare the parent curve with the argon curve. Why does the argon curve level off at about 11 %?
- 4Press New sample several times at a fixed age. How much does the age from counting 400 atoms vary? What would happen with billions of atoms?
- 5Open the Rb-Sr isochron. Slide the age from 0 to 4600 Myr and describe how each sample moves. Why do they always stay on a straight line?
- 6Raise the measurement error and press New sample a few times. How does the uncertainty of the isochron age change?
The model
Assumptions
- Closed system: since the mineral formed, no parent or daughter atoms have entered or left except by decay.
- In the decay clock, the sample starts with no daughter atoms. The isochron removes this assumption for Rb-Sr by fitting the initial ratio.
- Half-lives: C-14 5730 years, K-40 1.248 billion years with 10.72 % of decays giving Ar-40, U-238 4.468 billion years, Rb-87 from the conventional decay constant 1.42 × 10⁻¹¹ per year.
- U-238 is shown as a single step to Pb-206; the intermediate isotopes of the chain are short-lived and are ignored.
- Atom lifetimes and measurement errors come from a seeded generator, so each sample can be shown again exactly.
Try this in class
- Q1A zircon has 0.25 atoms of Pb-206 for every atom of U-238. How old is it?
- Q2A piece of charcoal has 12.5 % of the C-14 found in living wood. How old is it?
- Q3Why would a geologist not use C-14 to date a 2 million year old lava flow? Which system would you pick?
- Q4A volcanic rock lost all its argon when it erupted. Why is this useful for K-Ar dating?
- Q5An isochron has slope 0.0300 and intercept 0.7050. Find the age and the initial ⁸⁷Sr/⁸⁶Sr.
Frequently asked questions
How do we know decay rates were the same in the past?
Decay rates depend on the nucleus, which is barely affected by temperature, pressure or chemical bonding. Light from distant supernovae, the Oklo natural reactor in Gabon and the agreement between independent methods such as U-Pb, K-Ar and tree rings all show that decay constants have not changed measurably.
Why does the isochron method not need the starting amount of daughter?
All the minerals formed from one melt start with the same ⁸⁷Sr/⁸⁶Sr but different amounts of rubidium. Plotted together they make a straight line whose intercept is the starting ratio and whose slope is set only by the age, so both come out of the fit.
What if the rock was heated after it formed?
Heating can let daughter atoms escape, especially gases like argon, which resets the clock or makes the points scatter off the line. Geologists check for this by comparing minerals and methods; a poor straight-line fit is a warning sign.