Half-Lives and Ash Layers: Putting Years on a Cliff · Chapter 8

Learning target: I can graph the decay of a radioactive element, use half-lives to calculate the age of igneous rock, and use dated ash layers to bracket the ages of the sedimentary layers between them.

Directions

This sheet has two parts. Part A uses a teaching dataset for the decay of uranium-235 in a zircon crystal; the half-life is the real value, and the percentages follow from it. Part B uses invented lab results from a cliff; they were designed to be realistic, not measured. Plot carefully with a ruler and a sharp pencil, show every calculation, and write units on every number.

You will need: This worksheet, Pencil, Ruler, Calculator (optional), Scrap paper for the halving table

Part A: How a radioactive clock runs down

When a zircon crystal forms in cooling magma, it traps atoms of uranium-235 and almost no lead. From that moment the uranium-235 atoms decay, one by one, into lead-207 at a steady rate that heat and pressure do not change. The time for half of the uranium-235 to decay, its half-life, is 704 million years. The table shows what fraction of the original uranium-235 is left after each half-life.

Teaching dataset. The half-life of uranium-235 (704 million years) is real; the percentages are calculated from it, assuming the crystal has not gained or lost any atoms since it formed.

Decay of uranium-235 in a zircon crystal (teaching dataset)
Simulated teaching dataset: the numbers are invented to be realistic, not measured.
Time since the crystal formed (million years)	Half-lives passed	Uranium-235 remaining (%)	Lead-207 formed (%)
0	0	100	0
704	1	50	50
1408	2	25	75
2112	3	12.5	87.5
2816	4	6.25	93.75

2.Extend the table one more row. After 5 half-lives, what percent of the uranium-235 remains, and how old is the crystal? Show both calculations.2 pts

3.Describe the shape of your curve. Why does it drop quickly at first and then flatten, instead of falling in a straight line to zero?2 pts

4.At 1,408 million years, what is the ratio of lead-207 atoms to uranium-235 atoms in the crystal? Write it as a ratio in lowest terms.1 pt

5.A crystal is measured and 35% of its uranium-235 remains. Use your curve to estimate its age. Describe how you read the graph (find 35 on the vertical axis, go across to the curve, go down to the time axis).2 pts

Part B: Dated ash in the Red Gulch cliff

Red Gulch (an invented cliff) exposes five flat, undisturbed layers. Two of them are volcanic ash, which contains zircon crystals that formed when the ash erupted. A geologist sent three samples to a lab. The lab measured the percentage of uranium-235 remaining in each.

Teaching dataset: the layers and lab results are invented to be realistic. Layers are listed from the top of the cliff downward.

Zircon results from Red Gulch (teaching dataset)
Simulated teaching dataset: the numbers are invented to be realistic, not measured.
Layer (top to bottom)	Rock	Sample sent to the lab	Uranium-235 remaining (%)
1	White volcanic ash (0.2 m)	Zircon from the ash	50
2	Gray shale, thin-bedded, no fossils (3 m)	none (no zircon formed here)	-
3	Tan sandstone (2 m)	One zircon sand grain	12.5
4	White volcanic ash (0.3 m)	Zircon from the ash	25
5	Blue-gray limestone (4 m, bottom not exposed)	none	-

6.Calculate the age of ash layer 1 and the age of ash layer 4 in million years. Show how you turned each percentage into a number of half-lives and then into years.2 pts

7.What range of ages is possible for the shale (layer 2) and the sandstone (layer 3)? Explain which rule lets you use the two ash ages as limits.2 pts

8.A student calculates the sand grain's result (12.5% remaining) and announces, 'The sandstone is 2,112 million years old.' The grain's number is right, but the conclusion is wrong, and it even contradicts your answer to q7. Explain where the grain's clock started, why that makes the grain older than the sandstone, and what the sandstone's real age range is.3 pts

9.What can you say about the age of the limestone (layer 5)? Give the one limit the data supports and explain why there is no second limit.2 pts

A halving table

If the percentages are confusing, build a halving table on scrap paper: start at 100, halve it (50), halve again (25), again (12.5), again (6.25), again (3.125). Each halving is one half-life, and each half-life is 704 million years. To find an age, count how many halvings it takes to reach the measured percentage, then multiply that count by 704. For q5, the answer is between the first and second halving, so the age is between 704 and 1,408 million years; the curve tells you where.

Choosing a clock

A lava flow is only about 10,000 years old. Explain why uranium-235, with its 704-million-year half-life, is a poor choice for dating it (think about how much of the uranium would have decayed in 10,000 years and whether a lab could measure that tiny change). Then describe what kind of half-life, long or short, you would want in an element used to date something that young, and what kind you would want for something 3 billion years old.