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In this lesson, we will learn how to use isotope ratios to estimate sample age and how to compare the advantages and limitations of radiometric dating methods.

Q1:

The half-life of 1 4 C is 5 7 3 0 years. A sample of ancient plant material contains 32.42% of the original 1 4 C . Calculate the age of the plant material.

Q2:

Rubidium-87 decays into strontium-87 by 𝛽 emission, with a half-life of 4 . 7 × 1 0 1 0 years. A sample of rock contains 8.23 mg of rubidium-87 and 0.47 mg of strontium-87. Calculate the age of the rock.

Q3:

A rock contains 9 . 5 8 × 1 0 − 5 g of uranium-238 and 2 . 5 1 × 1 0 − 5 g of lead-206. The half-life of uranium-238 is 4 . 4 6 8 × 1 0 9 years. Assuming that all of the lead-206 formed from the decay of uranium-238, estimate the age of the rock.

Q4:

Carbon-14 decays to nitrogen-14 with a half-life of 5 7 3 0 years. A sample of plant material from an Ancient Egyptian tomb has an activity of 9.07 decays per minute per gram of carbon. If the initial activity was 13.6 decays per minute per gram of carbon, estimate the age of the tomb.

Q5:

Isotopes such as 9 3 Z r are believed to have been present in the solar system since its formation. The half-life of 9 3 Z r is 1 . 5 3 × 1 0 6 years and the age of the Earth is 4 . 7 × 1 0 9 years. Calculate the age of the Earth when only 0.000001% of the original 9 3 Z r remained.

Q6:

Carbon-14 decays to nitrogen-14 with a half-life of 5 7 3 0 years. A piece of paper from the Dead Sea Scrolls has an activity of 10.8 decays per minute per gram of carbon. If the initial activity was 13.6 decays per minute per gram of carbon, estimate the age of the Dead Sea Scrolls.

Q7:

A rock contains 6 . 1 4 × 1 0 − 4 g of rubidium-87 and 3 . 5 1 × 1 0 − 5 g of strontium-87. The half-life of rubidium-87 is 4 . 9 2 3 × 1 0 1 0 years. Assuming that all of the strontium-87 formed from the decay of rubidium-87, estimate the age of the rock.

Q8:

Uranium‑238 decays into lead‑206 via a series of relatively short-lived nuclides. The half-life of uranium‑238 is 4 . 4 7 × 1 0 9 years. A sample of uranium ore contains 9.22 mg of uranium‑238 and 2.84 mg of lead‑206. Calculate the age of the ore.

Q9:

The decay of 1 2 9 I produces 1 2 9 X e . The quantities of 1 2 9 I and 1 2 9 X e in a meteorite suggest an age of 15 million years. However, other radiometric dating methods suggest the meteorite is 10 million years old. Which of the following is a possible explanation for this discrepancy?

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