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Lesson: Radiometric Dating

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.

Worksheet • 9 Questions

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.

  • A 9 . 3 1 × 1 0 3 years
  • B 4 . 0 4 × 1 0 3 years
  • C 3 . 2 4 × 1 0 3 years
  • D 6 . 4 5 × 1 0 3 years
  • E 2 . 1 4 × 1 0 3 years

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.

  • A 3 . 8 × 1 0 9 years
  • B 8 . 7 × 1 0 8 years
  • C 4 . 0 × 1 0 9 years
  • D 4 . 0 × 1 0 8 years
  • E 2 . 6 × 1 0 9 years

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.

  • A 1 . 7 0 × 1 0 9 years
  • B 1 . 1 8 × 1 0 9 years
  • C 1 . 5 0 × 1 0 9 years
  • D 3 . 9 2 × 1 0 9 years
  • E 2 . 3 2 × 1 0 9 years

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.

  • A 3 . 3 5 × 1 0 3 years
  • B 4 . 3 6 × 1 0 3 years
  • C 3 . 8 6 × 1 0 3 years
  • D 4 . 1 3 × 1 0 3 years
  • E 3 . 5 9 × 1 0 3 years

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.

  • A 4 . 1 × 1 0 7 years
  • B 7 . 0 × 1 0 7 years
  • C 3 . 0 × 1 0 7 years
  • D 6 . 0 × 1 0 7 years
  • E 5 . 0 × 1 0 7 years

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.

  • A 1 . 9 1 × 1 0 3 years
  • B 2 . 4 8 × 1 0 3 years
  • C 2 . 3 7 × 1 0 3 years
  • D 1 . 6 6 × 1 0 3 years
  • E 1 . 9 9 × 1 0 3 years

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.

  • A 3 . 9 5 × 1 0 9 years
  • B 4 . 3 4 × 1 0 9 years
  • C 3 . 7 7 × 1 0 9 years
  • D 4 . 5 5 × 1 0 9 years
  • E 4 . 1 8 × 1 0 9 years

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.

  • A 2 . 0 × 1 0 9 years
  • B 2 . 8 × 1 0 9 years
  • C 1 . 2 × 1 0 9 years
  • D 2 . 4 × 1 0 9 years
  • E 1 . 6 × 1 0 9 years

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?

  • ASome 1 2 9 X e was already present when the meteorite formed.
  • BAdditional 1 2 9 I is formed by another decay process.
  • CThe half-life of 1 2 9 I in the meteorite is shorter than expected.
  • DSome of the 1 2 9 X e has further decayed.
  • ESome of the gaseous 1 2 9 X e has escaped the meteorite.
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