Worksheet: Radiometric Dating

In this worksheet, we will practice using isotope ratios to estimate sample age and comparing the advantages and limitations of radiometric dating methods.

Q1:

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

Q2:

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

Q3:

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

Q4:

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

Q5:

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

Q6:

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

Q7:

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

Q8:

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 2 . 3 2 × 1 0 9 years
  • B 1 . 5 0 × 1 0 9 years
  • C 3 . 9 2 × 1 0 9 years
  • D 1 . 7 0 × 1 0 9 years
  • E 1 . 1 8 × 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 of the gaseous 1 2 9 X e has escaped the meteorite.
  • BThe half-life of 1 2 9 I in the meteorite is shorter than expected.
  • CSome of the 1 2 9 X e has further decayed.
  • DSome 1 2 9 X e was already present when the meteorite formed.
  • EAdditional 1 2 9 I is formed by another decay process.

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