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 6.14×10 g of rubidium-87 and 3.51×10 g of strontium-87. The half-life of rubidium-87 is 4.923×10 years. Assuming that all of the strontium-87 formed from the decay of rubidium-87, estimate the age of the rock to three significant figures.

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

Q2:

Carbon-14 decays to nitrogen-14 with a half-life of 5,730 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, to three significant figures, the age of the Dead Sea Scrolls.

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

Q3:

Carbon-14 decays to nitrogen-14 with a half-life of 5,730 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 to three significant figures.

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

Q4:

The half-life of 14C is 5,730 years. A sample of ancient plant material contains 32.42% of the original 14C. Calculate the age of the plant material to three significant figures.

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

Q5:

Rubidium-87 decays into strontium-87 by 𝛽 emission, with a half-life of 4.7×10 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 to two significant figures.

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

Q6:

Uranium‑238 decays into lead‑206 via a series of relatively short-lived nuclides. The half-life of uranium‑238 is 4.47×10 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 . 4 × 1 0 years
  • B 1 . 9 6 × 1 0 years
  • C 1 . 6 × 1 0 years
  • D 2 . 8 × 1 0 years
  • E 1 . 2 × 1 0 years

Q7:

Isotopes such as 93Zr are believed to have been present in the solar system since its formation. The half-life of 93Zr is 1.53×10 years and the age of Earth is 4.7×10 years. Calculate, to two significant figures, the age of Earth when only 0.000001% of the original 93Zr remained.

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

Q8:

A rock contains 9.58×10 g of uranium-238 and 2.51×10 g of lead-206. The half-life of uranium-238 is 4.468×10 years. Assuming that all of the lead-206 formed from the decay of uranium-238, estimate the age of the rock to three significant figures.

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

Q9:

The decay of 129I produces 129Xe. The quantities of 129I and 129Xe 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?

  • AThe half-life of 129I in the meteorite is shorter than expected.
  • BSome 129Xe was already present when the meteorite formed.
  • CAdditional 129I is formed by another decay process.
  • DSome of the 129Xe has further decayed.
  • ESome of the gaseous 129Xe has escaped the meteorite.

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