Radiometric Dating

Question 1

A geologist studies a volcanic rock and measures 80 atoms of uranium‑238 (the parent isotope) and 240 atoms of lead‑206 (the daughter isotope). Which statement correctly explains how this parent‑to‑daughter ratio can be used to estimate the rock’s absolute age?

Accepted Answer

Because three‑quarters of the original uranium‑238 has decayed into lead‑206, the geologist can count how many half‑lives have passed and multiply by the known half‑life of uranium‑238 to find the rock’s age.

Answer

Since there is more lead‑206 than uranium‑238, the rock is older than one half‑life, but the exact age cannot be determined from the ratio alone.

Answer

The fact that some uranium‑238 is still present means the rock is younger than a half‑life, so its age must be less than the half‑life of uranium‑238.

Answer

The parent‑to‑daughter ratio is not useful for dating; instead the geologist should measure carbon‑14 in the rock.

Question 2

A team of scientists discovers a 120‑million‑year‑old fossilized fern leaf embedded in a volcanic tuff layer. To determine the absolute age of the leaf, they consider two radiometric methods: carbon‑14 dating and uranium‑lead dating. Which statement correctly explains why carbon‑14 is unsuitable and why uranium‑lead can be used for this sample?

Accepted Answer

Carbon‑14’s half‑life is only about 5,700 years, so after 120 million years virtually no carbon‑14 remains to measure, whereas uranium‑238 decays very slowly (half‑life ~4.5 billion years) and enough parent and daughter atoms are still present in the surrounding volcanic rock to calculate an age.

Answer

Carbon‑14 is the best choice because the leaf is organic, and its half‑life allows precise dating of any age, while uranium‑lead can only be applied to minerals that formed at the same time as the leaf.

Answer

Carbon‑14 can be used because trace amounts persist indefinitely, but uranium‑lead is unsuitable because the leaf does not contain uranium minerals.

Answer

Both methods rely on the same principle, so either carbon‑14 or uranium‑lead would give the same age; the choice depends only on which isotope is more convenient in the laboratory.

Question 3

A rock sample originally contained 800 atoms of the radioactive isotope X. After 30 million years, only 200 atoms remain. Which statement best describes the meaning of a half‑life for isotope X?

Accepted Answer

A half‑life is the time required for half of the original parent atoms to decay; because the sample went from 800 atoms to 200 atoms (a quarter), two half‑lives have occurred, making each half‑life 15 million years.

Answer

The half‑life is the total time that has passed, which is 30 million years.

Answer

The half‑life is the time it takes for the amount to drop from 800 atoms to 200 atoms, so it is 30 million years.

Answer

The half‑life is the time needed for the number of atoms to decrease by a fixed amount (600 atoms), therefore it is 30 million years.

Try three questions

A geologist studies a volcanic rock and measures 80 atoms of uranium‑238 (the parent isotope) and 240 atoms of lead‑206 (the daughter isotope). Which statement correctly explains how this parent‑to‑daughter ratio can be used to estimate the rock’s absolute age?

A rock sample originally contained 800 atoms of the radioactive isotope X. After 30 million years, only 200 atoms remain. Which statement best describes the meaning of a half‑life for isotope X?

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