Radiometric Dating & Half-Life — Drills · Grade 9 Science

Chapter: Earth’s History

What these drills covers

By the end of Radiometric Dating & Half-Life you should be able to:

8 questions, numeric, written answer and multiple choice, each with a worked explanation.

Vocabulary used: parent isotope, daughter product, closed system, half-life.

Problem 1

What percentage of parent isotope remains after four half-lives?
Answer and explanation

6.25 %

100 × (1/2)^4 = 6.25.

Problem 2

Would carbon-14 be a suitable choice for dating Earth’s formation?
Answer and explanation

No. Its useful timescale is far too short; long-lived isotope systems are needed.

Problem 3

A sample starts with 100 percent parent isotope. What percentage remains after 2 half-lives?
Answer and explanation

25 %

Half remains after one half-life, a quarter after two.

Problem 4

After 3 half-lives, what percentage of the original parent remains, to one decimal place?
Answer and explanation

12.5 %

100 → 50 → 25 → 12.5 percent.

Problem 5

An isotope has a half-life of 5,700 years. How many years are 3 half-lives?
Answer and explanation

17100 years

3 × 5,700 = 17,100 years.

Problem 6

A sample with a parent-to-daughter ratio of 1:3 has passed through how many half-lives?
  1. 1
  2. 2
  3. 3
  4. 4
Answer and explanation

2

A quarter parent to three quarters daughter is two half-lives.

Problem 7

Explain why an isotope with a short half-life cannot date very old rock.
Answer and explanation

After enough half-lives so little parent remains that it falls below what instruments can measure reliably, and the age calculated from a near-zero reading carries enormous uncertainty. Dating very old material therefore requires an isotope whose half-life is comparable to the age being measured, which is why different isotopes are used for different time ranges.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the data, mechanism, or calculation that supports it.
  • Include units, conditions, or limits where relevant.

Problem 8

Why is a radiometric date reported with an uncertainty rather than as a single number?
Answer and explanation

The measurement of parent and daughter quantities has a precision limit, the half-life itself is known only to within some range, and assumptions about the starting composition and whether the sample stayed closed add further uncertainty. Reporting a range states how well the evidence constrains the age and lets the date be compared honestly with others.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the data, mechanism, or calculation that supports it.
  • Include units, conditions, or limits where relevant.

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