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

Chapter: Earth’s History

What this practice covers

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

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

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

Problem 1

A sample retains 12.5% parent isotope. How many half-lives have elapsed?
Answer and explanation

3 half-lives

100 → 50 → 25 → 12.5.

Problem 2

Two half-lives of 30 million years have elapsed. Find the age.
Answer and explanation

60 million years

2 × 30 = 60.

Problem 3

Why should a date be checked against field relationships?
Answer and explanation

The isotope system may date a particular mineral event or have been altered; field evidence helps interpret it.

Problem 4

A closed sample retains 25% of its original parent isotope. Half-life is 8 million years. Find elapsed time. Explain the reasoning in your own words.
Answer and explanation

16 million years under the supplied closed-system assumptions.

100%→50%→25% is two half-lives.

2×8 million=16 million years.

Response criteria

  • Use the stated conditions.
  • Show the evidence or calculation.
  • Explain the conclusion and any stated limitation.

Problem 5

A sample retains 25% parent with half-life 6 million years. Find elapsed time. Show the reasoning, not just the conclusion.
Hints

The fraction is parent remaining, not daughter produced.

Answer and explanation

Two half-lives have elapsed: 2×6=12 million years.

Problem 6

Why can leakage of parent or daughter make a radiometric age unreliable?
Hints

State what the supplied observations or conditions establish, and separate that from any assumption.

Answer and explanation

The closed-system accounting no longer holds; measured ratios can reflect movement as well as decay.

Problem 7

A mineral date is tied to a particular clock eventA mineral date is tied to a particular clock eventOlder grain formsTransport / burialLater heatingGrain crystallizationSediment depositionPossible clock disturbanceName the dated material and the event its isotope system records.
Original hypothetical mineral-event timeline with no fixed interval scale. The diagram distinguishes possible clock-start and disturbance events rather than asserting that every heating episode resets every isotope system completely.
Interpret the supplied visual model. Why can a 200-million-year grain inside a younger sediment fail to date that sediment’s deposition?
Answer and explanation

The grain may have formed earlier and retained its isotope record through later transport and burial. Its age records the older grain event, not automatically the younger deposition.

The timeline separates grain formation, sediment deposition and later disturbance. Each is an event that could leave different evidence.

The grain may have formed earlier and retained its isotope record through later transport and burial. Its age records the older grain event, not automatically the younger deposition.

Response criteria

  • Read the labeled quantities, reference frame or objects correctly.
  • Explain the relation between the visual evidence and the mechanism.
  • Keep the drawing’s stated assumptions and limits in the conclusion.

Problem 8

A closed-system model begins with 96 parent units and now contains 12. Half-life is 8 million years and initial daughter assumptions are satisfied. Find elapsed time and name a condition that could invalidate the interpretation.
Answer and explanation

12/96 = 1/8, or three half-lives. Time is 24 million years. Parent/daughter gain or loss, unsuitable initial conditions, or dating a different closure event could invalidate the stated interpretation.

Compute remaining fraction: 12/96 = 1/8.

Count three halving intervals and multiply 3×8 = 24 million years.

Check closure, initial assumptions and the actual event recorded.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

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