Half-life — Science definition

Defined in 2 courses:

Time over which half of a large radioactive parent population remains statistically; not an individual atom’s scheduled decay time. (Earth & Space Science)
Time for the expected number of a specified radioactive parent population to halve under the exponential model; individual nuclei decay probabilistically. (Physical Science: Chemistry)

Where it is taught

Radiometric Dating & Half-Life — Earth’s History, Earth & Space Science, Grade 9
Nuclear Chemistry — Redox, Cells & Nuclear Chemistry, Physical Science: Chemistry, Grade 11

In use

A half-life is the time for half the parent atoms in a large sample to decay.
Radiometric Dating & Half-Life

A half-life describes the expected reduction of a specified parent population under an exponential model, not a fixed timer for each atom or disappearance of half the total material.
Nuclear Chemistry

Questions using half-life

Problem 1

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 2

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 3

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.

Problem 4

A sample retains 25% parent isotope with a 50-million-year half-life. Find its model age.

Answer and explanation

100 million years

Two half-lives × 50 = 100.

Taught alongside

Elsewhere

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