re:atomics

What changes after another half-life?

What is actually halved?

Start with a large population of one radioactive isotope. After one half-life, about half of the original parent atoms remain. After another, half of that half remains.

100%50%25%12.5%

The expected fraction remaining is N / N₀ = 2−t / T, where t is elapsed time and T is the half-life.

Definition: NRC · Half-life (radiological)

Try changing the timescale.

A hypothetical single isotope. A large population. No new parent atoms added.

25%of the original parent atoms remain2 half-lives have elapsed
Fraction of parent atoms remaining over 40 yearsExponential decay for a hypothetical isotope with an 8-year half-life. At 16 years, 25 percent remains.100%50%0%020 years40
Expected fraction of the starting parent population. Individual decays are random.

This is a decay model, not a used-fuel heat or safety calculation.

Can you work it through?

Use a percentage, a fraction, or a decimal: 25%, 1/4, or 0.25. Answers and hint use stay on this browser.

Problem 01

An imaginary isotope has a half-life of 4 hours. After 12 hours, what percentage of the original parent population remains?

Give me a hint

How many 4-hour intervals fit into 12 hours? Halve the remaining parent population once for each interval.

Show the solution

12 / 4 = 3 half-lives. (1/2)^3 = 1/8 = 12.5%.

Problem 02

A different imaginary isotope has a half-life of 9 hours. After 18 hours, what percentage of its original parent population remains?

Give me a hint

Use the new half-life, not the one from the first problem.

Show the solution

18 / 9 = 2 half-lives. (1/2)^2 = 1/4 = 25%.

Problem 03 / Predict it

During each additional half-life, what happens to the parent population in this model?

Give me a hint

Compare 100 to 50 with 50 to 25. Are those equal amounts or equal fractions?

Show the solution

Half of the remaining parent population decays in each half-life. From 100 to 50 removes 50; from 50 to 25 removes 25. The removed fraction stays one-half, but the absolute number changes. This is a population model, not a guaranteed decay time for each individual nucleus.

Problem 04 / Self-review

Compare with the reference reasoning

A real inventory contains multiple radionuclides and may have decay chains. A remaining parent fraction is not itself a heat-output or dose calculation. Handling decisions require the inventory, radiation, geometry, shielding, and thermal information relevant to the decision. No safety time follows from this toy curve.

  • Distinguish parent population from heat and dose.
  • Acknowledge multiple radionuclides and possible decay chains.
  • Do not infer a safety time from this model.
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