re:atomics / Radioactive decay
Half-life answer key
Single hypothetical isotopes, large parent populations, constant half-lives, and no new parent atoms added. These are learning exercises, not used-fuel safety calculations.
Problem 01
An imaginary isotope has a half-life of 4 hours. After 12 hours, what percentage of the original parent population remains?
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?
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?
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 / Explain it
Why can’t this one-isotope curve tell you when actual used fuel is safe to handle?
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.