Radioactive decay predicts the expected surviving population of unstable nuclei.
Difficulty
Intermediate
Read time
5 min
Prerequisites
Basic algebra, consistent units, and the stated model assumptions
Source
OpenStax, College Physics 2e, §31.4 (Paul Peter Urone and Roger Hinrichs)OpenFormulaGraph equation reference; FormuLab adaptation details and license are provided below.
Adapted from OpenFormulaGraph, under CC BY 4.0.
FormuLab adapted wording, notation, applicability conditions and topic placement, and expanded the numerical check into a worked example.
Radioactive decay predicts the expected surviving population of unstable nuclei. Individual decay events are random, so the calculated population can be fractional and need not equal one actual measurement.
| Symbol | Meaning | Units |
|---|---|---|
| Expected number of undecayed nuclei | ||
| Initial number of unstable nuclei | ||
| Positive decay constant | ||
| Time |
Estimate the mean surviving nuclear population.
Compare expected populations at different elapsed times.
An initial population of 1000 unstable nuclei has decay constant 0.100 s⁻¹. Find the expected number remaining after 10.0 s.
OpenFormulaGraph equation reference; FormuLab adaptation details and license are provided below.
Adapted from OpenFormulaGraph, under CC BY 4.0.
FormuLab adapted wording, notation, applicability conditions and topic placement, and expanded the numerical check into a worked example.
Assumptions
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