23.3 Radioactive Decay Law, Activity, and Half-Life
Apply exponential decay equations to connect nucleus count, activity, and half-life over time.
Estimated time: 20 minutes
IB syllabus: E.3 · SL and HL
Half-Life Connection and Fast Calculation Paths
Background Counts and Measurement Interpretation
In practical counting, measured rate includes source plus background. To model source decay correctly, subtract background before fitting or estimating half-life from data. If you ignore this offset, late-time activity appears to flatten too early and inferred half-life becomes inaccurate.
Simulation: Decay Curves, Half-Life, and Activity
Vary initial nuclei, half-life, and elapsed time to observe exponential decay, remaining nuclei, and changing activity.
Link nucleus composition, binding-energy trends, decay statistics, and strong-force evidence in one chapter workspace.
Remaining nuclei
2.00e+11
Decayed nuclei
1.40e+12
Activity A
2.31e+10 h^-1 nuclei
P(decay in next hour)
0.1091
Test Yourself
A sample starts with 1.6 x 10^12 nuclei and has half-life 6.0 h. Enter the number of nuclei remaining after 18 h.
Hint: 18 h is three half-lives, so multiply by (1/2)^3.