Half-life is the time required for the activity of a radioactive source to decrease to half of its initial value. It is also the time taken for half of the undecayed nuclei in a sample to undergo decay.
The half-life is a constant property for a specific isotope; it does not depend on the physical state (solid, liquid, gas) or the chemical environment of the atoms.
To determine half-life from a graph, one identifies the time interval required for the activity to drop from any value to . This interval remains the same regardless of the starting point chosen on the curve.
| Feature | Activity | Count Rate |
|---|---|---|
| Definition | Total decays per second in the source | Detected emissions per second |
| Unit | Becquerel (Bq) | Counts per second (cps) |
| Measurement | Calculated or absolute | Measured by a detector |
Unit Consistency: Always ensure time is converted to seconds when calculating total decays from activity (). If activity is in Bq and time is in minutes, multiply by 60.
Graphical Accuracy: When finding half-life from a graph, always perform at least two checks (e.g., from to and from to ) and average the results to improve precision.
Background Correction: If a problem provides a 'measured count rate' and a 'background count rate', subtract the background first before performing any half-life calculations or plotting points.
Reasonableness Check: Remember that after half-lives, the activity will be of the original. Use this to quickly verify if a calculated final activity makes sense.
