Definition of Half-Life: The half-life () is the constant time interval required for the number of radioactive nuclei in a sample—and therefore its activity—to decrease by half. It remains unchanged regardless of the sample size or initial activity.
Graphical Determination: To find half-life from an activity-time graph, identify the initial activity (), calculate the half-value (), and find the corresponding time on the x-axis. Repeating this from to should yield the same time interval.
Calculations: The amount of a substance remaining after half-lives can be calculated using the factor . For example, after 3 half-lives, the activity will be of its original level.
| Feature | Activity | Count Rate |
|---|---|---|
| Definition | Rate of decay at the source level | Rate of detection by a sensor |
| Measurement | Theoretical/Total decays per second | Experimental/Observed pulses per second |
| Device | Inferred via calculation | Measured via Geiger-Müller tube |
| Process | Contamination | Irradiation |
|---|---|---|
| Mechanism | Radioactive atoms move onto/into an object | Object is exposed to waves/particles from a distance |
| Result | The object becomes radioactive itself | The object does NOT become radioactive |
| Prevention | Airtight suits and careful handling | Lead shielding and distance |
Unit Precision: Always check the time units in Becquerel calculations. Since , any time given in minutes or hours MUST be converted to seconds before multiplying by activity.
Randomness Evidence: If an exam asks for evidence of the random nature of decay, cite the fluctuations or 'jitter' seen in the count rate on a graph over time. A perfectly smooth line would imply a non-random, deterministic process.
Half-Life Consistency: When using a graph to find half-life, always take at least two readings (e.g., from 100% to 50% and 50% to 25%) and average them. This accounts for measurement error and fluctuations in the data points.
The 'Radioactive' Error: A common mistake is assuming that irradiating food or medical equipment makes it radioactive. Irradiation only kills cells or bacteria; it does not transfer the unstable isotopes required for the object to emit its own radiation.
Disappearance vs. Stability: Students often think a nucleus 'disappears' when it decays. In reality, the unstable nucleus transforms into a different, usually more stable, daughter nucleus while emitting a particle or energy.
Activity vs. Mass: Activity is about the number of decays per second, not the mass of the sample. While a larger mass of a specific isotope has higher activity, different isotopes with the same mass can have vastly different activities based on their half-lives.
