Simple Calculations involving the Activity and Half-life of Radioactive Materials

Activity and Half-life

Activity is the term used to describe how many unstable atoms in a sample of radioactive material decay per second. It is measured in Becquerels (Bq).
Half-life is the time it takes for half of the unstable atoms in a sample to decay. It is a measure of how radioactive an isotope is.
To calculate the activity (A) of a radioactive source, use the equation A = n / t, where n is the number of the nucleus that has decayed, and t is the time taken for the decay.
The half-life can also be determined graphically from a graph of surviving nuclei (or remaining radioactivity) versus time.
For this, draw a line from 100% survival (at time 0) down to 50% survival. The time at which this point touches the x-axis (time) is the half-life.
The half-life of a radioactive isotope is constant. It doesn’t matter how many atoms you start with, it always takes the same amount of time for half of them to decay.
Using the half-life of an isotope, you can predict what fraction of a sample will remain after a certain amount of time. For example, after one half-life, 1/2 of the sample will remain. After two half-lives, 1/4 of the sample will remain, and so on. This exponential decay can be expressed as N = N0 * (1/2)^(t/h), where N is the remaining quantity of the substance, N0 is the initial quantity, t is the time that has passed, and h is the half-life.

The bold terms are your key points here: activity, Becquerels, half-life, A = n / t, and N = N0 * (1/2)^(t/h). Understanding these concepts and being able to work with them is crucial for handling radioactivity in a scientific context.