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

Radioactive decay is a random process where unstable atomic nuclei lose energy by emitting radiation in the form of particles or electromagnetic waves. This is called radioactivity.
Radioactive substances contain atoms with unstable nuclei. When these nuclei decay, they emit radiation in the form of particles and/or waves, and become a different substance.
The activity of a radioactive source is the number of decays per second. The unit of activity is the becquerel (Bq), one becquerel equals one decay per second.
Half-life is the time taken for the number of radioactive nuclei in a sample to halve. It is also the time taken for the count rate from a sample containing the radioactive isotope to fall to half its initial level.
The count rate is the number of decays recorded each second. The count rate is proportional to the number of radioactive nuclei present.
Simple calculations involving activity and half-life may require applying the formula for half-life: T1/2 = 0.693/decay constant.
For a given radioactive sample, when its half-life is less, it means its radioactivity would decrease more rapidly.
Repeat measurements over time can provide the count rate of a radioactive source, which can subsequently be used to calculate its half-life.
Knowledge of half-life can be applied to various contexts, such as carbon dating, medical diagnostics and treatments, and nuclear power plants.
You may also be asked to calculate initial activity from knowledge of the current activity and half-life. For example, if you know the activity of a substance after 2 half-lives, you can calculate the initial activity by multiplying the current activity by four (which is 2^2).
It’s important to become comfortable with converting units of time, as half-life can be expressed in any unit of time (e.g., seconds, minutes, years), and you must ensure the units are consistent in calculations.