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

## 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.