1.3 Radioactive Decay and Half-Life
Understanding how unstable atoms change over time is fundamental to radiation science.
The Process of Radioactive Decay
**Radioactive decay** is the spontaneous process by which an unstable atomic nucleus loses energy by emitting radiation. This process transforms the parent nucleus into a daughter nucleus, which may be a different element. For each radioactive isotope (or radionuclide), this decay happens at a predictable rate.
The number of nuclei that decay per second is called the **activity** of the radioactive substance.
What is Half-Life (\(T_{1/2}\))?
The **half-life** (\(T_{1/2}\)) of a radioactive isotope is the time it takes for half of the radioactive atoms in a sample to decay. It is a fundamental property of each radionuclide and does not depend on external factors like temperature or pressure.
For example, if you start with 100 grams of an isotope with a half-life of 10 years, after 10 years you will have 50 grams left. After another 10 years (20 years total), you will have 25 grams, and so on.
The Mathematical Model of Decay
The number of radioactive atoms or the activity of a sample decreases exponentially over time. This can be described by the following formula:
Where:
- \(A_t\): Activity at time \(t\)
- \(A_o\): Initial activity at time \(t = 0\)
- \(\lambda\): The decay constant, a value related to the half-life
- \(t\): The elapsed time
The relationship between the half-life (\(T_{1/2}\)) and the decay constant (\(\lambda\)) is: