How is the half-life of a radioactive isotope determined?

The half-life of a radioactive isotope is determined by measuring the time it takes for half of the isotope to decay.

In more detail, the half-life of a radioactive isotope, often denoted as T½, is the time required for half of the atoms in a sample to undergo radioactive decay. This is a fundamental property of the isotope and does not depend on the amount of the isotope present or the conditions it is under.

To determine the half-life of an isotope, scientists typically start with a known quantity of the isotope and then measure the amount of it that remains after a certain period of time. This can be done using a variety of techniques, such as mass spectrometry or radiation detectors, which can measure the number of decay events.

The decay of radioactive isotopes is a random process, but it follows a predictable pattern. This pattern is described by the law of radioactive decay, which states that the rate of decay is proportional to the number of atoms remaining. This means that if you start with a large number of atoms, a large number will decay in a short time. But as the number of atoms decreases, the rate of decay also decreases.

The half-life is calculated by observing how long it takes for the number of atoms to decrease by half. This is done by plotting the number of atoms remaining against time on a logarithmic scale. The half-life is the time at which the number of atoms has decreased to half of its initial value.

It's important to note that the half-life is a statistical measure. It does not mean that every atom in a sample will have decayed after this time. Instead, it means that on average, half of the atoms will have decayed. Some atoms may decay almost immediately, while others may take much longer.

Understanding the half-life of a radioactive isotope is crucial in many fields, including nuclear physics, geology, archaeology, and medicine. For example, it allows scientists to date ancient artefacts and rocks, to understand the processes happening inside nuclear reactors, and to design treatments for diseases like cancer.