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

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

Radioactive decay is a random process, meaning that it is impossible to predict when an individual atom will decay. However, the rate of decay for a large number of atoms can be predicted using the concept of half-life. The half-life of a radioactive element is the time it takes for half of the original number of atoms to decay.

To determine the half-life of a radioactive element, scientists perform experiments in which they measure the decay rate of a sample of the element over time. They then plot the data on a graph, with the number of remaining atoms on the y-axis and time on the x-axis. The resulting graph will show an exponential decay curve.

The half-life can then be determined by finding the time it takes for the number of remaining atoms to decrease to half of the original amount. This can be done by using the equation N = N0(1/2)t/T, where N is the number of remaining atoms, N0 is the original number of atoms, t is the time elapsed, and T is the half-life.

Knowing the half-life of a radioactive element is important for a variety of applications, including radiometric dating and nuclear medicine.