half-life of a radioactive substance

The half-life of a radioactive substance is the time it takes for half of the radioactive atoms in a sample to decay or transform into a different element or isotope. This concept is used to measure the rate of decay of radioactive materials.

Let's illustrate this with an example:

Consider a sample of a radioactive isotope, such as carbon-14, which is commonly used in radiocarbon dating to determine the age of organic materials. Carbon-14 has a half-life of approximately 5,730 years.

1. Initial Amount: Suppose you start with a sample that contains 1,000 carbon-14 atoms.

2. After One Half-Life (5,730 years): After one half-life has passed, half of the carbon-14 atoms (500 atoms) will have decayed into stable nitrogen-14 (^(14)N) atoms, while the other half (500 atoms) remains as carbon-14.

3. After Two Half-Lives (2 * 5,730 years = 11,460 years): After two half-lives, half of the remaining carbon-14 atoms (250 atoms) will have decayed, leaving 250 carbon-14 atoms, and the other 250 atoms will have become nitrogen-14.

4. This process continues, and after three half-lives (3 * 5,730 years = 17,190 years), you'll have 125 carbon-14 atoms, and so on.

The key point is that the half-life is a constant for a specific radioactive isotope. It means that after each half-life, half of the remaining radioactive atoms will have decayed, regardless of the initial amount. This property allows scientists to estimate the age of ancient objects, such as fossils and archaeological artifacts, by measuring the ratio of radioactive isotopes to their stable decay products.

In our example, if you find an object that has only 125 carbon-14 atoms and 875 nitrogen-14 atoms, you can infer that approximately three half-lives have passed (17,190 years), and therefore, the object is about 17,190 years old.