Background Information:

Radioactive Half-life

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Isotopes

Some elements have different forms, called isotopes, that each have the same number of protons but a different number of neutrons. Therefore, isotopes of the same element display the same chemical attributes, but sometimes display very different physical attributes. For instance carbon-12 is a stable isotope while carbon-14 is radioactive because it has two extra neutrons.

Radioactive Decay

Radioactive isotopes have unstable atomic nuclei that have a tendency to change, or decay, over time. The starting form of the element is called the parent isotope and the form that it changes into is called the daughter isotope. For example, U-238 is an ustable isotope of uranium that has 92 protons and 156 neutrons in the nucleus of each atom. Through a series of changes within the nucleus, it emits several particles, ending up with 82 protons and 124 neutrons. Once it reaches this point, the nucleus becomes stable and there are no more changes that occur. A nucleus with that number of protons is called lead (symbol Pb), and this particular isotope of lead is called Pb-206 because it has 82 protons + 124 neutrons, which totals 206.

Half-life

The half-life of any radioactive isotope is a measure of the tendency for the nucleus to decay, and this measure is based purely upon probability. It is impossible to know when a single radioactive atom will decay, but the time required for large numbers of identical radioactive atoms to decay is predictable. One half-life is the time it takes for half of the atoms present within a sample to decay. For instance, there is always a small chance that each of the nuclei of U-238 will suddenly decay. Although this chance is extremely small, it is always present. After conducting careful measurements on large numbers of U-235 atoms, scientists determined that each U-238 atom has a 50% chance of decaying into Pb-206 during about 4.5 billion years. In other words, the half-life of U-238 is 14 billion years.

Why does decay occur?

Atomic nuclei are held together by an attraction between the protons and neutrons (called the nuclear force), which has to be greater than the electrostatic repulsion between the protons within the nucleus in order for the nucleus to remain stable. In general, the number of neutrons in an atomic nucleus must at least equal the number of protons because electrostatic repulsion prohibits denser packing of protons. If there are too many neutrons, the nucleus has the potential to become unstable. Decay happens spontaneously at any time when the electrostatic repulsion is greater than the nuclear force that holds the nucleus together.

Many elements have isotopes that are unstable because they have too many neutrons to be balance by the number of protons in the nucleus. Each of these unstable isotopes has its own characteristic half-life, which is independent of almost any outside influence including the physical state, temperature, or pressure in which the nucleus finds itself. Some half-lives are billions of years long, as with U-238, while others are shorter than a second.

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