17.7: Radioactivity and Age Dating

Essential to Know

• Elements usually have several isotopes that have a different number of neutrons and differ in atomic weight but are essentially identical in chemical properties.
• Some individual isotopes of many elements are radioactive. Others are stable.
• Radioisotopes called “parent isotopes” decay by losing part of the atom, becoming a different isotope, called a “daughter isotope.” Often, the daughter is an isotope of a different element.
• Radioactive decay releases heat and radioactive particles, including alpha particles, beta particles, and gamma rays.
• Each radioisotope decays at a certain fixed rate, expressed by the isotope’s half-life.
• One half-life is the time it takes for exactly half of the atoms of a particular radioisotope in a sample to decay.
• The age of a rock, archaeological artifact, or skeletal or undecomposed remains of an organism can often be determined by measuring the concentrations of both the parent and daughter isotopes in the sample.
• For such age dating to be accurate, no daughter isotope must have been present when the sample was formed. In addition, no parent or daughter isotope atoms must have been gained or lost by the sample after it was formed. These conditions are often not met.
• Different parent-daughter isotope pairs must be used to date samples of different ages. Parent isotopes with long half-lives are useful only for dating older samples.
• Radioisotope dating is often used to calibrate other, less expensive dating techniques, such as fossil and stratigraphic dating, that reveal only the relative dates of samples from within a group of samples under study.

Understanding to Concept

Atoms of any element may occur in several different forms called isotopes. Isotopes differ from each other in atomic weight, but they are virtually identical in their chemical properties. Some isotopes are stable, and others are radioactive. Radioisotopes (but not stable isotopes) called “parent isotopes” are converted, or decay, by losing part of the atom to become a different isotope (often of a different element), called a “daughter isotope.”

During radioactive decay, the radioisotope releases heat and one or more types of radioactive particles, including alpha particles, beta particles, and gamma rays. Radioactive decay takes place at a fixed rate, different for each radioisotope. This rate is expressed by the radioisotope half-life. One-half of the atoms of a specific radioisotope in a sample will decay during one half-life for that isotope, regardless of how many atoms were present initially. Thus, after one half-life, one-half of the atoms originally present have decayed. After two half-lives, one-half of these remaining atoms have also decayed, and one-quarter of the original number of atoms of the isotope remain. After three half-lives, one-eighth of the original atoms of the isotope remain; after four half-lives, one-sixteenth of them remain; and so on.

The age of various materials, including rocks, archaeological artifacts, and the remains of living organisms, can be determined by radioisotope dating. To use this technique, the fraction of the atoms of certain radioisotopes that remain undecayed from the time the rock or other sample was formed must be determined. We can do this by measuring the concentrations of both the parent and daughter isotopes in the sample. If the sample is one half-life old, the parent and daughter will be present in equal concentrations. After two half-lives, there will be three times as many daughter atoms as parent atoms. After three half-lives, there will be seven times as many daughter atoms as parent atoms, and so on for other ages.

Radioisotope dating depends on several critical assumptions. We must usually assume that no atoms of the daughter isotope were present when the sample was formed and that neither parent nor daughter has been added or removed, except by radioactive decay, since then. These assumptions are often incorrect and are always difficult to test because samples undergo physical and chemical changes over time that can add or remove elements. Therefore, to be certain of the measured age, we must often date a sample by two or more different methods.

A particular radioisotope is not useful for age dating if only a very small fraction of the original parent atoms have decayed or, conversely, if almost all the original parent atoms have decayed. Hence, the ideal radioisotope for dating depends on the sample’s age. Several of the most frequently used radioisotopes and their daughters and half-lives are listed in Table CC7-1. We can see that carbon-14 is the most useful radioisotope for dating geologically recent samples (if they contain carbon), whereas uranium-235 is more suitable for older materials. The other radioisotopes listed are suitable only for dating ancient samples.

Table CC7-1. Some radioisotopes used for age dating and their half-lives

Parent Isotope	Stable Daughter Isotope	Half-Life* (years)
Carbon-14	Nitrogen-14	5560
Uranium-235	Lead-207	700 million
Potassium-40	Argon-40	1.3 billion
Thorium-232	Lead-208	1.4 billion
Uranium-238	Lead-206	4.5 billion

*Dating methods are most accurate when used on samples with ages between 0.5 and 3.5 times the half-life

The very sensitive, accurate measurements required for radioisotope dating, along with the equipment, can be expensive. In addition, the determined dates must be verified because the necessary assumptions for this technique are not always valid. For these reasons, radioisotope dating is often supplemented by relative dating techniques based on magnetic properties or fossils (Chap. 6). In some studies, radioisotope dating is performed on only a few representative samples, and the dates of these samples are used to calculate absolute dates for other samples dated by relative dating methods.