Radioactive Half-Life

After this reading this section you will be able to do the following:

  • Define radioactive half-life.
  • Explain how you measure the decay of radioactive isotopes.
  • Compare two radioactive sources and determine their specific activities in curies.

Not all of the atoms of a radioisotope decay at the same time, but they decay at a rate that is characteristic to the isotope. The rate of decay is a fixed rate called a half-life. The half-life of a radioisotope describes how long it takes for half of the atoms in a given mass to decay. Some isotopes decay very rapidly and, therefore, have a short half-life. Others decay at a much slower rate. Highly unstable isotopes have half-lives measured in fractions of seconds, more stable isotopes have half-lives measured in billions of years. 

How do you measure the decay of radioactive isotopes?

Now that we have an idea of how radioactive isotopes decay, let's look at how this is measured and apply the terms we just learned. The basic unit of measure for describing the activity (radioactivity) of a quantity of radioactive material is the curie, named after Marie Curie. A quantity of radioactive material is considered to have an activity of 1 curie or 1 Ci, when 37 billion of its atoms decay (disintegrate) in one second. In scientific terms, this is expressed by the equation: 1 Ci = 3.7 X 1010 disintegrations/sec. (This was determined to be the radioactivity of 1 gram of radium.) Remember that we said each isotope has its own decay pattern. If the rate of decay is greater than 37 billion atoms in one second, then the source would have an activity greater than one curie, and if that source had fewer than 37 billion atoms decaying in one second, its activity would be less than one curie.

The SI unit for activity is the Becquerel, Bq, named after Henri Becquerel, who shared the Nobel prize with the Curies. One Bq is equal to one disintegration per second. This discussion will continue using curies as units, however, SI units are encouraged in most places now.

Determining the activity of radioactive sources in curies

Now let's consider two radioactive sources. One decays at a rate of 18.5 billion atoms per second, and the other decays at a rate of 74 billion atoms per second.

Can you determine the  activities of the values below in curies?

  1. 18.5 x 109 dis/sec
  2. 74 x 109 dis/sec

If you said that the activities of these two sources were 1/2 Ci and 2 Ci, you were correct. It is fairly simple to determine the activity of a source when you know how many atoms decay per second. With radioactive sources, we compare the activities of the sources in terms of gram for gram. The activity, in curies, of 1 gram of any radioactive source is known as its specific activity. Please note that the decay rate or the activity of the radioisotope does not directly relate to how much radiation is produced. Different radioisotopes produce different amounts of radiation as their nuclei change. If you want to read more about this, you can read the material below.

How can we assess the amount of radiation coming from a source?

We have been talking about the activity of a radioactive material in terms of disintegration of the atoms in the material and not about the resulting radiation. This leads us to another distinction among radioactive materials. That is, one disintegration in a radioactive source does not necessarily result in the same amount of radiation emission.

Let's look at an example:

In a Cobalt-60 source (Co-60) each atom decays by emitting a beta particle. Almost immediately additional energy adjustments are made in the atom and two gamma rays are emitted. Each of the gamma rays possess a certain energy level that is always the same. Therefore, when a Co-60 source decays, each disintegration of an atom results in two gamma rays. Another example of characteristic decay patterns is that of Thulium-170 (Tm-170). When Tm-170 decays, approximately ¼ of its atoms emit beta particles and an associated gamma ray. The other ¾ of the atoms are beta emitters with no associated gamma emission. This decay pattern is always the same for Tm-170. The point here is that even though the activities of different isotopes may be the same, the number of gamma rays resulting from decay of their atoms can be different.

Now that you know that the activity of a radioactive source is the measure of the number of atoms that decay each second and that the activity varies as a function of the size of the source, let's see why half-life is important.


  1. The term half-life describes how long it will take for half of the atoms to decay, and is constant for a given isotope.
  2. The curie the unit of measure used to describe the radioactivity of radioactive material. (1 Ci = 3.7 X 1010 disintegrations/sec)
  3. The disintegration of the atoms from different isotopes can produce different amounts of radiation.