So, the curie or the becquerel describes radioactivity in terms of the number of atomic nuclei that transform or disintegrate per unit time, and not necessarily the corresponding number of nuclear particles or photons emitted per unit time. To obtain the latter, we usually need a little more information about the particular radioactive decay process. For example, each time an atom of the radioactive isotope cobalt-60 decays, its nucleus emits an energetic beta particle (of approximately 0.31 MeV) along with two gamma ray photons—one at an energy of 1.17 MeV and the other at an energy of 1.33 MeV. During this decay process, the radioactive cobalt-60 atom (60 27Co) transforms into the stable nickel-60 atom (60 28Ni).

Scientists cannot determine the exact time that a particular nucleus within a collection of the same type of radioactive atoms will decay. However, as first quantified by Rutherford and Soddy, the average behavior of the nuclei in a very large sample of a particular radioactive isotope can be accurately predicted using statistical methods. Their work became known as the law of radioactive decay. Before we address this important physical law, we should explore the concept of half-life (T1/2). The radiological half-life is the period of time required for one half the atoms of a particular radioactive isotope to disintegrate or decay into another nuclear form. The half-life is a characteristic property of each type of radioactive nuclide. Experimentally measured half-lives vary from millionths of a second to billions of years.

What percentage of the original radioactivity of a given initial quantity of radioactive material remains after each half-life? As shown in Figure 4.12, we can answer that question by plotting half-life increments along the x-axis and the percentage of radioactivity remaining along the y-axis of a Cartesian graph. The figure closely approximates a smooth, exponentially decreasing curve, called the decay curve. To create a generic decay curve, we select the data-point format (x = half-life, y = percentage of original radioactivity) and then locate the following data points on the graph: (1, 50%), (2, 25%), (3, 12.5%), (4, 6.25%), and (5, 3.125%). We also note that at the beginning, x = 0 half-life and y = 100 percent of the original radioactive material.

A decay chain is the series of nuclear transitions or disintegrations that certain families of radioactive isotopes undergo before reaching a stable end nuclide. Following the tradition introduced by the early nuclear scientists like Rutherford and Soddy, the lead radioisotope in a decay chain is called the parent nuclide, and subsequent radioactive isotopes in the same chain are called the daughter nuclide, the granddaughter nuclide, the great-granddaughter nuclide, and so forth, until we reach the last stable isotope for that chain. Some decay chains, like one described in equation 4.10, are very simple.

Radioactive Parent Nuclide → Stable Daughter Nuclide

More complicated decay chains (as shown in Figure 4.13) require a more sophisticated mathematical treatment than we use here, but the basic concept and approach are still the same. If we start with a given amount of a particular radioisotope (N0) at the starting time (designated as t = 0), how much of that isotope, symbolized as N(t), remains at a later time (t = t)? Assuming that the radioactive parent nuclide only decays into a stable daughter nuclide, we can use the law of radioactive decay to obtain an answer:

N(t) = N0 e–λt