



INTRODUCTION AND OVERVIEW 

One of the most important quantities associated with a sample or collection of radioactive material is its activity. Activity is the rate at which the nuclei within the sample undergo transitions and can be expressed in terms of the number of transitions per second (tps). Two units are used: the becquerel (Bq), equivalent to 1 tps, and the curie (Ci), equivalent to 3.7 x 10^{10 } tps. The becquerel is an Sl unit. The curie was first introduced as the activity of 1 g of radium. However, it was later discovered that the activity of 1 g of radium is not exactly 1 Ci, although the number of transitions per second per curie remains the same. Some useful conversions are



RADIOACTIVE LIFETIME 

A fundamental characteristic of radioactivity is that all nuclei, even of the same radioactive nuclide, do not have the same lifetime. This is illustrated below. There is no way to determine or predict the lifetime of a nucleus. However, we can determine the average lifetime of the nuclei of a specific radioactive nuclide. The average lifetime is a unique characteristic of each specific nuclide.



HalfLife 

It is generally more useful to express the lifetime of a radioactive material in terms of the halflife. T_{1/2}, rather than the average life, T_{a}. The halflife is the time required for onehalf of the nuclei to undergo transitions. The halflife is shorter than the average life. The specific relationship is



Transformation Constant (Decay Constant) 

Another way to express the lifetime characteristic of a radioactive substance is by means of the transformation constant, delta, often referred to as the decay constant. The transformation constant actually expresses the probability that a nucleus will undergo a transition in a stated period of time. In the example in the figure above, the value of the transformation constant is 0.115 per hour. This means that a nucleus has a probability of 0.115 or an 11.5% chance of undergoing a transition in 1 hour. The value of the transformation constant is inversely related to lifetime. The probability of undergoing a transition in 1 hour is obviously much less for a radionuclide with a long lifetime (halflife). The actual relationship between the transformation constant and lifetime is:



Quantity of Radioactive Material 

Although activity does not express the amount of radioactive material present, it is proportional to the amount present at a specific time. The amount can be expressed by quantities such as mass, volume, or number of nuclei. We now consider the relationship of activity and the number of nuclei, N, in a specific sample.



Cumulated Activity 

The quantity of radioactive nuclei that undergo transitions in a period of time is usually designated the cumulated activity, Ã, and is expressed in the units of microcuriehours. 1 µCihr is equivalent to 133 million (13.3 x
10^{7}) transitions.



ACTIVITY AND TIME 

One of the most important characteristics of a radioactive material is that the quantity and activity constantly change with time. As each nucleus undergoes transition, it no longer belongs to the radioactive material. In each transition one atom is removed from the parent radioactive material and converted into the daughter product. Because the activity is proportional to the quantity of radioactive material at any instant in time, both quantity and activity decrease continuously with elapsed time. This decrease is generally referred to as radioactive decay.



Remaining Fraction and HalfLife 

It is often necessary to determine the fraction of radioactive material (or activity) that remains after a specific elapsed time. If the elapsed time is one halflife, the remaining fraction, f, is always 0.5 . If the elapsed time is not one halflife, the remaining fraction is the fraction 0.5 multiplied by itself the number of times corresponding to the number of halflives. For example,
f = (0.5)^{5.5} .
f = 0.022 (2.2%).



RADIOACTIVE EQUILIBRIUM 

We have considered fixed quantities of radioactive material that decay with elapsed time. If the radioactive material is being formed or replenished during the decay process, however, the relationship between activity and elapsed time is quite different from a simple exponential decay. The form of this relationship depends on the relationship of the rate of formation to the rate of decay. If we began by forming radioactive material, we would expect the activity to increase with elapsed time as illustrated below. As the amount of radioactive material (and activity) increases, however, the rate of loss of material by radioactive transitions also increases.


Secular Equilibrium 

Assume that the radioactive material is forming at an almost constant rate. If, at the beginning, no radioactive daughter material is present, no nuclei will be under going transition. As soon as the radioactive material begins to accumulate, transitions will begin and some radioactive nuclei will be lost. As the number of radio active nuclei increases, the activity and rate of loss increase. Initially, the rate of loss is much less than the rate of formation. As the quantity of radioactive material builds, the activity or transition rate increases until it is equal to the rate of formation as shown below. In other words, radioactive nuclei undergo transitions at exactly the same rate they are forming, and a condition of equilibrium is established. The amount of radioactive material will then remain constant regardless of elapsed time. Under this condition, the activity is equal to the rate of formation and is referred to as the saturation activity. The important point is that the maximum activity of a radioactive material is determined by the rate (nuclei per second) at which the material is being formed. Although it is true that the activity gradually builds with time, a point is reached at which buildup stops and the activity remains at the saturation level.



Transient Equilibrium 

When the halflife of the parent is only a few times greater than the halflife of the daughter, the condition of transient equilibrium will occur. During the period of interest the parent will undergo radioactive decay. Daughter activity will build and establish a state of equilibrium with the parent activity. Transient equilibrium differs from secular equilibrium in two respects.
Molybdenum and Technetium Activity in a Generator



EFFECTIVE LIFETIME 

When a radioactive material is in a living organism, the material can be re moved from a particular organ or location by two mechanisms, as illustrated below. One is the normal radioactive decay, and the other is biological transport or elimination from the specific site.


