Decay and Half
Life
Decay and Half
Life
Why is this chapter on half-life being presented?
The purpose of this chapter is to explain the process of radioactive decay
and its relationship to the concept of half-life. The primary intent is to
demonstrate how the half-life of a radionuclide can be used in practical
ways to "fingerprint" radioactive materials, to "date" organic materials,
to estimate the age of the earth, and to optimize the medical benefits of
radionuclide usage.
What is meant by the "decay" of a radionuclide?
Remember that a radionuclide represents an element with a particular combination
of protons and neutrons (nucleons) in the nucleus of the atom. A radionuclide
has an unstable combination of nucleons and emits radiation in the process
of regaining stability. Reaching stability involves the process of radioactive
decay. A decay, also known as a disintegration of a radioactive nuclide,
entails a change from an unstable combination of neutrons and protons in
the nucleus to a stable (or more stable) combination. The type of decay
determines whether the ratio of neutrons to protons will increase or decrease
to reach a more stable configuration. It also determines the type of radiation
emitted.
How do radioactive atoms decay?
Radioactive atoms decay principally by alpha decay, negative beta emission,
positron emission, and electron capture.
How does the neutron-to-proton number change for each of these decay
types?
Alpha decay typically occurs in nuclei that are so big that they can't be
stable. In alpha decay, the nucleus ejects a helium nucleus (alpha particle)
composed of two neutrons and two protons, dropping the mass of the original
nucleus by four mass units. This smaller nucleus is easier to keep in a stable
form.
Beta decay?
In negative beta decay, the nucleus contains an excess of neutrons. To correct
this unstable condition, a neutron is converted into a proton, which keeps
the nucleus the same size (i.e., the same atomic mass) but increases the
number of protons (and therefore the atomic number) by one. In the process
of this conversion, a beta particle with a negative charge is then ejected
from the nucleus.
What about positron decay?
In positron decay, the opposite situation occurs: the proton to neutron ratio
is greater than desired. Accordingly, a proton is converted into a neutron
and a beta particle (but with a positive charge!) is ejected.Again, the nucleus
remains the same size, but the number of protons decreases by one.
And electron capture?
Electron capture results in the same outcome as positron decay in that, in
this process, the nucleus stays the same size and the number of protons decreases
by one. In this type of decay, however, the nucleus captures an electron
and combines it with a proton to create a neutron. X-rays are given off as
other electrons surrounding the nucleus move around to account for the one
that was lost.
Each one of these decay types may also involve the release of one or more photons of gamma radiation. These photons are pure energy given off by the nucleus in its process of achieving stability.
Does anything else occur during the decay process?
You may have noticed that the decay modes discussed above involve particles.
Therefore, decay of a radionuclide results in a loss of mass. The mass is
converted into energy (do you recall Einstein's equation?!) and released.
Is it possible to predict when a given radioactive atom will
decay?
No, its not. The decay of an individual atom is a random event. However,
it is possible to predict when decay will occur based on probability,
particularly when there are a lot of radioactive atoms around. Fortunately,
since atoms are so small, it doesn't take much radioactive material to represent
a lot of atoms.
What is meant by the decay rate?
The decay rate is simply the number of radioactive atom decays occurring
over a specified time.
Is there another designation for the decay rate?
Yes. The decay rate is conventionally known as the "activity" or "radioactivity"
of a material, sample or medium.
What kinds of units are used to reflect activity or decay rate?
Units of activity include disintegration per second (dps), disintegration
per minute (dpm), the curie (Ci), and the becquerel (Bq). Each of these units
is a measure of the number of atoms occurring over a specified time. A curie
of activity, for example, represents 37 billion atoms decaying every second
(37 billion dps) - a very large number! - while one (1) becquerel is equivalent
to a single atom decaying each second.
What factors can be used to characterize or "fingerprint" a
radionuclide?
There are basically three factors that separate one radionuclide from another.
These are its half-life, the particulate or photon energy associated with
its decay, and the type of emission
What do you mean by half-life?
A half-life is defined as the amount of time required for one-half or 50%
of the radioactive atoms to undergo a radioactive decay. This is also known
as the "radioactive" or "physical" half-life. Every radioactive element has
a specific half-life associated with it.
Since the half-life is defined for the time at which 50% of the atoms
have decayed, why can't we predict when a particular atom of that element
will decay?
The concept of half-life relies on a lot of radioactive atoms being present.
As an example, imagine you could see inside a bag of popcorn as you heat
it inside your microwave oven. While you could not predict when (or if) a
particular kernel would "pop," you would observe that after 2-3 minutes,
all the kernels that were going to pop had in fact done so. In a similar
way, we know that, when dealing with a lot of radioactive atoms, we can
accurately predict when one-half of them have decayed, even if we do not
know the exact time that a particular atom will do so.
What else can you tell me about the half life of atoms?
Half-lives range from fractions of a second to billions of years. For example,
Carbon-14 (C-14), a naturally occurring radionuclide, has a half-life of
5,730 years. After this amount of time passes, half of the initial amount
of C-14 is present. Therefore, if you began with two (2) curies of C-14,
one-half of that amount, or one curie, would be present 5,730 years later.
After two (2) half-lives, one-fourth of the initial activity, or 0.5 curies,
would be left. After three (3) half-lives, which is more than 17,000 years
later, one-eighth of the original C-14 activity, or 0.25 curies, would remain,
and so forth.
Well, 5,730 years seems like a long time to wait for the original C-14
activity to diminish by 50%.
You're right. This points out the fact that the rate of decay of short-lived
materials is much faster than for their long-lived counterparts.
Can I make the process hurry along?
Unfortunately, no. Each radionuclide has its own characteristic half-life.
No operation or process of any kind (i.e., chemical or physical) has ever
been shown to change the rate at which a radionuclide decays.
Where can I find a listing of half lives of various radionuclides?
Values for individual half-lives can be found in the literature. This includes
health physics textbooks and the Chart of the Nuclides, a copy of which appears
in the "Links" section of the IEM web page (red button on the left), under
the category entitled "Gadgets and Tools". In addition, the "Tool Box"
section of the IEM web page contains a listing of half-lives for
commonly-encountered radionuclides, in order by element name.
What is meant by the term specific activity?
The term "specific activity" refers to the activity of a particular radioactive
element (i.e., the number of decays per time) divided by the mass of material
in which it exists. Put another way, the specific activity defines the
relationship between the activity and the mass of material. Units for specific
activity include the curie per gram (Ci/g) and the becquerel per kilogram
(Bq/kg), etc.
How is specific activity related to half-life?
Half-life has a profound effect on the specific activity. The shorter the
half-life, the higher the specific activity. As a short-lived radionuclide
undergoes the process of radioactive decay, atoms of the radionuclide in
question emit radioactivity (alpha particles, beta particles, etc.) frequently
as they decay. The higher this rate of decay (activity) while maintaining
a (nearly) constant mass, the higher the specific activity. On the other
hand, atoms of a long-lived radionuclide (one with a long half-life) do not
decay nearly as frequently. Therefore, a lower rate of decay within a specified
mass of material results in a lower specific activity.
What are some examples of radionuclides with low specific activities?
Many radionuclides have half-lives of millions to billions of years. Uranium-238
(U-238), a naturally occurring radionuclide, has a half-life of 4.5 billion
years. Potassium-40 (K-40), another naturally occurring radionuclide found
in the air, water, soil (and therefore in foodstuffs and consequently in
our bodies), has a half-life of approximately 1.3 billion years. Plutonium-239
(Pu-239), a man-made element, has a half-life of only 240,000 years. Because
of their long half-lives, each of these radionuclides, and many others like
them, do not decay into other elements on a very frequent basis. For this
reason, their specific activities are considered to be low.
What about high specific activities?
Radionuclides with high specific activities must have short half-lives (seconds,
minutes, hours, or, at the most, a few years). Many radionuclides have short
half lives. For example, Nitrogen-16 (N-16), a radionuclide associated with
nuclear power plant operations, has a half-life on the order of seven (7)
seconds. Talk about a high rate of decay!
Are there other examples?
The metastable form of Technetium-99 (Tc-99m) and Iodine-131 (I-131), both
used in nuclear medicine procedures, have half-lives of only six (6) hours
and eight (8) days, respectively. Tritium (Hydrogen-3 or H-3), a radioactive
isotope of hydrogen and one that is produced both naturally and for man-made
purposes, has a half-life of 12.3 years. These radionuclides with short (or
relatively short) half-lives decay on a much more frequent basis than their
longer half-life counterparts. When each of their respective activities is
divided by the same mass (a gram of material, for example), a high specific
activity results.
So half-life and mass have some sort of a relationship?
Yes. To put this concept in a slightly different perspective, take the case
of the two radionuclides Sulfur-35 (S-35) and Phosphorus-32 (P-32). S-35
and P-32 have half-lives of 87 days and 14.3 days, respectively. Therefore,
the P-32 decays approximately six (6) times faster than the sulfur. On a
mass basis, then, one-sixth (1/6) of a gram of P-32 is essentially equivalent
to one (1) gram of S-35 in terms of radioactivity!
Where can I find a list of the specific activities of the various
radionuclides?
The best place to start is the IEM "Tool Box" (on the left), under the section
entitled "Specific Activities". You'll find a pretty comprehensive listing
there.
Can an element's half life be used to distinguish it from other
elements?
Yes, in many cases it can. Successful radionuclide identification is largely
determined by the three factors noted previously (half-life, energy, and
type of decay). Since many radionuclides have unique half-lives, the half-life
can be used for identification purposes. For example, if a sample containing
an unknown radionuclide is counted using an appropriate radiation detector,
and the observed activity decreases by one-half of the initial activity after
fourteen (14) days, the radionuclide is likely P-32, a pure beta emitter
(it only decays by beta emission) with a half-life of 14.3 days.
Are there times when this doesn't work?
Yes. Some radionuclides do have similar half-lives which would complicate
the identification process. However, in these cases, the energies of the
radiations they emit during the decay process will differ and can be used
to establish the radionuclide's identity.
How can the concept of half-life be used to determine the age of organic
materials?
Radiometric dating is a widely used technique that utilizes the half-life
of radioactive elements as a means to estimate the age of various materials.
Several approaches are used. Perhaps the most widely publicized has been
radiocarbon dating.
Tell me more about radiometric dating.
In the early 19th century, only a relative time scale (versus an absolute
scale) could be used by geologists. They could not determine the absolute
amount of time a rock or fossil had been in existence because they had no
way to measure their ages. Then, in 1905, less than 10 years after radioactivity
was discovered by Henri Becquerel, radiometric dating, using the principle
of radioactive decay to measure the age of rocks and minerals, was introduced.
Sounds impressive!
Considering that isotopes and decay rates were not known at this time is
certainly cause for amazement about these early studies!
So how does radiometric dating work?
Radiometric dating relies on the use of radioactive elements as "geological
clocks". Since each element decays at its own characteristic rate, geologists
can estimate the length of time over which the decays have occurred by measuring
the amount of the radioactive parent present relative to the amount of the
stable daughter. Put another way, the ratio of parent to daughter can tell
us the number of half-lives, which in turn, can be used to find the age in
years. As an example, if an equal number of parent and daughter atoms exist,
then one-half life has passed.
How does radiocarbon dating work?
Carbon-14 (C-14), a radioactive isotope of carbon, is naturally produced
in the upper atmosphere through bombardment of Nitrogen-14 (N-14) with cosmic
rays. The C-14 is then rapidly oxidized to radioactive carbon dioxide gas
which is absorbed and used by plants. This serves as its introduction into
the food chain.
Then what?
Radiocarbon dating relies on the assumption that C-14 exists in an "equilibrium"
concentration in the carbon of living biological materials, meaning the ratio
of C-14 in the body to that of stable Carbon, or C-12, stays constant. When
a plant or animal dies, it ceases breathing, eating, and/or absorbing carbon
(and therefore C-14). Thus, the C-14-to-C-12 ratio is no longer fixed. The
C-14 begins to decay back into N-14, resulting in a decrease in the C-14
concentration based on its half-life (a 50% reduction every 5,730 years).
Since the rate of decay is known, the concentration (specific activity) of
C-14 in organic (carbon-containing) materials can be measured and used to
calculate the date that the plant or animal died.
Wow. Does it work all the time?
Yes, but only on materials that contain carbon , and only on materials that
were once living.
Where is C-14 dating used?
Radiocarbon dating has been used to determine the age of certain fossilized
bones. In addition, this technique has been applied with great success in
archaeological dating and dating associated with the ice ages.
Are there any shortcomings of this method?
Yes. The C-14-to-C-12 ratio has not remained constant with time as determined
by measuring the levels of radiocarbon in tree rings. The fact that C-14
is also produced through man-made activities is another confounding factor.
With the beginning of the industrial age, large quantities of coal have been
burned. Coal is very old, meaning that the ratio of C-14 to C-12 is essentially
nonexistent. This has the effect of diluting the ratio in the atmosphere
following carbon dioxide releases. Without making a series of corrections
to account for these confounding factors, the resulting C-14 age determination
will be in error.
Any other limitations?
Just one. It has also been stated that this method can only be used on materials
less than 50,000-70,000 years old. Beyond that point, there are so few C-14
atoms remaining in the sample that it becomes difficult to measure them.
Can you provide other examples of radiometric dating?
Certainly. Potassium-Argon dating is another form. It relies on the decay
of Potassium-40 (K-40), a naturally occurring radionuclide, to Argon- 40
(Ar-40), to place an age on rocks and sediments. This method was used recently
to estimate the age at which the eruption of the volcano, Vesuvius, occurred
in the ancient Roman city of Pompeii. (Historians place the eruption around
79 A.D. or 1,919 years ago, while potassium-argon dating estimated this event
occurred 1,926 years ago, an error of less than one percent , but an error
nonetheless!)
Are there other types?
Rubidium-strontium dating, which relies on the decay of Rubidium-87 to
Strontium-87, has been used to date very old terrestrial rocks as well as
lunar samples. Thorium-230 (Th-230) has been utilized to date oceanic sediments
that are older than the useful range of radiocarbon techniques. The fission-track
method relies on the paths, or tracks, produced by charged particles traversing
a mineral's crystal lattice as a result of spontaneous fission by uranium
impurities.
Anything more?
Yes indeed! There are still other interesting methods used in age-dating.
One of these is known as thermoluminescence.
What is thermoluminescence and how has it been used?
Taken separately, the word "thermo" implies heating, while the word
"luminescence" refers to light. In brief, a thermoluminescent material stores
radiation energy once it is absorbed. Upon heating the material, this "trapped"
energy is released and emits light. The amount of light can be related to
the radiation dose received over time or, for the purposes of this chapter,
to the age of the material if the half-life is known (to account for radioactive
decay over periods of up to hundreds of thousands of years).
Can you provide an example?
Yes. Following the atomic bomb blasts in Hiroshima and Nagasaki Japan, samples
of ceramic roofing tiles, ornamental tiles and brick from various locations
within one (1) kilometer (km) of ground zero were collected, broken down
into much smaller fragments, and heated. The amount of light released was
used as a measure of the radiation dose at the location from which the samples
were taken. These doses can then be assigned to the survivors based on where
they were when the bombs were dropped.
Why are radionuclides with short half-lives used most often in medical
applications?
Medical procedures are designed, of course, to help the patient. When certain
procedures are performed utilizing radioactivity, it is advantageous and
important from a health perspective to use radionuclides that satisfy the
desired diagnostic or treatment objective and then decay away before they
expose the patient to unnecessary amounts of radiation.
Can you give me an example?
Radionuclides such as Tc-99m, with a half-life of six (6) hours, are routinely
used in bone scans because the medical objective is successfully reached
while the amount of radioactivity diminishes rapidly. Another example is
the treatment for thyroid disorders that utilizes I-131 with a short half-life
of eight (8) days. Many other examples with this same objective in mind are
used in the medical field.
Are long-lived radionuclides ever used in medical applications?
Yes. There are cases where using short-lived materials will simply not accomplish
the desired medical objective. A classic example involves the use of Pu-238
as the power supply in cardiac (heart) pacemakers. This radionuclide has
a pretty long half-life (87.7 years) and a relatively high specific activity
- two worthwhile attributes for this application. It is inserted into the
battery as a sealed source in the patient to provide power to the pacemaker.
Using a sealed source means that the radioactive material stays where it
was put. It is readily apparent that using shorter-lived radionuclides for
this purpose would not be advantageous because the sources would have to
be replaced on a routine basis. And every replacement source is another surgery!
Is Pu-238 used in non-medical applications?
Yes, Pu-238 is used as a power source in space missions, such as the relatively
recent NASA Galileo launch. The energy associated with the decay of this
radionuclide is converted into electricity to power the probe to its desired
destination. NASA used this type of power supply because the probe would
be traveling so far from the Sun that solar power couldn't be used. As with
the medical applications discussed previously, the half-life and associated
specific activity merits its use in this application.
I've heard the term "biological half life" before. Is it different
from the physical half-life we have been discussing?
Most definitely. In contrast to the radiological (physical) half-life, the
biological half-life is a measure of how long it takes to eliminate half
of the radioactivity taken into the body by biological processes (e.g.,
excretion).
Can you give me an example?
Be glad to. Cesium-137 (Cs- 137) has a physical half-life of approximately
30 years. Left outside the body, half of the initial radioactivity will decay
or disappear in that time frame. Inside the body, however, Cs-137 has a
biological half-life of only seventy (70) days. This means that biological
processes significantly accelerate the rate of clearance associated with
this radionuclide in comparison to the radiological half-life. Half of the
radioactivity will be gone after 70 days, another half of the radioactivity
in another 70 days, etc.
What is an effective half-life?
If radioactivity is taken into the body, decay of the radionuclide will occur
by both physical and biological means. The effective half-life is a measure
of the combined influences of these two distinct half-lives. In the case
of the Cs-137 example, the radiological and biological half-lives are thirty
(30) years and seventy (70) days, respectively. The effective half-life in
this instance is slightly less than seventy (70) days. It is important to
note that the effective half-life is always lower than either the biological
or the physical half life.
Where can I obtain more information about decay and half life?
There are a number of excellent references that discuss these concepts in
even more detail. Quite a few of them are listed in the "Bibliography" that
is located in this web page's "Tool Box" (press the red button on the left).
If you don't find the information you need there, please don't hesitate to
"Ask a CHP".
Copyright © 1998 Integrated Environmental Management, Inc.