This lesson provides an overview of basic atomic structure and the concept of radioactive decay. Topics include the particles that make up an atom, binding forces, and the concept of isotopes. There is also discussion of decay methods and half-life versus activity. The lesson includes an activity in which students use online applets to investigate the half-life and activity of selected isotopes and to examine possible decay chains for some others. They will also use a pair of dice to simulate the process of decay. Educational levels: Undergraduate lower division, High school

John Pratte

English

Digital Library for Earth System Education

 
Nuclear Energy: Nuclear Decay 
Introduction 
The Nucleus 
 
Almost any phrase that has the word “nuclear” in it has a bad reputation.  The term conjures up images of 
mushroom clouds and radioactive mutants. It is interesting to note that in the 1940’s and 50’s, the term 
that applied to energy derived from the decay radioactive material was atomic energy.  This term was 
somewhat correct, since the energy was coming from the breakdown of the atom.  It was not until later 
that the more appropriate term nuclear energy was used as more people began to understand that the 
energy was coming from the breakdown of the nucleus of the atom. 
 
The picture at the right is a popular image of the atom. While not a true 
depiction of the appearance of a real atom, it does mirror most of the 
features of it, such as a central nucleus composed of positively-
charged protons and neutrally-charged neutrons that is orbited by 
negatively-charged electrons.  The classic approach to discussing the 
atom is to tell students that it is held together by electrostatic attraction 
between the protons and electrons.  But this is only part of the picture.  
What rarely gets discussed is what is holding the nucleus together, as 
there is not electrostatic force whatsoever holding the protons to the 
neutrons. 
 
The forces that are binding the neutrons to the protons are the strong 
and weak nuclear forces.  Unlike the electrostatic force, which is 
relatively simple to explain (like charges repel and unlike attract), the 
strong and weak nuclear forces are rather complicated in that the 
discussion of them involves quarks, gluons, and vector bosons and their interactions.  However, intimate 
knowledge of these forces is not required in order to understand nuclear energy, and therefore, we will 
leave it to the reader to research this subject as they desire.  For the purposes of this discussion, we will 
merely note that the forces do exist, that they are important over very short distance scales (10-15 m and 
less), and that they bind neutrons to protons under certain conditions. 
Figure 1: Simplified diagram of an atom 
 
Isotopes 
 
If an atom is to be neutral, it must have the same number of electrons as it does protons, i.e. the total 
amount of negative charge must equal the total amount of positive charge (elements are defined by the 
number of protons in the nucleus).  Is there some type of rule like this that applies to the number of 
neutrons that an atom has?  It turns out that the answer is “No”.  The complicated nature of the strong 
and weak nuclear forces plus the numerous configurations that could be used for storing protons and 
neutrons in a nucleus means that there is no given rule for the numbers of neutrons an element has.  In 
fact, most elements have multiple numbers of neutrons that can be stored in the nucleus.  Atoms that 
have the same number of protons, but different numbers of neutrons, are known as isotopes of an 
element. 
 
Not all of these isotopes are stable.  For most 
naturally occurring elements, there is at least 
one isotope that is stable.  The picture to the 
left shows three different isotopes of hydrogen.  
The first of these, which is what we normally 
Figure 2: Bohr models of hydrogen, deuterium, and tritium 
 1
think of as hydrogen, is called hydrogen-1 and is stable.  The other two isotopes are called hydrogen-2 
(deuterium) and hydrogen-3 (tritium).  Deuterium, which is found in nature in about 1 in every 6500 atoms 
of hydrogen, is stable, whereas tritium, which is much rarer, is unstable and will undergo radioactive 
decay, if given enough time.  Other examples of isotopes with which you might be familiar are carbon-12 
(6 protons and 6 neutrons), which is stable, and carbon-14 (6 protons and 8 neutrons), which is unstable.  
Carbon-14 is one of the radioactive isotopes that is used to determine the age of biological fossils.  There 
are some elements for which there are no stable isotopes.  An example of this would be uranium.  If given 
enough time, all forms of these elements will decay. 
 
Isotopes of a particular element behave the same chemically.  That is to say, molecular compounds that 
can be made with one isotope of an element can be made in the same way with any other isotope of that 
same element.  For example, water (H2O) can be constructed using hydrogen-1, hydrogen-2 (deuterium), 
or hydrogen-3 (tritium).  The water molecules made from each of these will all look, taste, and feel like 
water.  The only physical difference between them will be that water molecules made with deuterium and 
tritium will be heavier and denser than the one made with hydrogen-1.  The one made with tritium will 
differ in one other way: they will also be radioactive.   
 
Radioactive Decay 
Methods of Decay 
 
When an atom decays, it can do so via one of three natural methods.  These methods are known as 
alpha, beta, and gamma.  In alpha decay, the unstable nucleus ejects an alpha particle, which is 
composed of two neutrons and two protons.  Another way of stating this is that the nucleus decays by 
ejecting a helium-4 nucleus.  In beta decay, the nucleus ejects a beta particle, which is either an electron 
(beta minus) or a positron (beta plus).  At first glance, this would seem to be wrong, as a nucleus is 
comprised of protons and neutrons and contains no electrons or positrons.  But they are produced in the 
nucleus whenever a neutron decays into a proton, an electron, and a neutrino or a proton decays into a 
neutron, a positron, and a neutrino.  The last way of decaying is via gamma decay, which is when 
electromagnetic radiation is given off by the nucleus as the protons and neutrons become more tightly 
bound. 
 
There is another way for a nucleus to decay, though this method usually involves the actions of humans.  
A nucleus can be forced to break apart if it is hit by particles from outside of the nucleus.  This was 
discovered by Ernst Rutherford in the early 1900’s when he bombarded nitrogen-14 (7 protons, 7 
neutrons) with alpha particles (helium-4) to produce oxygen-17 (8 protons, 9 neutrons) and a proton.  The 
easiest method for doing this type of decay is to bombard the nucleus with neutrons.  Since the neutrons 
have no net charge, they are not repelled electrostatically away from the nucleus like a proton would be, 
and thus, do not require large energies in order to strike it.  This will be important in our next activity, 
where we discuss the operation of a nuclear power plant. 
 
Half-Life Versus Activity 
 
If left on their own, unstable isotopes will decay in an exponential fashion.  That is, given a large enough 
quantity of an isotope, the same percentage of them will decay in the same amount of time.  This means 
that in a given year, the number of isotopes that decay, divided by the original number of isotopes, will be 
the same quantity.  Rather than listing this fraction for isotopes, though, we often turn the issue on its 
head and discuss the length of time it takes for a certain fraction of the material to decay.  In particular, 
we list the amount of time that it takes for half of the isotopes to decay, which is called the half-life of the 
substance.  For example, iodine-131 has a half-life of 8 days.  If one were to start with 100 kg. of it, after 8 
days, they would only have 50 kg.  After another 8 days, they would have 25 kg left, and so on and so 
forth.  Eventually, the amount of iodine-131 would become so small that it would no longer obey 
exponential decay, at which time we would have no way of determining when a particular amount of the 
substance would decay. 
 
This is not to imply, though, that the fraction of the substance that will decay in a given time period is not 
important.  It is very important, as this quantity is related to the activity, which is the number of decays that 
 2
occurs per unit time.  It is just that the activity and the half-life are inversely related, which means that 
knowledge of the half-life allows one to calculate the activity using the equation 
 
Activity = .69*number of isotopes/half-life 
 
While the half-life gives you some indication of how long a radioactive substance will be around, the 
activity tells you how much radiation it is currently emitting.  This relationship often confuses people.  For 
instance, a lot of people will look at a substance that has a half-life of a billion years as a bad thing.  They 
fixate on how long the substance will be around.  However, a very long half life is a good thing from a 
radiation standpoint, as it means that you would need an enormous quantity of the substance in order for 
there to be any appreciable activity.  Another way to think of it is that stable isotopes, the substances that 
are not radioactive, have an extremely long half-life; it is infinite. 
 
Before we proceed to the activity, there is one 
last thing that we need to clarify.  When a 
substance decays, it does not disappear.  The 
nucleus does lose energy, and possibly some 
particles, but there is still at least one nucleus 
left after the decay.  For instance, in the 
example above, the iodine-131 that decays will 
most likely decay into xenon-131, which is 
stable.  But what if the substance that a 
radioactive isotope decays into is itself 
radioactive?  The chart at the right shows a 
possible radioactive decay chain for uranium-
238.  As you can see, the uranium-238 decays 
into thorium-234, which is radioactive and 
decays into protactinium-234.  The isotopes 
that result keep being radioactive until lead-206 
is reached, at which point the decaying stops.  
This is one of the primary problems with 
radioactive waste from a nuclear reactor.  The 
material stays active for a long period time, 
with both long and short half-life isotopes, as a 
succession of radioactive materials is 
produced and decayed. 
Isotope Half-life Decay mode 
Uranium-238 4.5 billion years alpha 
Thorium-234 24.1 days beta, gamma 
Protactinium-234 1 minute beta, gamma 
Uranium-234 245,000 years alpha, gamma 
 Thorium-230 76,000 years alpha, gamma 
Radium-226 1,600 years alpha, gamma 
Radon-222 3.8 days alpha 
Polonium-218 3.0 minutes alpha 
Lead-214 27 minutes beta, gamma 
Bismuth-214 20 minutes beta, gamma 
Polonium-214 160 microseconds beta, gamma 
Lead-210 22 years beta, gamma 
Bismuth-210 5 days beta, gamma 
Polonium-210 138 days beta, gamma 
Lead-206 stable   
Figure 3: U-238 decay chain, in descending order 
                of daughter products 
 
Internet Exercises 
Half-life 
 
The following link will open up a new window that contains an interactive Java applet that simulates the 
decay of a quantity of radioactive isotopes into daughter products.  As this decay occurs, the applet plots 
the activity (energy released) and the number of radioactive isotopes left.  Some of the sample isotopes 
decay directly into stable daughters; some decay into unstable daughters that then decay into stable 
isotopes.  In particular, try using carbon-10, carbon-15, oxygen-20, oxygen-22, and fluorine-23 in the 
simulation, and note the concentrations and activity levels as the decays proceed. 
 
 
 
Physics 2000 
 
 
Topic: Radioactive Half-life 
Summary: Tutorial on the relationship between half-life and  activity from the 
University of Colorado’s Physics 2000 website. 
Link: http://www.colorado.edu/physics/2000/isotopes/radioactive_decay3.html 
 
 
 3
Decay Chains 
 
The next link opens up a new window that contains an interactive Java applet that shows possible decay 
chains for most known isotopes.  Note that some isotopes have more than one decay chain, such as 
uranium-238.  Isotopes that might be of particular interest are hydrogen-3 (H-3), carbon-14 (C-14), radon-
222 (Rd-222), uranium-235 (U-235), and uranium-238 (U-238).  Note the number of daughter products 
that are produced from each of these.  Is there a general difference between the lighter and heavier 
isotopes? 
 
 
 
Nuclides.net 
 
 
Topic: Radioactive Decay Chains 
Summary: Applet that displays radioactive decay chains on the 
Periodic Table of Elements from the Institute for Transuranium 
Elements 
Requirements: Java-Plugin 1.2.2 or higher 
Link: http://www.nucleonica.net/unc.aspx 
 
 
Laboratory Exercises 
Dice 
 
While it would be nice to do an actual decay experiment with radioactive materials, the idea of doing so 
gives many people the willies (and, quite possibly, the heeby-jeebies).  A decay experiment would require 
a safe storage facility on campus, enough safety and monitoring equipment to outfit both students and 
instructors, and time in the course to cover proper safety procedures, amongst other things.  The time, 
money, and equipment needed to do this is just too much for most institutions 
 
This does not mean, though, that we cannot study the behavior 
of radioactive isotopes.  As we said before, the decay of isotopes 
is a random process (we never know when any one isotope will 
decay) that follows very well studied group statistics (the same 
percentage of materials will decay over equal amounts of time).  
This process can be mirrored very nicely by another random 
group of dice that are thrown, no one can state for certain that a 
particular die will come up with a 1 or a 6 on it.  However, one 
can say that the same percentage of dice in the whole group 
should come up with the same number, on average. 
 
event that follows well-known statistics: dice rolling.  In a large 
or this activity, we will need two groups of different colored dice or cubes.  These two colors will 
ty 
Figure 4: Six-sided dice 
F
correspond to two different radioactive isotopes.  For purposes of discussion, we will call one color Group 
A and the other Group B.  You should have a large number of each group, with 100 dice or cubes being a 
good target.  For Group A, designate one side of each die or cube as the decay side, i.e. when this side 
comes up during a roll, the die or cube is considered to have decayed.  Group B should have 2 sides 
designated.  For example, if you use dice, you could designate 1 as the decay side in Group A and 2 and 
3 as the decay sides for Group B.  To make it easier to notice these sides when you are doing the activity, 
you might want to mark the decay sides with paint or ink. 
 
Because the dice or cubes are six-sided, the odds of any member of Group A “decaying” is 1 in 6; the 
odds for any member of Group B, 1 in 3.  Therefore, each roll of the Group A should see have an activi
that is 1/6th of the total number of members rolled, while each roll of Group B should have an activity that 
is 1/3rd of the total number of members.    
 
 4
Part A 
 
Once you have the two groups acquired and a bucket or container into which to place them for throwing, 
you are set to begin.  Start with all of the members of Group A in your container.  Roll them all at once, 
and then pick out all of the dice or cubes that have turned up with their decay side.  Count and record the 
number of these on your activity sheet, and place all of the remaining members of Group A back into the 
container.  Roll them all again, repeating the above procedure of counting, recording, and removing 
“decayed” members until you have no more dice or cubes left.  Repeat this exact same procedure with 
Group B.  When you have completed both groups, plot your results on the diagrams on the Activity 
Sheets. 
 
Part B 
 
In Part B, we consider the case of a daughter product being radioactive itself.  This time, when our initial 
cubes or dice “decay”, we will replace them with cubes from the other group and continue.  This is 
equivalent to saying that Group A decays into Group B, which decays into something stable.   
 
First, let us start with all members of Group A in the container.  We roll these, and then separate out the 
members of A that have “decayed”.  We count and record this number, and then add exact same number 
of cubes or dice from Group B into the mix.  We now roll these, and separate out the members from A 
that have “decayed” and the members of B that have “decayed”.  We record the number of both.  For all 
of the Group A dice or cubes that have “decayed”, we remove them and replace them with an equal 
number of members from Group B.  All of the members of group B that have decayed, though, get 
removed from the mix permanently.  We keep doing this until we have no Group B members left in the 
container.  For example, if we roll 100 dice from Group A the first time and 16 of them have their decayed 
side up, we remove those 16 Group A dice and replace them with 16 Group B dice.  We then roll these 84 
Group A and 16 Group B dice.  Supposed 13 Group A and 5 Group B dice have their decayed side up.  
We then remove the 5 Group B dice permanently, and replace the 13 Group A dice with 13 Group B dice. 
 
After we have completed this, we then repeat the procedure with Groups A and B switched, i.e. we start 
with all Group B dice or cubes and replace each of them with Group A when they decay.  Upon finishing 
this, we will plot our results on the diagrams on the Activity Sheets. 
 
 
 
 5
 
ESA21: Environmental Science Activities Activity Sheet 
Nuclear Decay
 
Name: 
Lecture Professor: 
 
Part A: 
 
Group A 
Roll No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Remaining                     
Decayed                     
 
Group B 
Roll No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Remaining                     
Decayed                     
 
   Group A      Group B 
 
 
 
 
1. How does the activity of each group correspond to your expected results? 
 
 
 
 
2. From the tables above, you should be able to estimate a “half-life” for each group by noting how  
many rolls it takes for half of the members to “decay”.  Which has a longer half-life, A or B?  Did  
you expect this? 
 
 
 
 6
Part B: 
 
Group A Decays Into Group B 
Roll No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
A Decay                     
B Decay                     
Total                     
 
Group B Decays Into Group A 
Roll No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
B Decay                     
A Decay                     
Total                      
 
 Group A Decays Into Group B Group B Decays Into Group A 
 
 
3. Which configuration had the higher activity: Group A decaying into Group B, or vice versa?  Is this  
what you expected?  Why? 
 7


Nuclear Decay

http://esa21.kennesaw.edu/activities/decay/decayactivity.pdf

Nuclear Decay

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