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E x p lo r a t io n G uid e : H a lf - lif e
Everything around you is made of atoms, including plants, animals, people, water,
furniture and buildings. Each atom contains tiny particles called protons and
neutrons in its center, or nucleus. The number of protons in the nucleus
determines which element the atom belongs to. For example, all hydrogen atoms
have one proton, and all carbon atoms have six protons.
Within a particular element, atoms with different numbers of neutrons are called
isotopes. Carbon-12 and carbon-14 are two different isotopes of carbon. Carbon-12
has 6 protons and 6 neutrons, while carbon-14 has 6 protons and 8 neutrons. Unlike
carbon-12, carbon-14 is an unstable or radioactive isotope. Like a kernel of
popcorn in the microwave, an unstable nucleus can suddenly change in a burst of
energy. This process is called radioactive decay, and the resulting stable atom is a
daughter product. The stable daughter product of carbon-14 decay is nitrogen-14,
which has 7 protons and 7 neutrons.
Half-life and Radioactive Decay
In this activity, you will measure the decay of radioactive atoms.
1. In the Gizmo™ there is a chamber of 128 radioactive atoms, represented by
red spheres. Click Play ( ), and observe.
a. Over time, what happens to the radioactive atoms? The gray spheres are
the daughter atoms.
b. Select the GRAPH tab. What is the shape of the decay curve?
c. Was the rate of particle decay constant through time? If not, did it speed
up or slow down over time? (Hint: If the rate of decay were constant, the
graph would be linear.)
d. Click Reset ( ), and then Play . Was the general shape of the decay
curve the same as in the first experiment? Was it exactly the same?
2. Click Reset . The rate of decay of a radioactive isotope is described by its
half-life. Check that the Half-life is set to 20 seconds, and select
Theoretical decay from the second dropdown menu. Check that the initial
Number of atoms is 128. (To quickly set a slider to a particular value, type
the value in the field to the right of the slider and press Enter .) Click Play .
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a. Select the TABLE tab. At 20 seconds, how many of the original 128
radioactive atoms remained?
b. How many remained at 40 seconds? 60 seconds? 80 seconds? 100
seconds? What is the pattern?
c. Suppose you began with 100 radioactive atoms and a half-life of 30
seconds. How many radioactive atoms will remain after one half-life (30
seconds)? How many will remain after two half-lives (60 seconds)? Three
half-lives? Use the Gizmo to check your answers.
3. The half-life of a radioactive isotope is defined as the amount of time it takes
for half of the radioactive particles to decay. Start with 128 particles and a
half-life of 30 seconds. ( Theoretical decay should still be selected.) Select
the GRAPH tab and click Play .
a. Turn on the Half-life probe , and drag the probe to the middle of the
graph. (You can "grab" the probe by clicking on one of the purple triangles
or the line between.) What is the time interval shown ahead of the probe?
b. What is the number of radioactive particles at the beginning of the interval
measured by the probe? What is the number of radioactive particles at the
end of this interval? How are these two numbers related to the definition
of half-life?
c. Drag the probe to different parts of the graph. Does the same pattern
persist?
4. While the overall pattern of radioactive decay is predictable, it is impossible to
predict when any particular atom will decay. To model the randomized decay
that occurs in nature, select Random decay from the right-hand menu.
Change the number of atoms to 16, and click Play .
a. On the GRAPH tab, turn off the Half-life probe and turn on Show
theory . (Use the "+" and "—"zoom controls to the right of the graph to
adjust the graph scales so the graph fills the screen.) On the graph, the
green line represents the theoretical decay, while the red line represents
the actual decay. How close was the actual decay to the theoretical?
b. Click the camera icon in the upper right corner to take a snapshot of the
graph, and paste the graph into a blank document. Now, repeat the
experiment starting with 32 particles. Paste an image of this graph next to
the first one.
c. Repeat with 64 and 128 radioactive atoms. Now look at the four graphs in
your document. In which graph was the decay curve closest to the
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theoretical decay?
d. If you are working in a class with other students, compare your results to
theirs. In general, in which experiments were the actual results closest to
the theoretical curve?
e. In the samples measured by scientists, billions of radioactive atoms are in
the process of decaying. Based on what you have seen, how close will the
decay of billions of atoms be to the theoretical decay? Justify your answer.
Radiometric Dating
Because radioactive decay is a predictable process, it can be used to determine the
age of rocks, fossils and artifacts. This method is called radiometric dating.
1. Click Reset . On the dropdown menus, select Isotope A and Theoretical
decay . Set the Number of atoms to 128, and click Play .
a. Based on the graph, what is the approximate half-life of isotope A?
b. Select the TABLE tab. What is the exact half-life of isotope A?
c. Click Reset . Change the Number of atoms to 50 and click Play . Does
this change the half-life of isotope A? Confirm this by experimenting with
other starting numbers.
d. Repeat the experiment for Isotope B with 128 radioactive atoms. What is
the half-life of isotope B? If possible, compare your answers to those of
your classmates.
e. Suppose you analyzed a sample. It contained 25 radioactive isotope B
atoms, and 103 stable daughter atoms. Approximately how old is the
sample?
f. About how old is a sample with 75 radioactive atoms and 53 daughter
atoms?
2. Click Reset , and select the Mystery half-life . In this setting, the half life is
random and will be different in each experiment. Run several Mystery
half-life experiments in the Theoretical decay mode. Paste images of the
resulting graphs into a document, and label each of these graphs with the
half-life of the isotope.
3. As you might imagine, the isotopes that are useful for measuring the age of
rocks and fossils have very long half lives. Carbon-14 has a half-life of 5,730
years, and uranium-235 has a half-life of 704 million years. Set the Number
of atoms to 100 and check that Isotope B and Theoretical decay are still
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selected. Click Play , and view the results on the GRAPH tab.
a. To model how scientists might date an artifact, imagine that the y-axis
represents the percentage of radioactive atoms, and that each second on the
x-axis represents 1,000 years. If this is true, what is the age of an artifact
with 50% radioactive atoms of isotope B?
b. What is the estimated age of a sample with 25% radioactive atoms of
isotope B? 12%? 6%?
c. About how old is a sample with 72% radioactive atoms of isotope B?
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