EXPLORELEARNING GIZMO
Half Life
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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.
1. Over time, what happens to the radioactive atoms? The gray spheres are the daughter
atoms.
2. Select the GRAPH tab. What is the shape of the decay curve?
3. 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.)
4. 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.
1. Select the TABLE tab. At 20 seconds, how many of the original 128 radioactive atoms
remained?
2. How many remained at 40 seconds? 60 seconds? 80 seconds? 100 seconds? What is the
pattern?
3. 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)?
Gizmo to check your answers.
Three half-lives?
Use the
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.
1. 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?
2. 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?
3. 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.
1. 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?
2. 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.
1st Graph:
2nd Graph:
3. 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 theoretical decay?
3rd Graph:
4th Graph:
4. 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?
5. 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.
1. Based on the graph, what is the approximate half-life of isotope A?
2. Select the TABLE tab. What is the exact half-life of isotope A?
3. Click Reset. Change the Number of atoms to 50 and click Play. Does this change the halflife of isotope A?
Confirm this by experimenting with other starting numbers.
4. 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.
5. Suppose you analyzed a sample. It contained 25 radioactive isotope B atoms, and 103
stable daughter atoms. Approximately how old is the sample?
6. 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.
Paste graphs here (note, several means more than two):
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 halflife of 704 million years. Set the Number of atoms to 100 and check that Isotope B and
Theoretical decay are still selected. Click Play, and view the results on the GRAPH tab.
1. 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?
2. What is the estimated age of a sample with 25% radioactive atoms of isotope B? 12%?
6%?
3. About how old is a sample with 72% radioactive atoms of isotope B?