Half-Life Gizmo
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Introduction
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.
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.
Click Reset . On the dropdown menus , select Isotope A and Theoretical decay . Set the Number of atoms to 128 , and click Play.
Based on the graph, what is the approximate half-life of isotope A?
Select the TABLE tab. What is the exact half-life of isotope A?
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.

Repeat the experiment for Isotope B with 128 radioactive atoms. What is the halflife of isotope B?
If possible, compare your answers to those of your classmates.
Suppose you analyzed a sample. It contained 25 radioactive isotope B atoms, and 103 stable daughter atoms. Approximately how old is the sample?
About how old is a sample with 75 radioactive atoms and 53 daughter atoms?
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.
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 selected. Click Play, and view the results on the GRAPH tab.
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?
What is the estimated age of a sample with 25% radioactive atoms of isotope B?
12% ?
6% ?
About how old is a sample with 72% radioactive atoms of isotope B?