Students will develop an understanding of how carbon dating works and also learn to solve for the age of an artifact using the carbon dating technique.
Key Equations
The amount of mass of the substance surviving after an original uclei decay for time with a halflife of .
Guidance
Radioactive carbon dating
is a technique that allows scientists to determine the era in which a sample of biological material died. A small portion of the carbon we ingest every day is actually the radioactive isotope
rather than the usual
. Since we ingest carbon every day until we die (we do this by eating plants; the plants do it through photosynthesis), the amount of
in us should begin to decrease from the moment we die. By analyzing the ratio of the number of
to
atoms in dead carbonbased life forms (including cloth made from plants!), we can determine how long ago the life form died.
Example 1
Question : The halflife of Pu is years. You have micrograms left, and the sample you are studying started with micrograms. How long has this rock been decaying?
Answer : We will use the equation for time and simply plug in the known values.
Watch this Explanation
Time for Practice
 The halflife of is years. You have micrograms left, and the sample you are studying started with micrograms. How long has this rock been decaying?
 A certain fossilized plant is years old. Anthropologist Hwi Kim determines that when the plant died, it contained of radioactive . How much should be left now?
 Jaya unearths a guinea pig skeleton from the backyard. She runs a few tests and determines that % of the original is still present in the guinea pig’s bones. The halflife of is years. When did the guinea pig die?
 You use the carbon dating technique to determine the age of an old skeleton you found in the woods. From the total mass of the skeleton and the knowledge of its molecular makeup you determine that the amount of it began with was grams. After some hard work, you measure the current amount of in the skeleton to be grams. How old is this skeleton? Are you famous?

Micol had in her lab two samples of radioactive isotopes:
with a halflife of
days and
with a halflife of
days. She initially had
of the former and
of the latter.
 Do a graph of quantity remaining (vertical axis) vs. time for both isotopes on the same graph.
 Using the graph determine at what time the quantities remaining of both isotopes are exactly equal and what that quantity is.
 Micol can detect no quantities less than . Again, using the graph , determine how long she will wait until each of the original isotopes will become undetectable.
 The goes through decay and the decays by means of electron capture. What are the two immediate products of the radioactivity?
 It turns out both of these products are themselves radioactive; the product goes through decay before it becomes stable and the product goes through decay before it reaches a stable isotope. When all is said and done, what will Micol have left in her lab?
Answers to Selected Problems
 years
 years
 years
 .