## Absolute dating using 14C

Carbon can be measured in the natural environment in 3 isotopes: 12C, 13C, and 14C. Only the last isotope, 14C, is radioactive. Radiocarbon has a half-life of 5730 years: this means that half the 14C in a sample is gone after 5730 years.

To complete this assignment, you need to know that 14C concentration data are measured relative to the 12C concentration of a sample and reported first as 'fraction modern,' or FM. In 1950 the Earth's atmosphere had a FM = 1.0000. Anything older than 1950 has an FM less than 1. Converting FM data to 14C years is done via the equation:

N = N0e-kt
where:

N0 = the initial 14C content of the sample at formation (always 1.0000 in FM units)
N = the measured FM of the sample today;
t = the age of the sample in years;
k = ln(2)/5730y = 1/(8267 y)

Example:
a 14C lab determines the FM of a sample to be 0.5000. What is the age of this sample?

 (1) start with the given information: N0=1.0000 N = 0.5000 k = 8267 t (2) plug it into the equation: 0.5000 = (1.0000)*e(-t/8267y) (3) solve for t, 0.5000/1.0000 = e(-t/8267y) ln(0.5000) = -t/8267y -0.69315 = -t/8267y (-0.69315)*(8267y) = -t ANSWER: t = 5730 y the sample is 5730 years old.

Problems:

1. A radiocarbon scientist receives a package of bones from a Brazillian art history student, who has found them in a sealed cave near putatively ancient cave paintings. The student wants to know if the bones, and potentially the associated artwork, could be pre-Columbian (older than 1492 AD.) The bones are found to have a 14 C activity of FM = 0.2500. When did this person live? Assuming that the person was responsible for the art on the wall, are the paintings pre-Columbian?

2. The Maya developed a written language about which we know very little because when the Spanish settled Mexico, they ordered all Mayan writing destroyed, believing it to be linked to a blasphemous religion. Only 4 written Mayan codices are known to have survived. In 2000 a putative 5th Mayan Codex was found and submitted for 14C dating, and was found to have a FM = 0.9528. Is this Codex really pre-Columbian, or is it a fake?

3. Past earthquakes can be dated via the principle of cross-cutting relationships.

In the fault shown above, pieces of charcoal were picked out of soil layers #1 and #2 and measured for 14C. The samples were measured to have 14C signatures of:

#1: FM = 0.9904
#2: FM = 0.9808

What can you say about when this fault was created?

4. The same fault was found to occur in a different soil. In this soil, layers #1 and #2 were measured to have
C signatures of:

#1: FM = 0.9832
#2: FM = 0.9690

Using the data from problems 3 and 4, can you say more about when this fault occurred?

5. Back to the putative 5th Mayan Codex. Suppose that the error on the FM measurement was ± 0.0080 (an unusually large error.) What can you say about the potential authenticity of this codex?

Grading will be based on the following scale:

Formatting: 1 point. Put your name, the date, and the course on the assignment. Also sign with the honor pledge.

Mathematical Calculations: 2 points per problem. Show your calcuations and please write legibly.