Handed out Monday February 14, 2005

Due Friday February 18, 2005

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

To complete this assignment, you need to know that ^{14}C concentration data are measured relative to the ^{12}C 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 ^{14}C years is done via the equation:

N_{0} = the initial ^{14}C 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 ^{14}C lab determines the FM of a sample to be 0.5000. What is the age of this sample?

(1) start with the given information:
N (2) plug it into the equation:
0.5000 = (1.0000)*e |
(3) solve for t,
0.5000/1.0000 = e |

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 5^{th} Mayan Codex was found and submitted for ^{14}C 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.

#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 5^{th} 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.