determing absolute age by half lives

Q: I was wondering how to determine the absolute age by using half lives. I looked at the
final practice questions and was unable to answer the first five or so questions. The
powerpoint on stratigraphy doesn't really explain how to solve these types of problems
very well. I looked over the slides a few times and am still confused. Thanks.

A: Radioactive decay occurs at a constant rate. As a result, you can use it like a clock. The rate of decay is measured in half lives. The half life of carbon is roughly 5000 years. Carbon-14 decays into Nitrogen-14. Carbon-14 is called the parent isotope, Nitrogen-14, the daughter isotope.

Say you have 16 atoms of carbon 14. After ~5000 years, half of the carbon has decayed away, so there are 8 atoms of carbon 14, 8 atoms of nitrogen. What about after 10,000 years? How many atoms of Carbon 14? (Answer: 4). How many total atoms of N-14? (Answer: 12 = 8 oldones, 4 new ones). After 15,000 years?

A Problem: You have find a fossil snail shell. It has carbon in it, so you can date it using Carbon-14 (C-14) methods. Let’s say you find that you have 15 grams of nitrogen-14 (N-14), and 1 gram of carbon 14. Assume all N-14 that’s there is the result of carbon 14 decay. So, when the snail was alive, it didn’t have any N-14 in it. How old is the snail?

Answer:

OK: how much C 14 was there to start?

15 + 1 grams = 16 grams.

How much carbon is left?

1 out of 16 original grams.

How many half lives is that?

Half-life #1: Carbon goes from 16 -> 8

Half-life #2: 8 -> 4

Half-life #3: 4 -> 2

Half-life #4: 2 -> 1

Four half-lives, each 5000 years: 4x5000 = 20,000 years.