Expert: Richard J. Raridon - 2/25/2004

Question
a radioactive substance decays over time. To scientists, a measure of how slowly it decays is called a "half-time"(means the amount of time ti takes half of the material to decay). A substances half-time is how long it takes fro 1/2 of the substance to decay. Unfortunately, many dangerous radioactive substances have very long half-lives. you will have to use the formula y=ab^x.

a. suppose you start with 20kg of radioactive uranium which has a half-time of 10,000 years. how many kilogrmas are still present after 20,000 years?
b. how many kilograms of uranium would be present after 85,000 years?
c. after how many years would there be 6 kiolgrams of uranium left?
d. Carbon-14 has a half-life of 5730 years. This fact is used to help date fossils. All living things have carbon-14 in them. Suppose an old humanoid bone is found and it has only .012% of its carbon-14 left that a new bone would have. How old is the bone? HINT: let the starting amount be '100' and you now want to know how long it took to get down to 012 left.


Answer
let x = no. of half-lives
a. y = 20(0.5)^2 = 5 kg
b. y = 20(0.5)^8.5 = 0.055 kg
c. 6 = 20(0.5)^x so x = 1.74 half-lives = 17,400 years
d. 0.012 = 100(0.5)^x so x = 13.0 half-lives = 74,631 years
This is not a very realistic problem since C-14 dating is usually limited to 35,000-40,000 years.