Half Lives

Question

Here are several questions about half-lives. Please help me answer them and explain step-by-step how you got the answer. Thank you!!

 

 

1.) You take a sample from a canyon wall and find trace amounts of uranium and lead. If the ratio between the two is 1:31, how many half lives have gone by?

 

 

2.) For what you found in the problem above, knowing that the half life of this particular decay is approximately 704 million years, how long ago did they rock solidify?

 

 

3.) Uranium has two isotopes that are used by geologists to determine the time of formation (age) of minerals and rocks. The isotope Uranium-238 has a half-life of 4.5 billion years. If you leave campus today and a meteorite falls on the ground next to you (a small one so you are not injured) and that meteorite formed at the same time that the Earth formed, approximately what percentage of the original radioactive Uranium-238 atoms would still be in the meteorite?

 

 

Answer 1

Hi Sarah!

1. 5 Half-Lives have gone by to reach a 1:31 ratio. After 1 half-life, we have a 1:1 ratio between Ur and Pb. After 2 half-lives, we have a 1:3 ratio. After 3, we have a 1:7 ratio and after 4, we have a 1:15 ratio. A pattern I use is for each half-life step the second number of our ratio is 2 times the last plus 1. For example, from step 3 (Ratio 1:7) to step 4, we take the second number (7), multiply it by 2 (14) and add 1 (to get 15 - the second number in step 4). If we follow this pattern until we reach 1:31, we see it occurs on the 5th half-life step. 

2. So from part 1, we know 5 half-lives have gone by. To find out the total amount of time that has passed, we just multiply the number of half-lives to how many years there are in each half life. So for this example,
5*704,000,000=3,520,000,000years (or 3.52 billion years)

 

3. We know the Earth is 4.5 billion years old. So a meteorite that formed 4.5 billion years ago would have undergone only one half-life of Uranium-238 and half of the original Uranium would be remaining (50% of the original)

Let me know if you need any clarification or have any other questions!