Question

3. Uranium-238 decays into lead. For a given amount of 238U, half is converted to lead every 4.5 million years.

a) If a sample is found with 1/8 (0.125) of the expected 238U, how old would this sample be? (2 points)
13.5 billion


b) For carbon-14, 60,000 years is the maximum age that can be accurately dated. What would be the maximum age of a sample if 238U were used? (3 points)

Answer 1

@mjdennis

Answer 2

OK, what formulas do you have for half-life or decay constant. That's a good place to start.

Answer 3

Well I know that half is converted to lead every 4.5 million years.

Answer 4

And when I got the answer for part a, I divided.

Answer 5

Hmmm. I'm not qualified to help with the physics part. We need to know the half-life of C-14 then. (Half-life of lead is 4.5 million years, because half is converted to lead every 4.5 million years). If you find the half-life of carbon-14, we can get started.

Answer 6

6,000 years

Answer 7

That is the half-life of carbon-14

Answer 8

Got it. So the limit is 60,000/6,000 = 10 half-lives. This is the limit because there is so little of the radioactive stuff left, you can't detect it accurately. Let's find out what fraction of C-14 is left after 10 half-lives:

Half is left after 1 half life, so (1/2)^1 = 1/2 is left
After 2 half lives, (1/2)^2 is left.

Makes sense, right?

So let's use the same rule for U-238... How long is 10 half-lives?

Answer 9

10

Answer 10

how long in billions of years is 10 half-lives of U-238 (read the problem statement again.)

Answer 11

1/2^10

Answer 12

For 238U, half is left every 4.5 million years.
So (1/2)^2 is left in 2*4.5 Myrs, or in 9 million years.
(1/2)^3 is left in 3*4.5 Myrs, or in 13.5 million years. (Just like part A)
Our ultimate limit was (1/2)^10. How many years for (1/2)^10 ? Just like part A, but 10 times instead of 3 times.

Answer 13

I have to go for the day. The answer is on the tip of your tongue. You can get this.

This problem, I was probably wrong to have you come over to physics, it was more like math. Sorry about that!

Answer 14

45?

Answer 15

45
or
45 _million_ ???

Answer 16

Well yeah, I know that lol :) But thanks so much for helping me, I always really appreciate it .

Answer 17

Glad to help. Just don't take a job as a time-traveler, OK? I'd hate to find out you missed your destination by a million years.

Answer 18

What do you mean?

Answer 19

It was a joke about our "well, duh" moment over whether you meant "45" or "45 million".

Answer 20

Hahaha oh okay :)