The half-life of P-32 is 14 days. How long after a sample is delivered can a laboratory wait to use a sample in an experiment if they need at least 10 percent of the original radioactivity?

Question

I need help on how to set up this problem. What is the general equation to use for a half-life problem? And a question specific to the problem, is how to I find 10% of the original?

Thanks for your help.

Answer 1

Here's how you do it.
k = 0.693/t_1/2
Substitute and solve for k. Substitute k into the below equation.
ln(No/N) = kt
No = atoms you start with.
N = atoms you end with
k from above
t = time.
The easy way to do this problem is to let No = 100 (but you can pick any number you like)
then N = 10 (or 0.1 x the number you picked for No.
Then solve for t.

I did this several years ago with Cu-64 which has a half life of about 13 hours. Since it took almost two days to get to me (by air) and another 12-14 hours to run the experiment, it had to be HOT HOT HOT when it left the manufacturer so it would be at least HOT when I started counting.

Answer 2

ok, so I got 3.32, so would I just multiply that by the half-life? Because the answer choices are 28 days, 14 days, 42 days, 56 days, and 70 days

Answer 3

Just Kidding I got 46.51, but that is not one of the answer choices, so which would I pick? or did I do it wrong?

Answer 4

I obtained 46.5 days, also. So pick 42 days for the answer. That's the closest choice you have. These multiple guess questions OFTEN don't have the exact answer but one close to it.

Answer 5

Ok thanks, yes that answer was right, thanks so much for explaining the equation to me, it makes total sense now!