# Chemistry (Dr.Bob222)

posted by .

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?

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?

• Chemistry (Dr.Bob222) -

Here's how you do it.
k = 0.693/t1/2
Substitute and solve for k. Substitute k into the below equation.
ln(No/N) = kt
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.

• Chemistry (Dr.Bob222) -

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

• Chemistry (Dr.Bob222) -

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?

• Chemistry (Dr.Bob222) -

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.

• Chemistry (Dr.Bob222) -

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

## Similar Questions

1. ### calc

The half-life of polonium is 139 days, but your sample will not be useful to you after 95 % of the radioactive nuclei present on the day the sample arrives has disintegrated. For about how many days after the sample arrives will you …

A Cesium 137 sample has a measured radioactivity of 50 microcuries.Cesium 137 has a half-life of 30 years. How long will it take this sample to be reduced to a residual radioactivity of 6.25 microcuries?

1) The number of radioactive nuclei in a particular sample decreases over a period of 15 days to one-seventeenth the original number. What is the half-life (in days) of these nuclei?
4. ### Calculus-Modeling Equations

An unknown radioactive element decays into non-radioactive substances. In 420 days the radioactivity of a sample decreases by 39 percent. 1.What is the half-life of the element?
5. ### chemistry

The half life of phosphorus -32 is 14.3 days. What percentage of an original samples radioactivity remains after 57.2 days?
6. ### Chemistry

A radioactive element has a half-life of 6.41 days. What percent of the original sample will be left after 15.0 days?
7. ### math

An unknown radioactive element decays into non-radioactive substances. In 100 days the radioactivity of a sample decreases by 64 percent. a)(a) What is the half-life of the element?