# Homework Help: Isotope decay, fairly simple.

1. Dec 10, 2012

### AryRezvani

1. The problem statement, all variables and given/known data

The isotope 239Pu has a half-life of 24,100 years. After 10,000 years, a sample of the isotope is reduced 1.6 grams. What was the intial size of the same (in grams)? How large was the sample after the first 1,000 years. Round your answer to four decimal places.

2. Relevant equations

A=Aoert

3. The attempt at a solution

Intially, for the value of A, I subbed in "Ao-1.6" and then did the following:

Ao-1.6=Aoer10,000

Divided each side by Ao, and then take the Ln of both sides.

That's where I get stuck. My calculator is indicating that it's not possible to take the Ln of a negative number.

2. Dec 10, 2012

### SteamKing

Staff Emeritus
How did you get a negative number after your algebraic manipulation?

3. Dec 10, 2012

### AryRezvani

The final isotope is the initial mass - 1.6.

When you divide by Ao, the negative stays there, right?

4. Dec 10, 2012

### Curious3141

You'd better show your algebra, exactly. You seem to be making an elementary mistake.

5. Dec 10, 2012

### Staff: Mentor

It's not clear (to me) what you're solving for. What is r? Since you're given a half-life, shouldn't there be a power of two involved? And a negative power of two at that.

6. Dec 11, 2012

### daveb

You might find it easier to solve for the exponential part, THEN just gather the A0 together on one side (and yes, don't forget that the equation should be A0-1.6 = A0e-rt/ln2