Isotope Half-Life and Sample Size Calculation

[AryRezvani]

Homework Statement

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.

Homework Equations

A=A_oe^rt

The Attempt at a Solution

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

A_o-1.6=A_oe^r10,000

Divided each side by A_o, 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.

 

[SteamKing]

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

 

[AryRezvani]

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

The final isotope is the initial mass - 1.6.

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

 

[Curious3141]

The final isotope is the initial mass - 1.6.

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

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

 

[gneill]

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.

 

[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