How much Plutonium 239 will remain after 20,000 years?

[yoleven]

Homework Statement

Plutonium 239 (P-239) decays at a rate of 0.00284 percent per year. If the initial sample size
of P-239 is 10 g, how much will remain as P-239 after 20,000 years?

Homework Equations

A=A0e^-rt

The Attempt at a Solution

A=10e^-0.00284*20000
lnA=ln10+lne^-56.4
lnA=1-56.4
A=8.7*10^-25
This answer doesn't seem reasonable and I don't have confidence that I did everything correctly.

 

[yoleven]

I tried the question again.
If A=A0*e^-rt
I want to find A
If I directly substitute and solve, I'll get..
A=10e^(-.00284*20000)
A=2.14*10^-24grams

 

[hage567]

I think the problem is that you are putting 0.00284 in your equation. The 0.00284 is a percentage. So how else could you express that?

 

[yoleven]

Its a percentage so .00284 becomes .0000284?
A=10*e^(-.0000284*20000)
A=5.66grams
That sounds more realistic. Is this correct?

 

[hage567]

Seems reasonable to me.

 

[yoleven]

Thank you.