Radioactivity homework question

[roam]

Homework Statement

A nuclear power plant breeds 1mg of ²³⁹Pu per week. What activity, in Bq, does that create?

Homework Equations

R_0 = \lambda N_0 (initial activity of the sample)

R = R_0 e^{-\lambda t} (exponential behavior of the decay rate)

T_{1/2}=\frac{ln 2}{\lambda} (Half-life)

The Attempt at a Solution

(a) First I find the number of moles in 1mg of ²³⁹Pu:

n= \frac{1\times10^{-3}}{239}=4.184 \times 10^{-6}

Now, I think to find N₀ I have to times n by 6.02x10²³ nuclei/mol. Which gives us N₀=2.518x10¹⁸.

But how can I find the decay constant λ, if we are not given the half life?

I tried out the 1 week as the half life but I didn't get the correct answer:

\lambda = \frac{0.693}{604800 \ s} = 1.1458 \times 10^{-6}

R_0 = \lambda N_0 = 2.88 \times 10^{12} \ Bq

R = R_0 e^{-\lambda t} = 1.44 \times 10^{12}

So, what should I do? The correct answer must be: 2.3 \times 10^6 \ Bq.

 

[CompuChip]

The half-life is usually something that you look up. Back in my time () we had a book of tables where you could find this, nowadays we have Wolfram Alpha.

 

[roam]

Right, I see. So there's no equation or anything you can use in this situation if you don't have a table?

 

[phyzguy]

The following is a good source for nuclear data, including half-lives. I've also zoomed into the page on Pu-239

http://atom.kaeri.re.kr/
http://atom.kaeri.re.kr/ton/nuc12.html