## 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: $2.3 \times 10^6 \ Bq$.

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