- #1
roam
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Homework Statement
A nuclear power plant breeds 1mg of 239Pu per week. What activity, in Bq, does that create?
Homework Equations
[itex]R_0 = \lambda N_0[/itex] (initial activity of the sample)
[itex]R = R_0 e^{-\lambda t}[/itex] (exponential behavior of the decay rate)
[itex]T_{1/2}=\frac{ln 2}{\lambda}[/itex] (Half-life)
The Attempt at a Solution
(a) First I find the number of moles in 1mg of 239Pu:
[itex]n= \frac{1\times10^{-3}}{239}=4.184 \times 10^{-6}[/itex]
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:
[itex]\lambda = \frac{0.693}{604800 \ s} = 1.1458 \times 10^{-6}[/itex]
[itex]R_0 = \lambda N_0 = 2.88 \times 10^{12} \ Bq[/itex]
[itex]R = R_0 e^{-\lambda t} = 1.44 \times 10^{12}[/itex]
So, what should I do? The correct answer must be: [itex]2.3 \times 10^6 \ Bq[/itex].