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Radioactivity homework question

  • Thread starter roam
  • Start date
  • #1
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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? :confused:

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].
 

Answers and Replies

  • #2
CompuChip
Science Advisor
Homework Helper
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The half-life is usually something that you look up. Back in my time (:-p) we had a book of tables where you could find this, nowadays we have Wolfram Alpha.
 
  • #3
1,266
11


Right, I see. So there's no equation or anything you can use in this situation if you don't have a table?
 
  • #4
phyzguy
Science Advisor
4,394
1,369

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