- #1

- 1,271

- 12

## Homework Statement

A nuclear power plant breeds 1mg of

^{239}Pu 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

^{239}Pu:

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

Now, I think to find N

_{0}I have to times n by 6.02x10

^{23}nuclei/mol. Which gives us N

_{0}=2.518x10

^{18}.

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].