# Homework Help: Radioactivity homework question

1. Oct 26, 2011

### roam

1. The problem statement, all variables and given/known data

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

2. Relevant 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)

3. 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: $2.3 \times 10^6 \ Bq$.

2. Oct 27, 2011

### 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.

3. Oct 27, 2011