# Difficult nuclear physics exercise

1. Oct 4, 2004

### broegger

nuclear physics exercise

The activity from a mixed radioactive sample is measured at different times and given in a table like this:

Time (h).....Decays/sec
-----------------------
0.0 ................... 7500
0.5 ................... 4190
1.5 ................... 3100
: ....................... :
: ....................... :
12.0 .................. 280

I am now supposed - based on this table - to determine how many different nuclids the sample consists of along with their half-lives. How can I possibly extract that information uniquely from that table (the numbers in the table aren't exactly the right ones, since I can't remember them).

maybe the table needs some explanation, because of the crappy layout; the left-hand column is the time in hours and the right-hand column gives the corresponding activities (I haven't written the complete table).

Last edited: Oct 4, 2004
2. Oct 4, 2004

### Tide

First, I would suggest making a plot of the data to get a feel for it.

One approach is to do a least squares fit but you'd have to do it several times for varying numbers of isotopes.

You might also try doing a numerical Laplace transform. I'm not sure if it can be done but ideally you would see a spike for each nuclide.

3. Oct 4, 2004

### broegger

I'm not sure; do you mean I should try to fit the data to functions like this:

$$f_n(t) = A_1e^{\lambda_1 t} + A_2e^{\lambda_1 t} + \ldots + A_ne^{\lambda_n t}$$

for various $$n$$ (corresponding to the number of different isotopes) and see which fit is the best. If so, how can I do this?

I have no idea what LaPlace transformation is, so I don't think this is what we're supposed to do.

4. Oct 4, 2004

Tiiiiide! ;)

5. Oct 4, 2004

### Tide

Yes, that is what I mean with regard to fitting the data.

Also, if you have no idea what a Laplace transform is then nevermind!

6. Oct 4, 2004

### broegger

Weee! I managed to show that n = 2 using Matlabs curve fitting toolbox. Thank you very much for helping me.