Difficult nuclear physics exercise

In summary, the table has data on the decay rates of different nuclids over time. The person is supposed to use the table to determine how many nuclides are in the sample and their half-lives. They should try to fit the data to a function, and if they have no idea what a Laplace transform is then they should nevermind.
  • #1
broegger
257
0
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).
 
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  • #2
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
Thanks for answering.

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

[tex] f_n(t) = A_1e^{\lambda_1 t} + A_2e^{\lambda_1 t} + \ldots + A_ne^{\lambda_n t} [/tex]

for various [tex]n[/tex] (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
Tiiiiide! ;)
 
  • #5
broegger said:
Thanks for answering.

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

[tex] f_n(t) = A_1e^{\lambda_1 t} + A_2e^{\lambda_1 t} + \ldots + A_ne^{\lambda_n t} [/tex]

for various [tex]n[/tex] (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.

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

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