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Use a high-quality data plotting and fitting program (e.g. Origin) to analyze the data. The fitting ''must'' take the uncertainty into account (do not use Excel), otherwise you will get the wrong result.
Notice that you always shall use the 1/3 of the time into each measurement as the "middle time point". This is due to decay - after 1/3 of the time you will have equally many counts before and after the 1/3 point (i.e. it is the "middle point".
- For each data point calculate the net count (gross count - background count), the uncertainty of the net count (based on uncertainty of both the gross count and the background count). You might want to use e.g. MS Excel or similar for doing this.
- Enter your data in a table ("worksheet" in Origin jargon): Include measurement time (relative to end of irradiation) as x-value, the net count as y-value, and the uncertainty as y-error.
- Plot the data - does it look OK?
- Look at the decay curve and identify the part where you only have the longest living component. Make a new curve where you only include this part of the data.
- Fit the slow component and note down the parameters describing the decay.
- Use the fitted parameters from the slow component to calculate the amount this component contributed to the total for each of the measured data points.
- Now plot the new data set, which only should include the fast component.
- Fit the fast component. Does it look right?
- Calculate the R0 (count rate if you had measured exactly at the end of of the irradiation) for each component.
Use the Origin data-fitting functionality to determine the measured half-life of both components simultaneously.
'''Alternative/Extra:''' Plot the gross counts instead of the net counts and ask Origin to fit both the background and the two components at the same time.