Determine the half lives of two radioisotopes

[robbo157]

Hi,

I am trying to determine the half lives of two radioisotopes in a neutron activated sample of copper. I have plotted the the ln(activity) vs. time and then used the linest function on excel to get a decay function for the longer half-life by assuming after a certain time, only the longer halflife isotope would contribute. This was then subtracted from the total activity and thus a value for the shorter halflife component could be determined through the linest function again. A minimum chi squared value was found through 'solver' on excel by altering the constants in this fitted function. Because I am fitting a hypothesis to data each chi squared component will be (observed count rate - fitted function rate)^2/fitted function rate. This then produced the best possible function to fit the data. The problem with determining the error on this function is: how does the poisson error of +-sqrt(N) on each data point affect the error on the fitted function?
I have tried settin the minimum chi squared to +1 its original value but this gives very small error values as might be expected...

Any help on this could well save my life.

Thanks,
Ben

 

[anathema]

Hi Ben,

Thank you for reaching out for help with your research. It sounds like you have made some good progress in determining the half-lives of the two radioisotopes in your sample of copper. However, you are now facing the challenge of determining the error on your fitted function due to the Poisson error on each data point.

First, it is important to understand that the Poisson error on each data point is a result of the counting statistics and is inherent in any measurement of radioactivity. This error represents the uncertainty in the measured activity due to the random nature of radioactive decay. Therefore, it is important to consider this error when determining the error on your fitted function.

One approach you can take is to use a Monte Carlo simulation to estimate the error on your fitted function. This involves randomly generating a large number of data sets, each with Poisson errors on each data point, and fitting a function to each data set. By analyzing the distribution of the fitted function values from these simulations, you can estimate the uncertainty in your fitted function.

Another approach is to use a statistical analysis method called bootstrapping. This involves resampling your data set multiple times, each time with replacement, and fitting a function to each resampled data set. By analyzing the distribution of the fitted function values from these resampled data sets, you can also estimate the uncertainty in your fitted function.

Both of these methods take into account the Poisson error on each data point and can provide a more accurate estimation of the error on your fitted function.

I hope this helps and good luck with your research!

 

[thepatientmental]

Hi Ben,

Thank you for sharing your approach and concerns regarding determining the half-lives of two radioisotopes in a neutron activated sample of copper. It seems like you have taken a thorough and well-thought-out approach to your analysis. However, as you mentioned, the main issue lies in determining the errors on your fitted function.

The poisson error on each data point, as you pointed out, can greatly affect the error on the fitted function. One way to account for this is to use a weighted least squares method, where the weight of each data point is taken into consideration in the calculation of the errors. This can be done by multiplying the chi squared values by the inverse of the square of the poisson error for each data point. This will give more weight to data points with smaller errors and less weight to data points with larger errors.

Another approach could be to use a Monte Carlo simulation, where you generate multiple sets of data points based on the original data and their poisson errors, and then fit a function to each set. The errors on the fitted function can then be determined from the spread of the fitted function values from the different sets of data. This method takes into account the uncertainties in the data points and can give a more accurate estimate of the error on the fitted function.

I hope these suggestions can help you in determining the errors on your fitted function. Good luck with your analysis!