Data Fitting Quiz
The exited state of Barium-137, 137Ba*, γ decays to the stable isotope 137Ba. The decay half-life is 2.55 minutes. You are given a substance and a Geiger counter and asked to determine if the material contains 137Ba*. You do an experiment to count the γ-rays from the substance and get the results in the file DecayData.txt. The file gives the time from the beginning of the experiment and the number of γs detected in 60-second intervals. The number of detected photons is governed by Poisson statistics so the uncertainty in the number of counts is equal to the square root of the number of counts.
For radioactive decay number of γs detected ΔN in the time interval Δt is ΔN = K e-t/τ, where K is a constant, t is the time since the beginning of the experiment, and τ is the lifetime of the radioactive substance.
Write a program to fit the data in DecayData.txt. What is the best-fit value for the half-life? (The half life t½ = τ ln(2)). Don't forget to include uncertainties. Plot the data and the fit together. Include error bars on the data points. HINT: If you take the logarithm of the equation for ΔN you can do a linear fit.
Given the χ2 value and the goodness-of-fit parameter, how likely is it that the substance contains 137Ba*? Explain.