Hey, first time poster here, I'm current writing up a lab report I just wanted to check my method is correct. I'm doing alpha particle spectroscopy using a cloud chamber setup. Most published reports seem to vary pressure (so the mass thickness varies). Our chamber let us vary pressure and distance, I decided to write my report explicitly around varying distance.
I've used the classical Beth-Bloch equation as the model. By plotting x vs alpha energy E I used function fitting to get a third order polynomial out, by taking the derivative of this I found dE/dx as a second order polynomial. Substituting the energy at each point I evaulated -dE/dx at each point and thus, -dX/dE. By plotting E vs -dX/dE I can integrate this to determine the range.
It gets complicated as theres a singularity at 160 KeV (From the log part of the BB equation). So far I overcame this by integrating to the limits of initial energy to the singularity point giving me an under estimate for the area (and hence range). Im not sure if this is the best approach, or how to quantify uncertainty. I used 2 integration methods, the trapezium rule and fitting the function as a high order polynomial and integrating that analytically, is that acceptable?
The Attempt at a Solution
Thanks, sorry if this is unclear, feel free to point that out.