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 there's 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). I am 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.