This problem will look at the Bethe-Bloch ionization formula (a.k.a. “stopping power”), and in particular we are going to use the function which is built into Mathematica for this.  You will work through this in multiple steps, and should be using the notebook linked to the syllabus as the 5th homework problem set.

Starting in Mathematica version 10.1.0, StoppingPowerData exists as a built in function.  However when I first tried this, I was using an older version (10.0.2).  I am not sure what I have given to you all, but you can look by clicking “Mathematica” -> “About Wolfram Mathematica” to see.  To be sure you have version 10.1.0, try this exercise.

1) Execute the command without any arguements, e.g., type as input "StoppingPowerData[]" (without the apostrophes) and execute it.  You should get a page full of substances for which the stopping power can be calculated.  If you get nothing, you probably have the wrong version of Mathematica.  Please try it now.

If you bring up the Wolfram Documentation window, you can find that the function requires 2 parameters, the “entity” and the “property”.  Basically the entity is the medium (e.g, air, tissue, etc.) and the property has all of the stuff about the particle, it’s energy, and what you want to know about it (e.g., the range, mass stopping power, etc.).
Mathematica is a bit convoluted in how we pass this information along.  For example, what if I want to look at the energy loss of the 5.3 MeV α-particle coming from the  decay of Polonium-210 as it travels through air?  I would have to type:
StoppingPowerData[Interpreter[“Entity”][“DryAir”],{“Particle”->”AlphaParticle”,”Energy”->Quantity[5.3,”Megaelectronvolts”]},”MassStoppingPower”]
2a) Enter this into Mathematica; what is the answer?


2b) From the units on the quantity returned (which should numerically be between 700 and 800), is this ((-dE)/dx) or ((-dE)/(ρdx)) ?


3) We are going to next look at how the stopping power and the path length are related -- i.e., at some point this particle will run out of energy and stop.  Let’s figure out what the range of this α-particle is.  Start by making a table with the range and stopping power of the α-particle.  You can do this with the Table function in Mathematica (I am giving you an example here for a 7 MeV proton in dryair -- modify it for a 5.3 MeV α-particle).

Table[{StoppingPowerData["DryAir",{"Particle"->Entity["Particle","Proton"],"Energy"->Quantity[7*10^x,"Electronvolts"]},"CSDARangeLinearStoppingPower"],StoppingPowerData["DryAir",{"Particle"->Entity["Particle","Proton"],"Energy"->Quantity[10^x,"Electronvolts"]},"LinearStoppingPower"]},{x,3,6,0.1}]

4) This is great, but the tabular output can be hard to visualize.  Let’s instead make a plot of the same data.  Below is the command to plot a 7 MeV proton.  Modify it to plot the 5.3 MeV α-particle:

ListPlot[
Table[{StoppingPowerData["DryAir",{"Particle"->Entity["Particle","Proton"],"Energy"->Quantity[7*10^x,"Electronvolts"]},"CSDARangeLinearStoppingPower"],StoppingPowerData["DryAir",{"Particle"->Entity["Particle","Proton"],"Energy"->Quantity[10^x,"Electronvolts"]},"LinearStoppingPower"]},{x,3,6,0.1}],
AxesLabel->Automatic,Joined->True]

5) OK, this one is meant to challenge you.  Find the best energy electrons to use to treat a cancer located 4 cm inside human tissue (HINT: use SoftTissueICRP).  Be sure and include enough detail to show me why you are using that energy -- whatever type of detail or plot you like.  To get you started, I used a command something like: 
StoppingPowerData[“Water”,{“Particle”->”Electron”, “Energy”->Quantity[125,”Megaelectronvolts”]},”CSDARangeLinearStoppingPower”]
to find the maximum depth.