Homework $4$ Part B

You have at your disposal an accelerator capable of accelerating any ion up to a maximum kinetic energy of $500$MeV per nucleon. For $)=12,Z=(6,$ the maximum kinetic energy of the ion beam is $6000$MeV. You want to conduct a cell irradiation experiment. The carbon ion must be able to penetrate the cell target, i$.$e$.,$ have a range of $>10$ micrometers in water.

$($a$)$ Using the Bethe$-$Bloch equation, calculate the stopping power of the carbon ion beam in the cell culture. $($Hint: Determine the $F()$ and $$ for a proton traveling at the same velocity as the carbon ion in water$).$

$($b$)$ Calculate what is the maximum range of the carbon ion? Does it penetrate the full thickness of the cell target?

$($c$)$ What is the approximate range of delta rays resulting from a maximum energy transfer from the carbon ion? Will the delta rays escape the cell culture? Hint: Make an approximation here using a Table $($from Turner reproduced on the exam formula sheet$),$ do not interpolate to answer this question.

$($d$)$ If a delta electron has a range of $($approximately$)$ the thickness of the cell sample, calculate what is the fraction of the electron's kinetic energy is emitted as bremsstrahlung? $($Hint: Assume $Z$ equivalent for cell tissue is $Z=7\mathrm{.}7).$