 Solution

TODO: Biology deferred at the user's request: the cancer-treatment account, clinical dose choices, treatment planning and clinical interpretation of the numerical model.

For the specified energy-loss model, multiply $dE/dx=-k/E$ by $2E$ and integrate from the entrance:The positive stopping power is $S=-dE/dx=k/E$. The model reaches zero kinetic energy atAt the entrance,Half a centimeter before the formal endpoint, $E^2=2k(0.5\mathrm{cm})=770\mathrm{Me}{\mathrm{V}}^2$, soThe signed derivatives are the negatives of the quoted stopping powers. This inverse-energy stopping-power model deposits energy more strongly toward the endpoint. Its divergent endpoint derivative is integrable, giving finite total deposited energy $E_0$; a real stopping curve includes finite energy spread, range straggling, scattering and a more accurate low-energy stopping law. These numbers are consequences of the supplied ideal equation.