Question

In proton-beam therapy, a high-energy beam of protons is fired at a tumor. As the protons stop in the tumor, their kinetic energy breaks apart the tumor’s DNA, thus killing the tumor cells. For one patient, it is desired to deposit $0.10J$ of proton energy in the tumor. To create the proton beam, protons are accelerated from rest through a $10,000kV$ potential difference. What is the total charge of the protons that must be fired at the tumor?

Short answer

The total charge of the protons that must be fired at the tumor is$\mathbf{10}\mathbf{}\mathit{n}\mathit{C}$

Step-by-step solution

Given information and theory used 

Given :

For one patient, desired proton energy to be deposited : $0.10J$

Protons are accelerated through a potential difference of : $10,000kV$

Theory used :

Charge $q$will acquire an energy of $E=q∆V$if it is propelled through a potential difference $∆V$.

Calculating the total charge of the protons that must be fired at the tumor

If we want a certain amount of energy and our potential difference is constant, the required charge will be$q=\frac{E}{∆V}$

In terms of numbers, we have :

$$\begin{gathered} q=\frac{0.1}{{10}^7}=1\times {10}^{-8}C \\ =\boxed{\mathbf{10}\mathbf{}\mathit{n}\mathit{C}} \end{gathered}$$