In proton-beam therapy, a high-energy beam of protons is fired at a tumor. As th
ID: 1268104 • Letter: I
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 0.12J of proton energy in the tumor. To create the proton beam, protons are accelerated from rest through a 9000kV potential difference.
What is the total charge of the protons that must be fired at the tumor?
Express your answer to two significant figures and include the appropriate units.
Explanation / Answer
From conservation of energy, the increase in kinetic energy of the protons equals their decrease in potential energy. In other words, .
?K=??U=?q?V
In the following figure, the source of the potential difference is a capacitor, with the negatively charged plate having a hole cut in the center to allow protons through. Notice that while the protons are between the plates, they are accelerating, but once they pass through the plate on the right, they maintain a constant speed. This is because there is no electric field outside an ideal capacitor
If we solve the equation for q, we get:
?K =?q?V
?K = 0.12 J
?V = 9000 KV= 9*10^6
q= 0.12/9*10^6 = 0.0133*10^-6 = 1.33 *10^-8 = 13.33 nC
Here we have used the fact that since the protons are accelerating, they must be traveling through a decreasing potential. Consequently, ?V is negative and ??V=?V