In proton-beam therapy, a high-energy beam of protons is fired at a tumor. The protons come to rest in the tumor, depositing their kinetic energy and breaking apart the tumor’s DNA, thus killing its cells. For one patient, it is desired that 0.10 J of proton energy be deposited in a tumor. To create the proton beam, the protons are accelerated from rest through a 13 MV potential difference.
What is the total charge of the protons that must be fired at the tumor to deposit the required energy?
Express your answer to two significant figures and include the appropriate units.
U = qv
KE = 1/2mv^2
E = 0.10 J
change in v = 13 000 000 V
The Attempt at a Solution
I took 0.10 J as the total energy, seeing as this is the amount that must be deposited in the tumor. The protons start from rest, so KE = 0 while U = qv, where q is the total charge of the protons and v is the potential difference, which is 13x10^6 V.
E = qv
0.10/13000000 = q
q = 7.0x10^-9 C
This is not the right answer though...is there something wrong with my logic?