Energy Conservation - Electric Potential Energy

[darkblue]

Homework Statement

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.

Homework Equations

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?

 

[ideasrule]

You did the calculation wrong. Recheck.

 

[darkblue]

I don't quite understand what I've done wrong. I did the calculation again and I'm still getting 7.0x10^-9 C. I'm assuming the units of C are correct since the division yields Joules/Volt, and Joule = Coulomb * Volt. I also checked over my conversion of MV to V and that is correct as well.

 

[physx_420]

"Express your answer to two significant figures and include the appropriate units."

It should be 7.7x10^-9 C

 

[darkblue]

Oh I see...my calculator didn't show me those last few digits. Thanks so much for your help!