What is the maximum speed of a proton if its kinetic energy is 1.28x10^-14 J?

[lilymay992]

Homework Statement

Hi! So for my a levels I’ve been doing practice papers and I’m stuck. I have to calculate the kinetic energy of a proton after acceleration except I’m only given the charge of +1.6x10^-19 , a potential difference of 80kV, and a mass of 1.7x10^-27kg

Relevant Equations

Kinetic energy = 1/2 x mass x velocity^2

So first I tried to use KE=1/2 x m x v^2 but then realized I didn’t have the velocity and I can’t figure out a way to obtain it. I then tried to work out the energy using a different equation, W= q x v but that left me with 1.28x10^-14 J which seemed too small.

I also then have to calculate the maximum speed of the proton which I’m confused at how to do if I don’t have the velocity.

Thanks in advance!

 

[Orodruin]

You have the charge and you have the change in electric potential. What does this mean for the change in the potential energy of the proton and where does this potential energy go during acceleration?

 

[lilymay992]

Oh so do I use V= p.e. / q because the electrical energy has been transferred to kinetic energy during the acceleration?

 

[Orodruin]

That does seem like a viable option, yes.

 

[lilymay992]

Thank you for your help!

 

[PeroK]

Thank you for your help!

Note that the joule is the SI unit of energy. In particle physics, however, it's more usual to use the electron-volt as the unit of energy. This is the energy gained by an electron ( or other particle with the same charge) accelerated through 1 volt.

Another way to do your problem is to use the immediate answer in terms of electron volts and then look up the conversion to joules.