Quantum and solid state physics

[zacl79]

Homework Statement

An electron and a proton are each accelerated through a potential difference of 10MV. find the momentum in MeV/c and the kinetic energy in MeV of each using relativistic formulae and compare with the results of using the classical formulae. Are the particles moving at relativistic speed?

Homework Equations

p=1/c*sqr((E^2)- (mc^2)^2)
p=ymc^2
p=mv
Ek=1/2mv^2

Rest energy of electron is 0.511MeV
Rest energy of proton is 938MeV

The Attempt at a Solution

i have found the momentum of the electron to be 10.5Mev/c by p=1/c sqr(((10+.511)^2)-(0.511)^2). And i believe that the kinetic energy of the electron is 10MeV.
The problem arises when i try to calculate the classical momentum and compare it to the relativistic. I think once shown how to do that i can apply it to the proton. But this question has had me going around in circles for quite some time.
I appreciate the help anyone can give me.

Thanks

 

[ehild]

You are right, the KE of the electron is 10 MeV.
How do you calculate kinetic energy and momentum in Classical Mechanics?

ehild

 

[zacl79]

Ek=1/2mv^2 and p=mv, v/c=sqr(1-((mc^2)/E)^2)
i only have a problem when it asks to compare them, they have to be in the same units to compare properly don't they?

 

[ehild]

Ek=1/2mv^2 and p=mv, v/c=sqr(1-((mc^2)/E)^2)
i only have a problem when it asks to compare them, they have to be in the same units to compare properly don't they?

Yes, of course, but you can converse MeV to joules, don't you?

ehild

 

[zacl79]

yes, i can convert to joules 1eV=1.6x10^-19 J, but what about momentum? obviously there is somethign that I am not quite clicking onto unit wise, how does Mev/c convert into kg.m/s?

 

[ehild]

Convert MeV to joules [kgm^2/s^2] Dividing by c [m/s] results in kgm/s.

ehild

 

[zacl79]

by doing so, won't i be out out by a factor of 2, as Ek=1/2mv^2 and p=mv?