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Homework Help: Quantum and solid state physics

  1. Mar 13, 2010 #1
    1. The problem statement, all variables and given/known data
    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?



    2. Relevant 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


    3. 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
     
  2. jcsd
  3. Mar 13, 2010 #2

    ehild

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

    ehild
     
  4. Mar 13, 2010 #3
    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 dont they?
     
  5. Mar 13, 2010 #4

    ehild

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

    ehild
     
  6. Mar 13, 2010 #5
    yes, i can convert to joules 1eV=1.6x10^-19 J, but what about momentum? obviously there is somethign that im not quite clicking onto unit wise, how does Mev/c convert into kg.m/s?
     
  7. Mar 14, 2010 #6

    ehild

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

    ehild
     
  8. Mar 14, 2010 #7
    by doing so, wont i be out out by a factor of 2, as Ek=1/2mv^2 and p=mv?
     
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