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How to convert Gev/c into m/s

  1. Apr 19, 2012 #1
    As the title said :)

    I'm trying to find the velocity of a particle with a momentum of between 23 and 150 GeV/c. I found that 1 GeV/c = 5.36 x 10^-19 kg-m/s, and tried to divide by the mass of the particle - this just game me values between 7m/s and some crazy numbers.

    What am I doing wrong :(
  2. jcsd
  3. Apr 19, 2012 #2
    One way is to use the relation
    [tex] E^2=\left(mc^2 \right)^2+\left(pc \right)^2 [/tex]
    where [itex] pc [/itex] is 23 to 150 GeV (momentum in energy units), and [itex] mc^2 [/itex] is the particle's rest mass (proton is 0.938 GeV). Then use [itex] \beta =pc/E [/itex] to get [itex] \beta [/itex], and [itex] v=\beta c [/itex].
    Last edited: Apr 19, 2012
  4. Apr 21, 2012 #3
    Thank you for your help Bob S - I still can't manage to get the answer though.

    When I set m to 5.5208x10^27kg, and p to 25GeV/c I end up getting a value that is faster than c when I solve for v. Can anyone help with this?
  5. Apr 21, 2012 #4
    If 1 GeV/c = 5.36 x 10-19 kg-m/s though, why can't I do 25(5.36x10^-19)/particle's mass?
  6. Apr 21, 2012 #5
    Using the relation
    [tex] E^2=\left(mc^2 \right)^2+\left(pc \right)^2 [/tex]
    where [itex] pc= [/itex] 50 GeV and [itex] mc^2= [/itex] 0.938 GeV, E = 50.008798 GeV.
    So β= 50/ 50.008798= 0.99982 and βc = 2.9974 x 1010 cm/sec
  7. Apr 21, 2012 #6


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    Staff: Mentor

    Because p ≠ mv, if you're using the particle's "rest mass" in kg. The correct equation is

    $$p = \frac{mv}{\sqrt{1 - v^2/c^2}}$$
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