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Velocity of a proton

  1. May 6, 2013 #1

    I regard a particle in an accelerator. The particle has the kinetic energy of 7TeV.

    I have callculated the momentum $$
    \Rightarrow p=\frac{1}{c} \sqrt{E^2 -(mc^2)^2} =7,00094~ TeV/c

    After that I want to callculate the "velocity" and the "[itex] \gamma[/itex]-factor".
    But I am irritated and don't know which equations are allowed for this relativistic callculations.

    For example I have found the equation $$


  2. jcsd
  3. May 6, 2013 #2


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    Science Advisor

    If it's the LHC you're talking about, 7 TeV represents the total energy of the particle, not just the kinetic energy.

    Try E = γmc2.
  4. May 15, 2013 #3


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    That should be
    \Rightarrow p=\frac{1}{c} \sqrt{E^2 -(mc^2)^2} \approx 7 TeV/c

    The last assumes that the mass energy is very small compared to 7 TeV. If it's a proton then the mass is 0.938 GeV, which is quite small compared to 7 TeV.

    You've got either gamma or beta wrong. I don't know your convention.

    But there's an easier way. The kinetic energy is [itex] (\gamma -1) m c^2 = 7 TeV[/itex] and so you can work out [itex] \gamma= (7 TeV - m c^2) / m c^2 [/itex], and to three digits that's 7460. And then you can work out v. (Assuming I did the arithmetic correctly.)

    v = c \sqrt{1-\frac{1}{\gamma^2}} \approx c (1 - \frac{1}{2(7460)^2})
    \approx c(1-8.89 \times 10^{-9})
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