Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Velocity of a proton

  1. May 6, 2013 #1
    Hello,

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

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

    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 $$

    \vec{p}=m\gamma\vec{v}$$
    and
    $$
    \gamma=\frac{1}{\sqrt{(1-\beta)}}~~~~~~~;\beta=\frac{v}{c}=\frac{pc}{E}
    $$


    THX
    Abby
     
  2. jcsd
  3. May 6, 2013 #2

    Bill_K

    User Avatar
    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

    DEvens

    User Avatar
    Education Advisor
    Gold Member

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

    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.
    $$
    \gamma=\frac{1}{\sqrt{(1-\frac{v^2}{c^2})}}
    $$

    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.)

    $$
    v = c \sqrt{1-\frac{1}{\gamma^2}} \approx c (1 - \frac{1}{2(7460)^2})
    \approx c(1-8.89 \times 10^{-9})
    $$
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Velocity of a proton
  1. LHC forces on a proton (Replies: 2)

  2. Proton Acceleration (Replies: 12)

Loading...