1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Special Relativity: Collision of a Particle and Antiparticle

  1. Feb 11, 2015 #1
    1. The problem statement, all variables and given/known data
    A particle and its anti-particle are directed toward each other, each with rest energy 1,000 MeV. We want to create a new particle with rest energy 10,000 MeV and total energy 100,000 MeV. What must the speed of the particle and antiparticle be before the collision.

    ERest0 = m0c2 = 1,000 MeV
    ERestFinal = 10,000 MeV
    ETotal = 100,000 MeV

    2. Relevant equations
    γx = 1 / √[1 - (vx2 / c2)]

    Conservation of Energy:
    EInitial = EFinal
    Conservation of Momentum:
    PInitial = PFinal

    Total energy:
    ETotal = √[(pc)2 + (ERest)2]
    ETotal = ERestγ

    Relativistic Momentum for the particles:
    PInitial = m0 / c2 * [v1γ1 + v2γ2]

    Solving for momentum in terms of the total and rest energies:
    PFinal = 1 / c * √[(ET)2 - (ERestFinal)2]

    3. The attempt at a solution
    First I laid out conservation of energy.
    EInitial = EFinal
    ERest01 + γ2] = 100,000 MeV
    100 = γ1 + γ2

    Then I solved for the final momentum using the expression above which is derived from the total energy formula.
    PFinal = 1 / c * √[(100,000)2 + (10,000)2]
    PFinal = 1 / c * 99,498 MeV

    The I setup conservation of momentum.
    PFinal = PInitial
    1 / c * 99,498 MeV = m0 / c2 * [v1γ1 + v2γ2]

    1 / c * 99,498 MeV / [1,000 MeV / c2] = [v1γ1 + v2γ2]

    99.498c = [v1γ1 + v2γ2]

    This is where I get stuck. I don't know whether I should attempt to solve for one of the velocities or just in general which step to take next. I tried solving by setting one of the velocities to zero but I'm not sure if this is the correct way to do it.

    If I substitute v2 = 0:
    γ2 = 1

    100 = γ1 + 1
    99 = γ1
    √[1-(v12 / c2)] = 1 / 99
    v12 / c2 = 1 - (1 / 99)2
    v1 = √[1 - (1 / 99)2] c
    v1 = .99995c

    Is this answer right? v1 = .99995c and v2 = 0c

    Can someone please either verify my answer or give me a step in the right direction? Thank you.
     
    Last edited: Feb 11, 2015
  2. jcsd
  3. Feb 11, 2015 #2
    I actually figured it out, no need to reply
     
  4. Feb 14, 2015 #3
    Wait what did you do? I'm stuck.
     
  5. Feb 14, 2015 #4

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    It's generally better to work in terms of energy and momentum and then find velocities using ##v = E/p##. It simplifies the algebra.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Special Relativity: Collision of a Particle and Antiparticle
Loading...