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Question regarding Rutherford's atomic model

  1. Feb 24, 2013 #1
    1. The problem statement, all variables and given/known data
    ScreenShot2013-02-24at100839PM_zps1ff6fa80.png

    I am basically wondering how they got to the assumption that the Ve = 2Vα. I've tried it a few times and I keep on getting that based off of their other assumptions, Ve should =0, even though I know that this cannot possibly be the case.
    2. Relevant equations

    Conservation of momentum: Mava = Mav'a + meve

    Conservation of energy: .5Mava2 = .5Mav'a2 + .5Meve2

    3. The attempt at a solution

    I really don't know what to do. I've tried starting under the assumption as given that Va≈Va', which leads to getting Ve=0. I tried to do a binomial expansion using the fact that Me<<Ma, but again I got zero. I'm really not sure how to approach this. Any help would be appreciated.
     
  2. jcsd
  3. Feb 24, 2013 #2

    tms

    User Avatar

    It's not an assumption, it's a conclusion.

    Set up the equations for an elastic collision in one dimension, then get a general solution for the final velocities of both particles. Don't put in any numbers or the like, just get a general solution. Then assume that [itex]m_1 >> m_2[/itex], and see what you get for [itex]v_{2f}[/itex].
     
  4. Feb 27, 2013 #3
    Thank you very much. That makes much more sense, I'm not really sure why I didn't just do that the first time. My mistake was not solving for Valpha' in terms of the other equations. Once I realized that I had to do that, it was much clearer.
     
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