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Time it takes for an electron and proton to collide

  1. Sep 10, 2011 #1
    1. The problem statement, all variables and given/known data
    An electron and positron have mass me and separation R and are initially at rest. Find the time T it takes for them to collide.


    2. Relevant equations
    F=kq1q2/R2


    3. The attempt at a solution
    My problem is that the force is not constant. Do I integrate the force then? And from what bounds?
     
  2. jcsd
  3. Sep 10, 2011 #2

    vela

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    What do you get when you use F=ma?
     
  4. Sep 12, 2011 #3
    I don't know, acceleration is changing. Let say we have F=kq1q2/r2=ma. Since this problem is symmetrical, I was thinking the two particles would meet in the middle, so each would travel a distance of R/2. So I could divide by m and integrate twice to find the position function, and set that equal to R/2. The only problem with that idea is the force is changing with respect to r, so I can't integrate with respect to t. So I guess that method won't work.
     
  5. Sep 12, 2011 #4

    vela

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    The difference in masses breaks the symmetry. The proton won't move as far as the electron because it's so massive in comparison.
    The standard trick is to multiply by [itex]\dot{r}[/itex]. You'll find it makes both sides of the equation integrable, but first you need to find the correct equation.

    Are you familiar with the concept of the reduced mass?
     
    Last edited: Sep 12, 2011
  6. Sep 14, 2011 #5
    It's a positron not a proton, so the mass is the same.
     
  7. Sep 16, 2011 #6

    vela

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    Oops, not sure why I thought it was a proton. Yes, you're right, they'll meet in the middle.
     
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