Time it takes for an electron and proton to collide

  • #1
gsingh2011
115
1

Homework Statement


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.


Homework Equations


F=kq1q2/R2


The Attempt at a Solution


My problem is that the force is not constant. Do I integrate the force then? And from what bounds?
 
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  • #2
What do you get when you use F=ma?
 
  • #3
vela said:
What do you get when you use F=ma?

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.
 
  • #4
gsingh2011 said:
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.
The difference in masses breaks the symmetry. The proton won't move as far as the electron because it's so massive in comparison.
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.
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?
 
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  • #5
The proton won't move as far as the electron because it's so massive in comparison.
It's a positron not a proton, so the mass is the same.
 
  • #6
Oops, not sure why I thought it was a proton. Yes, you're right, they'll meet in the middle.
 
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