# Time it takes for an electron and proton to collide

1. Sep 10, 2011

### gsingh2011

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. Sep 10, 2011

### vela

Staff Emeritus
What do you get when you use F=ma?

3. Sep 12, 2011

### gsingh2011

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. Sep 12, 2011

### vela

Staff Emeritus
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 $\dot{r}$. 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
5. Sep 14, 2011

### gsingh2011

It's a positron not a proton, so the mass is the same.

6. Sep 16, 2011

### vela

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