00:01
All right, so let's say we have an alpha particle moving towards a proton with a speed we'll call v alpha of 3 times 10 to the 5th meters per second, and then we have a proton moving towards the alpha particle with a speed of 10 to the 5th meters per second, and we want to find the minimum possible distance between the two particles.
00:25
So by momentum conservation, the momentum of the system is the mass of our alpha particle, which i'll say we'll call it 4m, and the mass for our proton is m, so let's write this as 4m v alpha minus m v p.
00:50
That's our initial momentum, and so that should be constant, and our initial potential energy we're told is zero, so our final potential energy is going to be, since the charge of an particle is 2e, this will be 2k e squared over r, and our initial kinetic energy is going to be basically one half of the alpha particle's mass, so that's 2m v alpha squared plus one half m v p squared, and the final momentum is when they're basically traveling at the same speed, so we'll have 4m plus m times some speed we'll just call v, and so the kinetic energy at that point is going to be 2m plus one half m times v squared, so obviously this is going to be like 5m v, and this is going to be five halves m v squared...