**Diffusion angle of a ball as a function of kinematic energy and targeting error**
I'm working on an idealized mechanical model of the electromagnetic interaction between an incident alpha particle and an atom's nucleus, like in the Rutherford experiment and his golden sheets. The idea is to launch a ball with a targeting error b (the distance between the initial direction of movement and the parallel line that would hit the center of repulsion) and a kinematic energy K on a potential hill equivalent to the electric repulsion in 1/rē (thus the electric potential in 1/r), and from analyzing the case, evaluating how the diffusion angle depends on b and K.
I already know that the angle decreases as K increases and b increases. I would suspect that the angle varies as 1 / (b K), but I'd like to make the formal calculation to demonstrate it (or show the exact relation if I'm not right about powers of the variables).
I was thinking either to analyze the forces in presence, or else to go though energy and quantity of movement considerations, but I'm not sure whether those approaches are sufficient, or if the calculation can be made through basic calculus. I've worked a few pages, but for now that doesn't seem to go anywhere.
If you have clues to orient me in the right direction and let me use the right mathematics to tackle this problem, I would appreciate.
I'm self-studying an old French physics manual from PSSC ("Physique," 3rd edition, 1974), and I'm trying to go a bit further than their exercises to better grasp the subject. The present question is derived from problem 23-7.
Thanks.
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Last edited by Steph; Feb 10th 2013 at 06:09 PM.
Reason: Adding details
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