How to find minimum distance of approach?
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If an alpha particle with a kinetic energy Ea is fired directly towards a gold nucleus it will feel a repulsion which increases as it gets closer - climbing the potential hill surrounding the nucleus. When all the kinetic energy has been converted to potential energy the alpha particle (charge q) has reached its distance of closest approach (d0) and comes to rest. At that point :
Eα = qVE = (1/4πεo)qQ/do so therefore: do = (1/4πεo)qQ/Eα
The diagram shows the paths of other alpha particles that were not travelling directly towards the centre of the nucleus. These are scattered.

Distance of closest approch animation
For the schoolphysics animation showing the distance of closest approach please click the animation symbol:
Eα = qVE = (1/4πεo)qQ/do so therefore: do = (1/4πεo)qQ/Eα
The diagram shows the paths of other alpha particles that were not travelling directly towards the centre of the nucleus. These are scattered.

Distance of closest approch animation
For the schoolphysics animation showing the distance of closest approach please click the animation symbol:
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