I was reading about how potential energy in atoms is measured by how far apart they are from one another. From what I have heard of potential energy, it's a way of showing how fast an object could move. E.G. if a basketball was lifted up off the ground, it could move because of more room to accelerate due to gravity. In the case of atoms, though, I don't see why the potential to move is dictated by how far apart the atoms are from one another. Could someone please explain?
In the same way that the basketball on a shelf could move faster (meaning, could reach a higher speed) if it was placed on a higher shelf and rolled over the edge then at a lower shelf, the atoms have a longer distance to travel when they are further apart and so could move faster (could reach a higher speed if the were set free) than if they where closer.
For two opposite charges that attract each other that means that the potential difference is the highest, when they are infinitely far from each other.
If they are let go and start moving closer to each other, the potential energy is converted into kinetic energy of the two. The more the potential energy drops (that is, the farther they were from each other from the start), the more the total kinetic energy rises and the faster they move.
Usually this level of potential energy infinitely far away is set to be $0$. Then, the closer they come, the more negative the potential energy becomes.
Are the charges equal so they repel each other, then the potential energy gets higher if they get closer together (which will require force, of course - like putting the ball back up on a shelf (to a higher potential)).
In that case, we usually still define "infinitely far from each other" to be the potential energy of $0$ joules. So the closer two equal charges get, the more positive the potential energy is (meaning, larger potential to speed up the charges). And if you let them go, they will seek towards lowest possible potential energy, which is the case when they are infinitely far from each other again.