What happens to the electric force of attraction between an electron and a proton as they approach one another?

The force of attraction increases as an electron and a proton approach each other. And it varies inversely as the square of the distance between the particles. Let's break it down. Ready? Jump with me. The electron and the proton have a negative electrostatic charge and a positive electrostatic charge respectively. Each charge - and the force associated with that unit of charge - is constant - and equal. (The electron and proton have equal, but oppositely polarized, electrostatic charges.) But there is more. According to the law of electrostatics, like charges repel, and opposite charges attract, so they will be attracted to each other. And as they get closer, the force acting on them to pull them together increases - by the inverse square of the distance that separates them. Keep going. If an electron and a proton are a given distance apart, they will attract each other. The electron, because it is only about 1/1836th (or so) of the mass of the proton, will do almost all of the moving. The force acting on each particle is the same, but because the electron is lighter by a ton, the force acting on it will cause it to accelerate much more than the proton will accelerate. When the distance between the two particles is half of what it was at the start, the force of attraction between the two bodies will be four times what it was at the start. It is Coulomb's Law that is at work here, and this is the statement of that law: The magnitude of the electrostatic force between two point electric charges is directly proportional to the product of the magnitudes of each charge and inversely proportional to the square of the distance between the charges. Need links? You got 'em.