physics
posted by rick .
An electron and a proton are initially very far apart (effectively an infinite distance apart). They are then brought together to form a hydrogen atom, in which the electron orbits the proton at an average distance of 5.11 1011m. What is EPEfinal  EPEinitial, which is the change in the electric potential energy?

They attract, so the potential energy will go down as they get close. (the result will be negative)
the force is a constant *1/r^2 = k/r^2
(You can do the charges and Coulomb's law)
So the real question is what is the integral from r = infinity to r = R (which is given as 5.11*10^11) of 1/r^2 dr ?
int from infinity to R of dr/r^2 = 1/r at R  (1/r) at infinity
= 1/R
now use that with k Q1 Q2 /r^2
to get
 k (charge of electron)^2 / R
for the change in potential energy coming in from infinity.
Of course that loss of potential went somewhere, so the thing must have that amount of kinetic energy, which is probably the next problem.