The ionization is often defined as ________. The energy needed to remove one or more electrons from a neutral atom to form a positively charged ion. But what is meant by removed? Suppose we have an infinitely large closed system with no content except a single atom (g). Now the ionisation energy can actually be as high as you like, at some point the electron will return to the atomic nucleus as it slowly slows down due to the constant (rapidly decreasing but always present) force of attraction, or not? So what does the energy quantity on ionisation energy refer to ________. I mean, if I take the energy E = F * s with s equal to infinity and F decreases with 1/r², then I would have to integrate to infinity and even if F continues to approach the x axis asymptotically, it remains only an approach to zero and viewed at x (so r, the distance between electron and nuclei) infinity, E would also have to be infinite? That is why I ask myself how a finite amount can be given in standard value tables for the ionisation energies of certain elements. For example, I also don't understand why you can use infinity for n in the rydberg formula to get the ionisation energy, does that work more because of the definition of the rydberg constant? Infinity would imply that the Rydberg constant builds in some kind of finite absolute scale that even knows what potential energy an electron would have at infinite distance from a proton (wouldn't that be infinite again??). It is very difficult for me to understand that something can escape an everlasting attractive force (even if it continues to decrease with distance) with a finite amount of energy.