Coulomb's Law Inside the Atom

Opposite charges attract, and Coulomb's law gives the exact rule: force equals a constant times the product of the two charges, divided by the square of the distance between them. The nucleus is positive, the electron is negative, so there's always a pull holding the electron in. That pull falls off fast with distance, since distance is squared in the denominator. Double the distance and the force doesn't drop by half, it drops to one quarter. Triple it and the force drops to one ninth. That squared relationship is the whole engine behind atomic structure: it decides why electrons settle into layers rather than drifting away.

This is also why a core electron, sitting close to the nucleus, feels a far stronger grip than a valence electron sitting out at the edge of the atom. Small distance means a huge force; large distance means a weak one. That is the mechanical reason core electrons are nearly impossible to remove while valence electrons come and go easily in bonding.

There's a catch for atoms with more than one electron. An outer electron doesn't feel the nucleus's full positive charge, because the electrons sitting between it and the nucleus block, or shield, part of that charge. The outer electron responds to an effective nuclear charge, smaller than the actual number of protons. This shielding idea connects straight into why atomic size, ionization energy, and other periodic trends behave the way they do across a row or down a column.