What are the anatomical, physiological, and cellular mechanisms?

What are the underlying physical mechanisms responsible for the Periodic Law of Elements?

• Perhaps the best "explanation" for the Periodic Law of elements is given by quantum mechanics. Though, we may pragmatically argue that since quantum mechanics mostly explains the Periodic Law, we "understand" what is responsible for the Law. However, looking for a more complete answer, what physical mechanisms underlie the quantum mechanical mathematics involved, and/or what other mechanisms are involved?

• Answer:

  Well, if you want it simply, atoms with more positive nuclear charges have room for more electrons, to  balance out the charge. The number of nuclear charges is the number  place on the periodic table. These electrons go into the atoms in pairs, in every possible type of three-dimensional wave that will fit around the atom. Each type of wave only has room for two electrons, which for reasons that have no natural and simple explanation, do not like each other when forced to crowd closer. These waves form things like surfaces that become parts of the atom, like nested layers of an onion. As electrons are added to outer reaches atoms of higher number that have more room for them, more and more of them have room to fill up the various wave modes in a larger shell which is farther away from the nucleus. Each set of electrons at a given distance forms a kind of shell of electrons of similar energy, but each shell only has room for a limited number of electrons. As the atoms get bigger, the shells repeat in structure, with each shell repeating the one below it, but also having room for more electron in more wave "slots" when it is large enough. The next shell repeats and again adds. That periodicity of electron shell filling results in a periodicity of chemical properties and physical properties, which are set by the outer electrons in the outer shell of each kind of atom. Okay, that's horribly simplified and wrong in some ways, but truth and clarity are conjugate variables. Let's see you do better. ;')