Thanks to the efforts of the physicists, we now know that atoms are made from other, smaller particles. For a while it was thought that there were just three such particles: the neutron, the proton, and the electron. The neutron and proton have almost equal masses, while the electron is tiny in comparison; the neutron has no electrical charge, the proton has a positive charge, and the electron has a negative charge exactly opposite to that of the proton. Atoms have no overall charge, so the numbers of protons and electrons are equal. There is no such restriction on the number of neutrons. To a good approximation, you get an element's atomic weight by adding up the numbers of protons and neutrons, for example oxygen has eight of each, and 8 + 8 = 16, the atomic weight.
Atoms are incredibly small by human standards, about a hundred millionth of an inch (250 millionths of a centimetre) across for an atom of lead. Their constituent particles, however, are considerably smaller. By bouncing atoms off each other, physicists found that they behave as if the protons and neutrons occupy a tiny region in the middle, the nucleus, but the electrons are spread outside the nucleus over what, comparatively speaking, is a far bigger region. For a while, the atom was pictured as being rather like a tiny solar system, with the nucleus playing the role of the sun and the electrons orbiting it like planets. However, this model didn't work very well, for example, an electron is a moving charge, and according to classical physics a moving charge emits radiation, so the model predicted that within a split second every electron in an atom would radiate away all of its energy and spiral into the nucleus. With the kind of physics that developed from Isaac Newton's epic discoveries, atoms built like solar systems just don't work. Nevertheless, this is the public myth, the lie-to-children that automatically springs to mind. It is endowed with so much narrativium that we can't eradicate it.
After a lot of argument, the physicists who worked with matter on very small scales decided to hang on to the solar system model and throw away Newtonian physics, replacing it with quantum theory. Ironically, the solar system model of the atom still didn't work terribly well, but it survived for long enough to help get quantum theory off the ground. According to quantum theory the protons, neutrons, and electrons that make an atom don't have precise locations at all, they're kind of smeared out. But you can say how much they are smeared out, and the protons and neutrons are smeared out over a tiny region near the middle of the atom, whereas the electrons are smeared out all over it.
Whatever the physical model, everyone agreed all along that the chemical properties of an atom depend mainly on its electrons, because the electrons are on the outside, so atoms can stick together by sharing electrons. When they stick together they form molecules, and that's chemistry. Since an atom is electrically neutral overall, the number of electrons must equal the number of protons, and it is this 'atomic number', not the atomic weight, that organizes the periodicities found by Mendeleev However, the atomic weight is usually about twice the atomic number, because the number of neutrons in an atom is pretty close to the number of protons for quantum reasons, so you get much the same ordering whichever quantity you use. Nevertheless, it is the atomic number that makes more sense of the chemistry and explains the periodicity. It turns out that period eight is indeed important, because the electrons live in a series of 'shells', like Russian dolls, one inside the other, and until you get some way up the list of elements a complete shell contains eight electrons.
Further along, the shells get bigger, so the period gets bigger too. At least, that's what Joseph (J. J.) Thompson said in 1904. The modern theory is quantum and more complicated, with far more than three 'fundamental' particles, and the calculations are much harder, but they have much the same implications. Like most science, an initially simple story became more complicated as it was developed and headed rapidly towards the Magical Event Horizon for most people.
But even the simplified story explains a lot of otherwise baffling things. For instance, if the atomic weight is the number of protons plus neutrons, how come atomic weight isn't always a whole number? What about chlorine, for instance, with atomic weight 35.453? It turns out there are two different kinds of chlorine. One kind has 17 protons and 18 neutrons (and 17 electrons, naturally, the same as protons), with atomic weight 35. The other kind has 17 protons and 20 neutrons (and 17 electrons, again), an extra two neutrons, which raises the atomic weight to 37. Naturally occurring chlorine is a mixture of these two 'isotopes', as they are called, in roughly the proportions 3 to 1. The two isotopes are (almost) indistinguishable chemically, because they have the same number and arrangement of electrons, and that's what makes chemistry work; but they have different atomic physics.
It is easy for a non-physicist to see why the wizards of UU considered this universe to be made in too much of a hurry out of obviously inferior components ...
Where did all those 112 elements come from? Were they always around, or did they get put together as the universe developed?
In our Universe, there seem to be five different ways to make elements:
• Start up a universe with a Big Bang, obtaining a highly energetic ('hot') sea of fundamental particles. Wait for it to cool (or possibly use one you made earlier ...). Along with ordinary matter, you'll probably get a lot of exotic objects like tiny black holes, and magnetic monopoles but these will disappear pretty quickly and only conventional matter will remain, mostly. In a very hot universe, electromagnetic forces are too weak to resist disruption, but once the universe is cool enough, fundamental particles can stick together as a result of electromagnetic attraction. The only element that arises directly in this manner is hydrogen, one electron joined with one proton. However, you get an awful lot of it: in our universe it is by far the commonest element, and nearly all of it arose from the Big Bang. Protons and electrons can also associate to form deuterium (one electron, one proton, one neutron) or tritium (one electron, one proton, two neutrons), but tritium is radioactive, meaning that it spits out neutrons and decays into hydrogen again. A far more stable product is helium (two electrons, two protons, two neutrons), and helium is the second most abundant element in the universe.
• Let gravity get in on the act. Now hydrogen and helium collect together to form stars, the wizards' 'furnaces'. At the centre of stars, the pressure is extremely high. This brings new nuclear reactions into play, and you get nuclear fusion, in which atoms become so squashed together that they merge into a new, bigger atom. In this manner, many other familiar elements were formed, from carbon, nitrogen, oxygen, to the less familiar lithium, beryllium and so on up to iron. Many of these elements occur in living creatures, the most important being carbon. For reasons to do with its unique electron structure, carbon is the only atom that can combine with itself to form huge, complex molecules, without which our kind of life would be impossible. Anyway, the point is that most of the atoms from which you are made must have come into being inside a star. As Joni Mitchell sang at Woodstock:: 'We are stardust.' Scientists like quoting this line, because it sounds as though they were young once.
• Wait for some of the stars to explode. There are (comparatively) small explosions called novas, meaning 'new (star)', and more violent ones, supernovas. (What's 'new' is that usually we can't see the star until it explodes, and then we can.) It's not just that the nuclear fuel gets used up: the hydrogen and helium that fuel the star fuse into heavier elements, which in effect become impurities that disturb the nuclear reaction. Pollution is a problem even at the heart of a star. The physics of these early suns changes, and some of the larger ones explode, generating higher elements like iodine, thorium, lead, uranium, and radium. These stars are called 'Population II' by astrophysicists, they are old stars, low in heavy elements, but not lacking them entirely.