Why are the properties of elements/atoms so varied? How come atoms can have such a wide range of appearance, as well as atomic & chemical properties?
At one point you have something invisible & gaseous at room temperature, add a few protons/neutrons/electrons, and you have something solid & shiny. Seems like a huge difference for a small change.
Even within the same element you can have a wide spectrum of properties - carbon for example has a few quite different allotropes (e.g. diamond vs graphite vs Q-carbon).
I'm not so much interested on how these differences arise (e.g. valence electrons), but rather why they are so varied. (Which is why I don't think this is a duplicate of either Do current models of particle physics explain the chemical properties of elements/compounds? or What enables protons to give new properties to an atom every time one is added?)
 A: The most obvious issue is that the electronic configuration determines periodicity in chemical behavior. Further, each new proton also shrinks the mean orbital radius of the outermost electrons, while electrons entering a higher energy level expands said radius. Charge-to-size ratios (for atoms, never mind the more numerous kinds of molecule) thereby end up all over the place, with implications for density, electronegativity and melting and boiling point. All this results in characteristic behaviours of s- and p-block elements, becoming truer in later periods for left-hand groups and less true in later periods for right-hand ones, and molecules being nothing like their constituent atoms (as usually they have full outer electron shells). For example, later alkali metals (halogens) more (less) readily lose (gain) electrons because of smaller $Z/r^2$ values.
A: Let's take the contrast between Helium and Lithium as an example. He has two protons and therefore two electrons, and they completely fill up the 1s orbital. So He cannot make any covalent bond in its atomic form. Add one proton to get Li, and therefore one electron as well. This electron will go on the next orbital, 2s, which has therefore room for another electron. So Li can make one covalent bond. The electron on the 2s orbitals can also "escape" their respective nuclei and make a "sea" of electrons shared by a macroscopic amount of atoms: that's why Li is a metal.
Now add some more protons to get to Neon. Its electrons distribute as follow between the atomic orbitals (number of electrons between parentheses): 1s(2) 2s(2) 2p(6). So all the three 2p orbitals are full, and Ne cannot make covalent bond. As He, and that's why they are on the top of each others in the Periodic Table.
Now add one more proton to get Na. The extra electron will go on the next available orbital, 3s, which has therefore room for another electron. As Li, it can make one covalent bond, or share that electron in the metallic manner. So they have very similar chemical properties, and that's why they are on the top of each others in the Periodic Table.
