What repeats periodcally in the periodic table?

Answer 1

The "periods" of the Periodic Table are the rows (horizontals). In each group (column, verticals), a variety of chemical properties are very similar, in a predictable pattern.

Each group tends to have very similar melting points and boiling points (with the exception of those groups crossing the metal-nonmetal boundary, and whichever group contains hydrogen on your table - hydrogen doesn't really follow the table's rules), as well as electronegativities (a fairly advanced concept in the study of ionic behavior of atoms, but basically a measure of how able it is to accept an electron).
This last concept is illustrated by comparisons of how simple compounds form. Take sodium and chlorine, and their respective groups (Li, Na, K, Rb, Cs, Fr for sodium; F, Cl, Br, I, At for chlorine). Because we know Sodium chloride (NaCl) forms (it's table salt), we can conclude that it is reasonable to assume that any pair generated from one element of each of these groups will form (though this isn't a perfect system, even ionic chemistry isn't THAT simple)

Realistically, these repeats in the periodic table should only be taken as general trends. They used to be extremely useful back when a lot of elements hadn't been discovered, but now that it's been filled out (unless you find a way to make a half proton, or stabilize something with over 110 protons long enough to perform this kind of test), it's not as useful. Renaissance chemists could identify newly isolated elements by comparing its physical properties to those of known elements, thus identifying its position on the table long before the technology needed to measure the number of protons existed (heck, before the concept of protons was fully understood or even accepted). These days chemists don't have to worry about unidentified elements cropping up - short of something overturning the current atomic theory completely, the only possible unknown elements only exist in specialized particle physics labs and only for extremely short periods of time before fission spontaneously occurs. If you want more accurate predictions of chemical behaviors, look up the literature on the elements in question and study thermodynamics and chemical dynamics.