The Modern Periodic Table
With are knowledge of atomic structure, the modern Periodic Table is now laid out in order of atomic (proton) number and is directly linked to the electronic structure of elements.
Knowledge of the proton number and electronic structure sorted out the inconsistencies which Mendeleev had recognised purely from the physical and chemical properties of the elements known at the time (~1869).
We now know that due to the presence of, the relative atomic mass does go 'up/down' occasionally, BUT as Mendeleev recognised, chemically Te (tellurium) is like S (sulfur) and Se (selenium) etc. and I (iodine) is like Cl (chlorine) and Br (bromine) etc. and this is now backed up by modern knowledge of electron structure.
We know the electronic structure of elements and can understand sub-levels and the 'rules' in electron structure (see atomic structure page) e.g. 2 electrons in shell 1 (period 1, 2 elements H to He), 8 in shell 2 (period 2, 8 elements Li to Ne), there is a sub-level which allows an extra 10 elements (the transition metals) in period 4 (18 elements, K to Kr). this also explains the sorting out of Mendeleev's A and B double columns in a group (but that's for much more advanced chemistry!).
The periods are complete now that we know about Noble Gases