Periodic Properties and Table:

Upon the discoveries made which led us to the current, most-commonly-accepted representation of the atom for practical purposes today, more insight was also given into the relationships between them. One handy way to group atoms is the period table--a concept that has seen many reenditions over the years but has been rather ubiquitous in its current form for the last century or so.

Notably, the concept of a periodic table came before the existence of theory sufficient enough to explain the electronic effects responsible for the similarities between certain atoms, however, despite being arrange merely based on emperical data, there is a remarkably close correlation between it and certain key properties that explain this phenomenon.

Starting with groups, the table is arranged in several collumns and rows. We call each collumn a group, and we see that they tend to have similar properties. When looking at the electronic distribution for them, we see this appears to be no mere coincidence: groups have a common characteristic within their members being that they all share the same number of valence (or outer-most) electrons. These electrons are specifically the most relevant ones because they typically have substantially higher energy levels than their inner counterparts.This way, we observe that the period table is divided into groups of the same number of valence electrons on the vertical, changing mostly their mass through proton and neutron count heading down.

On the horizontal we have periods or rows, which show a different pattern. Sequentially speaking, each atom in a period has exactly one extra proton and one extra electron in its neutral state. As such, we see that the mass for periods also increases in a direction, this time left to right. Note: It is worth noting that each period also corresponds to a valence layer or shell number, increasing downwards.

Beyond this property, it is also worth examining the periodic table in terms of a nother wildly influential property: the atomic radius (defined by half the distance between two nuclei of the same atom, be it through covalent or ionic bonds with eachother, giving the adjective assigned to the property) is somewhat counterintuitive. As a whole, we notice that groups tend towards bigger radii as they descend further down, however periods tell a different story. One of the factors influencing the radius of an atom as defined through this is the extent to which their electrons expand to; for our purposes, we see that electrons in lower shells/layers of the atom contribute to an effect we call shielding, in which the charge of the electrons effectively counteract that of the same number of protons in a nucleus when found between the electron in question and the nucleus. As such, with less of an attractive force, we can imagine that the electron has more space to roam, thus yielding a higher radius despite the physical bulk expected from the extra matter at its core.

Because of this, we see one main pattern: as the number of proton increases within a period, the atomic radius decreases. We can explain this further looking at two cases. Consider Lithium (z=3) and Fluorine (z=9). As both are on the second period, we know their valence electrons also lie on the second shell. Belonging to family IA, Lithium has an electronic distribution of [He]2s¹ and Fluorine [He]2s² 2p⁵. We can calculate the effective charges for an electron on both of them like so: z_effective = 3 protons - 2 shielding electrons in the core = 1; z_effective = 9 protons - 2 electrons in the core = 7. Here, the pull on the electrons of the Fluorine atom is far stronger than that of the Lithium atoms, thus yielding in a tighter radius.