Comprehensive Guide to Periodic Properties of Elements

Principles of Atomic Radius

Atomic radius is defined as the average distance from the most external electron to the nucleus of an atom. To determine this value, the atomic radius is calculated as half the distance between the nuclei of two identical atoms, expressed as:

$Radio\,Atómico = \frac{d}{2}$

where $d$ represents the distance between nuclei. The atomic radius fluctuates according to specific patterns within the periodic table. In a group, the atomic radius increases as the number of electron shells or layers increases. In a period, the atomic radius increases as the atomic number decreases; as the atomic number increases within a period, the radius decreases because the nucleus pulls more strongly on the electrons.

Ionic Radius and Ion Formation

The radius of an ion differs significantly from its original neutral atom. Anions are larger than the original atoms from which they are formed. This occurs because the attraction of the nucleus on the electrons becomes weaker, and additionally, the electrons push against one another due to repulsion. In contrast, cations are smaller than the original atoms. This happens because the number of electrons decreases, which leads to a stronger attraction from the nucleus on the remaining electrons. Specific elements such as Wat and Sodium ($Na$) are notes in this context. In terms of periodic trends, ionic radius increases within a group and increases across a period (typically documented as increasing towards the left).

Electron Affinity

Electron affinity ($AE$) is defined as the energy released when an electron is added to an atom in its gaseous state. A clear relationship exists between the size of an atom and its affinity for electrons: the smaller the atomic radius, the easier it is to add electrons, which results in a higher electron affinity. For an atom like Chlorine ($Cl$) in a gaseous state with an atomic number of $Z = 17$ and $17$ initial electrons, adding one electron results in the following reaction:

$Cl_{(g)} + 1e^{-} \rightarrow Cl^{-}_{(g)} + E$

In this process, the atom becomes a Chlorine anion with $18$ electrons, and the energy released is $3.61\,eV$. Electron affinity increases moving up a group and increases across a period from left to right.

Electronegativity and Electropositivity

Electronegativity is the capacity of an atom to attract electrons toward itself within a chemical bond. When two identical atoms bond, the pair of electrons is attracted equally by both nuclei because they possess the same electronegativity. Among the elements, Iodine is identified as the most electronegative. Noble gases like Krl (Criptón) and Xenon ($Xe$) also exhibit electronegativity. This property increases moving up a group and increases across a period from left to right.

Electropositivity is the capacity of an atom to lose electrons. Elements like Sodium ($Na$) and Potassium ($K$) are among the most electropositive elements, a trait characteristic of metals. This property is directly proportional to atomic size: the larger the radius of the element, the greater its electropositivity. Therefore, electropositivity increases down a group and increases across a period from right to left.

Density and Energy of Ionization

Density is a physical property of elements, with Osmium ($Os$) being recognized as the densest element in the periodic table. Ionization energy ($E_{I}$) is the energy required to extract an electron from an atom in the gaseous state, where atoms are separated from each other. For example, to remove an electron from a gaseous Sodium ($Na$) atom ($Z = 11$, $11$ electrons) to form a Sodium cation ($Na^{+}$) with $10$ electrons, the system must gain energy:

$Na_{(g)} + E_{I} \rightarrow Na^{+}_{(g)} + 1e^{-}$

The energy required for this specific extraction is $5.1\,eV$. It is possible to extract more than one electron from an atom through successive steps. In Chromium or Magnesium ($Mg$), the energy required for successive ionization follows this progression:

First Ionization: $Mg_{(g)} + 1^{\circ}E_{I} \rightarrow Mg^{+}_{(g)} + 1e^{-}$

Second Ionization: $Mg^{+}_{(g)} + 2^{\circ}E_{I} \rightarrow Mg^{2+}_{(g)} + 1e^{-}$

Third Ionization: $Mg^{2+}_{(g)} + 3^{\circ}E_{I} \rightarrow Mg^{3+}_{(g)} + 1e^{-}$

A higher amount of energy is invariably required to extract an electron from a cation than from a neutral atom. The trend for ionization energy is that it increases as the atomic radius becomes smaller, making it more difficult to remove an electron. Consequently, ionization energy increases moving up a group and increases across a period from left to right.