2.6 Periodicity

---

2.6.1 Atomic radius

I. Atomic radius: half the distance between the centers of neighboring atoms

1. Although there are no exact boundaries of electron clouds, the nuclei are found at definite distances from one another in solids and metals (bonding!)

II. Covalent radius: half the distance between the nuclei of atoms joined by a chemical bond (used for nonmetal or metalloids).

III. van der Waals radius: half the distance between centers of neighboring atoms in a sample of the solidified gas (used in monoatomic gases)

IV. Atomic radius generally decreases from left to right across a period and increases down a group

1. With each new period, the valence electrons occupy shells with increasing principal quantum number and therefore its electrons lie farther away from the nucleus

2. As you go towards the right of the periodic table, the number of protons increases and therefore grasps the electrons more strongly, pulling them closer to the nucleus

3. Across a period, Zeff dominates, and going down a group, n dominates.

V. Ionic radii trends are very similar to atomic radii

1. as electrons are added, the size of the ion increases as there are more electron-electron repulsions while having the same number of protons.

2. as electrons are removed, the size of the ion decreases as there are less electron-electron repulsions while having the same number of protons.

2.6.2 Ionization Energy

VI. Ionization energy: the energy required to remove an electron from a gaseous atom or ion

$A^{n+}(g) \rightarrow A^{(n+1)+}(g) + e^{-}$

$I = \Delta U$

VII. Some of the common characteristics of first ionization energies of the periodic table are:

1. High IE1 for noble gases: ns2np6 configurations are particularly stable and require more energy for an electron to be removed.

2. Very low IE1 for Group I: removing one electron gives a noble gas configuration.

3. Be-B drop in IE1: The np-electron is shielded by the ns-electrons and therefore easier to remove.

4. N-O drop in IE1: two electrons in the same orbital (paired electrons) leads to repulsion

VIII. Ionization energy measures how difficult it is to remove an electron; as effective nuclear charge increases, the nuclei grips the electron more tightly and more energy is needed to take it out

IX. When an electron is removed, the shielding constant (S) decreases and therefore Zeff increases; as a result, the cation size decreases holding the electrons tighter. Therefore, ionization energy increases with each step.

2.6.3 Electron Affinity

X. Electron affinity: the energy released when an electron is added to a gas-phase atom

1. Electron affinity have different variations of definitions that all mean the same thing:

   1. Atkins: The definition shown above

   2. Miessler: The energy required to remove an electron from a negative anion $A^{-}(g) \rightarrow A(g) + e-$ where $E_{ea} = \Delta U$

   3. Housecroft: $-\Delta U$ for the gain of an electron by a gaseous atom (at 0 K) $Y(g) + e- → Y^{-}(g)$ where $E_{ea} = \Delta U$

2. sometimes, the 1st electron affinity is referred to as the "zeroth ionization energy"

3. when an electron is added to a neutral atom, most elements tend to release heat

   1. Exception: noble gases (disrupts full-shell stability) and alkaline earth metals

4. Greater Zeff tends to release more energy when an electron is attached

2.6.4 Inert-Pair Effect and Diagonal Relationships

XI. Inert-Pair effect: the tendency to form ions two units lower in charge than expected from the group number

1. The energy separation between ns and np orbitals increase down the group as s orbitals have much greater penetration compared to p orbitals

2. Because ns orbitals are much lower in energy than np orbitals, electrons in the ns valence orbitals are not lost

   1. In group 13, aluminum forms Al3+ ions, while indium forms both $In^{3+}$ (rare) and $In^{+}$ ions.

XII. Diagonal relationships: similarity in chemical properties among diagonal neighbors in the main groups of the periodic table

1. lithium - magnesium: forms only normal oxides ($O^{2-}$), and reacts with nitrogen, etc.

2. Some other examples are beryllium - aluminum, boron - silicon, etc.