1.4 Periodic Trends in Atomic and Ionic Properties

Atomic and Ionic Size

Atomic and Ionic Radii

Atomic radius is defined as half the distance between the nuclei of two adjacent atoms in a metallic or covalent solid. This definition matters because isolated atoms don't have a sharp boundary, so we rely on internuclear distances in bonded systems.

Trends across the table:

• Across a period, atomic radius decreases. Each added proton increases the effective nuclear charge ($Z_{\text{eff}}$), pulling valence electrons closer to the nucleus. The added electrons enter the same shell and don't shield each other very well.
• Down a group, atomic radius increases. Each new period adds a principal energy level, so valence electrons sit farther from the nucleus despite the higher nuclear charge.

Ionic radii follow related but distinct patterns:

• Cations are smaller than their parent atoms. Removing electrons reduces electron-electron repulsion and often eliminates an entire outer shell. For example, $\text{Na}$ has a radius of about 186 pm, but $\text{Na}^+$ shrinks to roughly 102 pm.
• Anions are larger than their parent atoms. The extra electron increases repulsion in the outer shell without adding any nuclear charge. $\text{Cl}$ is about 99 pm, while $\text{Cl}^-$ expands to around 181 pm.
• Isoelectronic species (ions with the same electron count, like $\text{O}^{2-}$, $\text{F}^-$, $\text{Na}^+$, $\text{Mg}^{2+}$) decrease in size as nuclear charge increases. More protons pulling on the same number of electrons means a tighter electron cloud.

Effective Nuclear Charge and Shielding

Most periodic trends trace back to one concept: effective nuclear charge ($Z_{\text{eff}}$). This is the net positive charge that valence electrons actually "feel" after accounting for the shielding provided by inner (core) electrons.

A simple estimate uses Slater's approximation:

$Z_{\text{eff}} = Z - S$

where $Z$ is the actual nuclear charge (number of protons) and $S$ is the shielding constant (a measure of how much core electrons block the nuclear pull).

• Across a period, $Z_{\text{eff}}$ increases. Each step to the right adds a proton, but the new electron enters the same shell and provides poor shielding for its neighbors. So the valence electrons get pulled in more tightly.
• Down a group, $Z_{\text{eff}}$ felt by valence electrons stays relatively similar. Both $Z$ and $S$ increase together because each new period adds a full shell of core electrons that effectively shields the added nuclear charge.

This single quantity drives the trends in atomic radius, ionization energy, and electron affinity.

Electron Interactions

Ionization Energy

Ionization energy (IE) is the energy required to remove an electron from a gaseous atom or ion. It's always an endothermic process for neutral atoms.

• First ionization energy ($IE_1$) removes the highest-energy (outermost) electron.
• Second ionization energy ($IE_2$) removes the next electron, and so on. Each successive IE is larger than the last because you're pulling an electron from an increasingly positive ion.

Periodic trends:

• Across a period, IE generally increases because rising $Z_{\text{eff}}$ holds electrons more tightly.
• Down a group, IE decreases because valence electrons occupy higher principal shells and are farther from the nucleus.

Watch for irregularities. The trend across a period isn't perfectly smooth:

• There's a dip from $\text{Be}$ ($1s^2 2s^2$) to $\text{B}$ ($1s^2 2s^2 2p^1$). The lone $2p$ electron in boron is higher in energy and easier to remove than a $2s$ electron.
• There's another dip from $\text{N}$ (half-filled $2p^3$) to $\text{O}$ ($2p^4$). Oxygen's fourth $p$ electron is forced to pair in an already-occupied orbital, and the extra electron-electron repulsion makes it easier to remove.

These irregularities reflect subshell structure and exchange energy stabilization, not exceptions to the underlying $Z_{\text{eff}}$ trend.

Electron Affinity and Electronegativity

Electron affinity (EA) is the energy change when a gaseous atom gains one electron. By the most common sign convention, a negative EA means energy is released (the process is favorable).

• EA generally becomes more negative (more exothermic) across a period as $Z_{\text{eff}}$ increases, making the atom more "eager" to accept an electron.
• EA generally becomes less negative down a group because the added electron enters a shell farther from the nucleus.
• Irregularities mirror those in IE. For instance, nitrogen has a near-zero EA because its half-filled $2p^3$ configuration is particularly stable, and adding an electron disrupts that stability.

Electronegativity is a related but distinct concept. It describes an atom's ability to attract shared electrons within a chemical bond, not the energy of adding an electron to an isolated atom.

• The Pauling scale is the most widely used measure. Fluorine tops the scale at 4.0, and electronegativity decreases toward the lower left of the periodic table (cesium and francium are the least electronegative).
• Electronegativity increases across a period and decreases down a group, following the same $Z_{\text{eff}}$ logic as the other trends.

Chemical Behavior

Oxidation States and Reactivity

Oxidation states describe the hypothetical charge an atom would have if all bonds were fully ionic. They're a bookkeeping tool, but they connect directly to periodic trends.

• Main-group metals (groups 1 and 2) have low ionization energies and readily lose their valence electrons, forming $+1$ and $+2$ oxidation states, respectively. This is why sodium and potassium are so reactive.
• Nonmetals on the right side of the table have high electron affinities and tend to gain electrons, forming negative oxidation states. Chlorine commonly forms $\text{Cl}^-$ ($-1$).
• Transition metals can access multiple oxidation states because the energy gap between their $ns$ and $(n-1)d$ electrons is small. Manganese, for example, exhibits oxidation states from $+2$ to $+7$.

A general pattern: the highest oxidation states of transition metals tend to be strongly oxidizing (reactive), while the lower oxidation states are often more thermodynamically stable for a given element. However, this varies considerably across the $d$-block.

Electronegativity and Bond Character

The electronegativity difference ($\Delta \chi$) between two bonded atoms determines bond character:

• $\Delta \chi \approx 0$: nonpolar covalent bond (electrons shared equally). Example: $\text{Cl}_2$.
• $\Delta \chi$ moderate (roughly 0.4–1.7): polar covalent bond (electrons shared unequally). Example: $\text{H–Cl}$ ($\Delta \chi \approx 0.9$).
• $\Delta \chi$ large (roughly > 1.7): ionic bond (effective electron transfer). Example: $\text{NaCl}$ ($\Delta \chi \approx 2.1$).

These cutoffs are approximate guidelines, not rigid boundaries. Bond character exists on a continuum. The degree of polarity affects physical properties like melting point, solubility, and conductivity.

Ionization Energy and Periodic Reactivity

Ionization energy ties the atomic-level trends to observable chemical behavior:

• Alkali metals (group 1) have the lowest $IE_1$ values in each period, which is why they lose electrons so easily and are the most reactive metals. Reactivity increases down the group as IE drops further.
• Noble gases have the highest $IE_1$ values in each period, explaining their chemical inertness under normal conditions.
• Halogens have high IE values but also strongly negative electron affinities, so they prefer to gain electrons rather than lose them. Their reactivity as oxidizers decreases down the group as EA becomes less negative.

Taken together, atomic radius, ionization energy, electron affinity, and electronegativity form an interconnected web. If you understand $Z_{\text{eff}}$ and shielding, you can reason through almost any periodic trend rather than memorizing each one independently.