Periodicity of Properties

Concept of Periodicity

When the chemical elements are arranged in order of increasing atomic number (as in the modern periodic table), many of their properties vary in a regular, repeating way. This repeating pattern is called periodicity.

Two main directions matter:

• Across a period (left → right in a row)
• Down a group (top → bottom in a column)

Many properties show:

• A more or less smooth trend across a period.
• A more or less smooth but opposite trend down a group.
• Repetition of the pattern from one period to the next.

The underlying causes (like nuclear charge, electron–electron repulsion, and shielding) belong to atomic structure and are discussed in detail elsewhere; here the focus is on how the properties themselves vary.

In this chapter, “typical” periodic trends are described for:

• Atomic and ionic radius
• Ionization energy
• Electron affinity
• Electronegativity
• Metallic/nonmetallic character and chemical reactivity
• Basic and acidic character of oxides and hydroxides

All trends are generalizations; real data show exceptions, especially for transition elements and heavier p‑block elements.

Atomic Radius and Ionic Radius

Atomic Radius

Definition (qualitative): a measure of the “size” of an atom—often derived from half the distance between nuclei in a diatomic molecule or in a crystal.

Trend across a period

From left to right in a main‑group period:

• Atomic radius generally decreases.

Reason (qualitatively): more protons in the nucleus attract the valence electrons more strongly without a corresponding increase in shielding in the same shell, so electrons are drawn closer.

Example (period 2, approximate pattern):

• Li > Be > B > C > N > O > F

Trend down a group

From top to bottom in a group:

• Atomic radius generally increases.

Reason (qualitatively): additional electron shells are occupied, placing the outer electrons farther from the nucleus.

Example (group 1):

• H < Li < Na < K < Rb < Cs

Ionic Radius

Definition (qualitative): a measure of the size of ions in crystals or in other environments.

General rules:

• Cations (positively charged ions) are smaller than their parent atoms.
• Anions (negatively charged ions) are larger than their parent atoms.

This is due to changes in electron count and electron–electron repulsion.

Trends within isoelectronic series

An isoelectronic series is a set of ions/atoms having the same number of electrons but different nuclear charges.

Example: O$^{2-}$, F$^-$, Na$^+$, Mg$^{2+}$, Al$^{3+}$ (all have 10 electrons).

Within such a series:

• As nuclear charge (atomic number) increases, ionic radius decreases.

So for the example above:

$$
r(\mathrm{O^{2-}}) > r(\mathrm{F^-}) > r(\mathrm{Na^+}) > r(\mathrm{Mg^{2+}}) > r(\mathrm{Al^{3+}})
$$

Group and period trends for ions

For main‑group elements:

• Down a group: both cation and anion radii increase, paralleling atomic radii.
• Across a period: for ions that belong to the same “block” and charge type, ionic radii tend to decrease with increasing atomic number, similar to atomic radii.

For transition metals, trends are more complex, but the general decrease in size with higher charge and higher nuclear charge still applies.

Ionization Energy

Ionization energy (IE) is the energy required to remove an electron from a gaseous atom or ion.

• First ionization energy, $I_1$: energy to remove the first electron
• Second ionization energy, $I_2$: to remove the second electron, and so on

Symbolically for $I_1$:

$$
\mathrm{X(g) \rightarrow X^+(g) + e^-}
$$

General periodic trends

Across a period

From left to right (main‑group elements):

• First ionization energy generally increases.

Reason (qualitatively): increasing nuclear charge and similar shielding bind the valence electrons more strongly.

Example (period 2, general trend):

$$
I_1(\mathrm{Li}) < I_1(\mathrm{Be}) < I_1(\mathrm{B}) < I_1(\mathrm{C}) < I_1(\mathrm{N}) < I_1(\mathrm{O}) < I_1(\mathrm{F}) < I_1(\mathrm{Ne})
$$

In real data, there are small deviations (for example, Be vs. B, N vs. O) related to subshell structure and electron pairing.

Down a group

From top to bottom:

• First ionization energy generally decreases.

Outer electrons are farther from the nucleus and more shielded, so they are easier to remove.

Example (group 1):

$$
I_1(\mathrm{Li}) > I_1(\mathrm{Na}) > I_1(\mathrm{K}) > I_1(\mathrm{Rb}) > I_1(\mathrm{Cs})
$$

Successive ionization energies

For a given atom, ionization energies increase with each electron removed:

$$
I_1 < I_2 < I_3 < \dots
$$

A very large jump appears when an electron is removed from a new, more tightly bound shell (for example, after all valence electrons are gone). This is a clue to the number of valence electrons an element has.

Electron Affinity

Electron affinity (EA) is the energy change when a gaseous atom gains an electron to form an anion. Conventionally, one often quotes the energy released:

$$
\mathrm{X(g) + e^- \rightarrow X^-(g)}
$$

• When energy is released, EA is often given as a positive value (larger value = more energy released).
• In thermodynamic sign convention, this corresponds to a negative enthalpy change.

Because different sources use different sign conventions, it is important to pay attention to definitions, but in introductory periodic trends, “higher electron affinity” usually means “releases more energy on gaining an electron.”

General periodic trends

Across a period

For main‑group elements:

• Electron affinity tends to become more exothermic (larger in magnitude) from left to right, especially across the p‑block, up to a point.

Approximate pattern in period 2 p‑block:

• B < C < O < N vs. F, with some irregularities

Halogens such as Cl and F have particularly large (exothermic) electron affinities: they readily accept one electron to achieve a noble gas configuration.

Down a group

Down a group, trends are less simple than for ionization energy or radius:

• In the halogen group, EA is generally high (exothermic) throughout, but the magnitude can decrease or fluctuate down the group.
• For many groups, electron affinities become less exothermic down the group on average.

Again, details are influenced by subshells and the sizes of atoms.

Electronegativity

Electronegativity is a dimensionless measure of how strongly an atom in a chemical bond “attracts” the shared electrons to itself.

Different numerical scales (Pauling, Mulliken, Allred–Rochow) exist, but they show similar periodic trends.

General periodic trends

Across a period

From left to right:

• Electronegativity increases.

Typical high values for nonmetals on the right side (especially halogens), and low values for electropositive metals on the left side.

Down a group

From top to bottom:

• Electronegativity generally decreases.

Larger atomic size and increased shielding weaken the ability of the nucleus to attract bonding electrons.

Electronegativity extremes

• Fluorine: highest electronegativity in the periodic table.
• Cesium and francium (for main‑group): among the lowest electronegativities.

Relationship to bonding character

Differences in electronegativity between bonded atoms correlate with bond type:

• Small difference: more covalent character.
• Moderate difference: polar covalent character.
• Large difference: ionic character becomes significant.

Metallic and Nonmetallic Character

The periodic table shows a broad separation into:

• Metals: left and center
• Nonmetals: upper right
• Metalloids: around the dividing “staircase”

Periodic trends in metallic character

Metallic character is associated with:

• Tendency to lose electrons (form cations)
• Good electrical and thermal conductivity
• Malleability and ductility
• Luster

Nonmetallic character is associated with:

• Tendency to gain electrons (form anions) or share electrons (form covalent bonds)
• Poor electrical conductivity (in the solid state, for most nonmetals)
• Brittle solids or gaseous/liquid states at room temperature

Across a period

From left to right:

• Metallic character decreases, nonmetallic character increases.

Example in period 3:

• Na (metal) → Mg (metal) → Al (metal) → Si (metalloid) → P, S, Cl (nonmetals) → Ar (noble gas)

Down a group

Down a group among main‑group elements:

• Metallic character increases.
• Nonmetallic character decreases.

Example in group 14:

• C (nonmetal) → Si (metalloid) → Ge (metalloid) → Sn (metal) → Pb (metal)

Chemical Reactivity Trends

“Reactivity” depends on reaction type and conditions, but there are useful general patterns for typical reactions of metals and nonmetals.

Reactivity of alkali metals and alkaline earth metals

For group 1 (alkali metals) and group 2 (alkaline earth metals):

• They react as reducing agents (they are oxidized, lose electrons).
• Reactivity toward water and oxygen increases down the group.

Examples:

• Li, Na, K react with water to form hydroxides and H$_2$; the reactions become more vigorous from Li to K (and even more for Rb, Cs).
• Group 2 metals: Be is relatively unreactive toward water at room temperature, whereas Ca, Sr, Ba react more easily, especially with hot water or steam.

Reactivity of halogens

For group 17 (halogens):

• They react as oxidizing agents (they are reduced, gain electrons).
• Reactivity toward many reductants decreases down the group.

Typical pattern:

• F$_2$ > Cl$_2$ > Br$_2$ > I$_2$ (as oxidizing agents in many aqueous redox reactions)

Thus, fluorine is the strongest oxidizing agent among halogens; iodine is the weakest.

Reactivity and position in the periodic table

Combining these trends:

• Highly reactive metals are found in the lower left (for example, Cs, Rb, K, Na, Ca, Ba).
• Highly reactive nonmetals (as oxidizing agents) are found in the upper right (for example, F, Cl, O), excluding noble gases.

Periodic Trends in Acid–Base Behavior of Oxides and Hydroxides

Oxides and hydroxides of elements show changing acid–base character across periods and down groups.

Across a period (main groups)

Looking at period 3 as a typical example:

• Left side (metals): oxides/hydroxides are mainly basic.
• Example: Na$_2$O, MgO, NaOH, Mg(OH)$_2$
• Middle (metalloid region): oxides can be amphoteric (both acidic and basic).
• Example: Al$_2$O$_3$
• Right side (nonmetals): oxides are mainly acidic.
• Example: SO$_3$, P$_4$O$_{10}$, Cl$_2$O$_7$

This general left‑to‑right change from basic → amphoteric → acidic character is a characteristic periodic trend.

Down a group

For many metal groups (such as group 1 and 2):

• Basic character of oxides and hydroxides increases down the group.

Example:

• Group 2 oxides: BeO (amphoteric) → MgO (basic, weak) → CaO, SrO, BaO (increasingly basic)

For nonmetal groups, acidity of oxides can vary but often remains significant throughout the group, especially for higher oxidation states.

Summary of Main Periodic Trends

To consolidate:

• Atomic radius:
• Increases down a group.
• Decreases across a period (left → right).
• Ionic radius:
• Cations smaller than parent atoms, anions larger.
• Increases down a group.
• Decreases (for a given charge type) across a period.
• Ionization energy:
• Decreases down a group.
• Increases across a period.
• Electron affinity (magnitude):
• Often becomes more exothermic across a period in the p‑block.
• Tends to become less exothermic down a group (with exceptions).
• Electronegativity:
• Decreases down a group.
• Increases across a period.
• Highest at upper right (F), lowest at lower left (Cs, Fr).
• Metallic vs. nonmetallic character:
• Metallic character increases down a group and to the left.
• Nonmetallic character increases up a group and to the right.
• Acid–base character of oxides/hydroxides (main groups):
• Across a period: basic → amphoteric → acidic.
• Down a metal group: basicity generally increases.

These regular changes in properties, repeating from period to period, are what is meant by the periodicity of properties in the periodic table.