Periodic Trends: Valency, Atomic Size & Electronegativity - Tenth Grade Science
The organization of chemical elements in the modern periodic table reveals recurring patterns in physical and chemical properties known as periodic trends. These trends are not coincidental; they arise from systematic variations in atomic structure, specifically the interplay between increasing positive nuclear charge and the screening or shielding effect of inner electron shells. As one traverses across a period or descends down a group, the effective nuclear charge experienced by outermost valence electrons changes predictably, dictating atomic size, ionization energy, electron affinity, electronegativity, and metallic character. Understanding these periodic trends enables chemists to predict the bonding, reactivity, and properties of any element from its coordinates on the periodic grid. In this chapter, you will investigate effective nuclear charge and the shielding effect, analyze trends in atomic and ionic radii, examine valency progressions, and explore the gradations of ionization energy, electronegativity, and metallic character.
Nuclear Charge and the Shielding Effect
All periodic trends are governed by two competing electrostatic forces operating within the atom: positive nuclear attraction and inter-electronic repulsion.
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| EFFECTIVE NUCLEAR CHARGE DYNAMICS |
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| |
| [ Nucleus: +Z ] |
| | |
| ================================================= |
| | Inner Core Electrons: Shielding Screen (sigma)| |
| ================================================= |
| | (Attenuated pull) |
| v |
| ( Valence Electron e- ) |
| |
| Formula: Z_eff = Z - sigma |
| Across a Period: Z increases rapidly, sigma increases slowly -> Z_eff RISES. |
| Down a Group: New shells added; Z_eff experienced by valence stays similar. |
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The Concept of Effective Nuclear Charge ($Z_{\text{eff}}$)
The full positive charge of an atomic nucleus is determined by its total number of protons, designated as the atomic number ($Z$). However, an outer valence electron does not experience this full nuclear attraction. The intervening core electrons residing in inner shells act as an electrostatic shield, repelling the valence electron and canceling a portion of the positive nuclear pull.
The net positive charge experienced by an outer valence electron is defined as the effective nuclear charge ($Z_{\text{eff}}$), expressed mathematically by Slater's formula:
$$Z_{\text{eff}} = Z - \sigma$$
where $Z$ is the actual nuclear charge (atomic number) and $\sigma$ is the shielding or screening constant representing the repulsive effect of inner electrons.
Across a period from left to right, each successive element adds one proton to the nucleus and one electron to the same principal valence shell. Because electrons in the same shell shield one another poorly, the nuclear charge ($Z$) increases faster than the shielding constant ($\sigma$). Consequently, $Z_{\text{eff}}$ increases steadily across a period, pulling the valence electron cloud closer to the nucleus.
Down a group from top to bottom, each successive element adds an entire new principal quantum energy shell of core electrons. Although nuclear charge ($Z$) increases, the additional inner electron shells provide substantial shielding ($\sigma$). Consequently, the effective nuclear charge experienced by the outermost valence electrons remains relatively constant or increases only slightly down a group.
Periodic Trends in Atomic Radius and Ionic Radius
The atomic radius is defined as one-half the internuclear distance between two identical bonded atoms in a homonuclear diatomic molecule (covalent radius) or in a metallic crystal lattice (metallic radius).
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| ATOMIC RADIUS VECTORIAL DRIFT |
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| |
| ACROSS A PERIOD (Left to Right): DOWN A GROUP: |
| - Z_eff increases steadily. - New electron shells |
| - Electrons pulled closer to nucleus. added at each period. |
| - Atomic Radius DECREASES. - Distance increases. |
| - Atomic Radius |
| Li (152 pm) > Be (112) > B (88) > C (77) > F (72 pm) INCREASES. |
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| Li (152 pm) |
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| Na (186 pm) |
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| K (227 pm) |
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Variations in Atomic Radius Across Periods and Groups
Across a period (left to right), atomic radius decreases continuously. As the effective nuclear charge ($Z_{\text{eff}}$) increases while electrons are added to the same principal energy shell, the electrostatic attraction pulls the electron cloud inward, shrinking atomic size. In Period 2, lithium ($\text{Li}$) has the largest atomic radius ($152\text{ pm}$), while fluorine ($\text{F}$) has the smallest ($72\text{ pm}$).
Down a group (top to bottom), atomic radius increases continuously. Although nuclear charge increases, each successive period adds an entire new principal electron shell. The physical distance between the outermost valence shell and the nucleus increases, and the shielding from intervening inner shells offsets the nuclear charge. In Group 1, atomic radius expands from lithium ($152\text{ pm}$) to cesium ($265\text{ pm}$).
The noble gases (Group 18) exhibit an apparent deviation: their reported atomic radii appear larger than those of preceding halogens. This is because noble gases do not form covalent bonds under standard conditions; their size is measured using van der Waals radius (the distance between non-bonded contacting atoms in a solid gas crystal), which is inherently larger than a covalent bonding radius.
Cations and Anions: Ionic Radii Dynamics
Ionic radius reflects the size of an ion within an ionic crystal lattice, exhibiting systematic differences compared to parent neutral atoms:
A cation is always smaller than its parent neutral atom. When an atom loses valence electrons to form a cation, the remaining electrons experience reduced mutual repulsion and are pulled inward by the unchanged positive nuclear charge. If all valence electrons are lost (e.g., $\text{Na} \rightarrow \text{Na}^+$), an entire outer energy shell is eliminated, causing a significant reduction in radius:
Neutral Sodium Atom (Na): Radius = 186 pm -----> Sodium Cation (Na+): Radius = 102 pm
An anion is always larger than its parent neutral atom. When an atom gains electrons to form an anion, the added electrons increase inter-electronic repulsion within the valence shell without any change in nuclear charge. The electron cloud expands outward:
Neutral Chlorine Atom (Cl): Radius = 99 pm -----> Chloride Anion (Cl-): Radius = 181 pm
In an isoelectronic series (ions containing identical numbers of electrons, such as $\text{O}^{2-}, \text{F}^-, \text{Na}^+, \text{Mg}^{2+}, \text{Al}^{3+}$, all possessing 10 electrons), ionic radius decreases with increasing nuclear charge ($Z$):
$$\text{Al}^{3+} (Z=13, 54\text{ pm}) < \text{Mg}^{2+} (Z=12, 72\text{ pm}) < \text{Na}^+ (Z=11, 102\text{ pm}) < \text{F}^- (Z=9, 133\text{ pm}) < \text{O}^{2-} (Z=8, 140\text{ pm})$$
Periodic Trends in Valency and Oxidation States
Valency represents the combining capacity of an atom, determined by the number of valence electrons in its outermost shell.
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| VALENCY VARIATION ACROSS PERIOD 3 |
+--------------------+----+----+----+----+----+----+----+----+---------------------+
| Element | Na | Mg | Al | Si | P | S | Cl | Ar | Trend Pattern |
+--------------------+----+----+----+----+----+----+----+----+---------------------+
| Valence Electrons | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | Increases 1 to 8 |
| Valency with Hydr. | 1 | 2 | 3 | 4 | 3 | 2 | 1 | 0 | Rises 1-4, then 4-0 |
| Formula of Hydride | NaH|MgH2|AlH3|SiH4|PH3 |H2S |HCl |-- | Stoichiometric peak |
| Maximum Ox. State | +1 | +2 | +3 | +4 | +5 | +6 | +7 | -- | Matches group number|
+--------------------+----+----+----+----+----+----+----+----+---------------------+
Valency Patterns
Across a period, the number of valence electrons increases steadily from 1 in Group 1 to 8 in Group 18. The valency of elements with respect to hydrogen increases from 1 to 4 and then decreases back to 0: For Groups 1 through 4: $\text{Valency} = \text{Number of valence electrons}$. For Groups 5 through 8: $\text{Valency} = 8 - \text{Number of valence electrons}$.
With respect to oxygen, valency can rise up to the group number, as in chlorine heptoxide ($\text{Cl}_2\text{O}_7$, where chlorine exhibits a $+7$ oxidation state).
Down a group, valency remains constant because all elements in a group share identical valence electron configurations. All Group 1 alkali metals possess a valency of 1, all Group 2 alkaline earth metals have a valency of 2, and all Group 17 halogens have a valency of 1.
Electronegativity, Ionization Energy, and Metallic Character
Electronegativity, ionization energy, and metallic character reflect how tightly an atom holds its own electrons and attracts external electrons.
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| ELECTRONEGATIVITY AND METALLICITY MATRIX |
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| ACROSS A PERIOD (Left to Right): DOWN A GROUP: |
| - Effective nuclear charge increases. - Atomic radius expands. |
| - Ionization Energy INCREASES. - Ionization Energy |
| - Electronegativity INCREASES. DECREASES. |
| - Non-Metallic Character INCREASES. - Electronegativity |
| - Metallic Character DECREASES. DECREASES. |
| - Metallic Character |
| Most Electronegative Element: Fluorine (4.0) INCREASES. |
| Most Electropositive Element: Cesium (0.79) |
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Ionization Energy Trends
First Ionization Energy is the minimum energy required to remove the most loosely held valence electron from an isolated neutral gaseous atom in its ground state:
$$\text{X(g)} + \text{IE}_1 \longrightarrow \text{X}^+\text{(g)} + \text{e}^-$$
Across a period, ionization energy increases because the higher effective nuclear charge ($Z_{\text{eff}}$) and smaller atomic radius hold valence electrons tightly. Small local dips occur at filled and half-filled subshells (e.g., nitrogen has a higher first ionization energy than oxygen because nitrogen possesses a stable half-filled $2p^3$ subshell).
Down a group, ionization energy decreases because the added electron shells place valence electrons further from the nucleus, where they are shielded by core electrons and more easily removed.
Electronegativity: The Pauling Scale
Electronegativity is the relative tendency of an atom in a covalent bond to attract the shared bonding electron pair toward itself. Measured on Linus Pauling's dimensionless scale: Across a period, electronegativity increases from left to right as smaller atomic radii and higher effective nuclear charges pull shared electron pairs closer. Fluorine is the most electronegative element, assigned a value of 4.0. Down a group, electronegativity decreases because larger atomic radii and increased shielding weaken the nucleus's ability to attract shared electrons. Cesium and francium are the least electronegative elements ($\sim 0.79$).
Metallic versus Non-Metallic Character
Metallic character (electropositivity) reflects the tendency of an element to lose electrons and form positive cations. Non-metallic character (electronegativity) reflects the tendency to gain or share electrons: Across a period, metallic character decreases and non-metallic character increases as ionization energy and electronegativity rise. Down a group, metallic character increases and non-metallic character decreases as valence electrons are more easily lost from larger atoms.
In the periodic table, a diagonal staircase of metalloids (boron, silicon, germanium, arsenic, antimony, tellurium) separates reactive metals on the lower left from non-metals on the upper right.
Chapter Exercises
Exercise 1: Consider the elements of Period 3: sodium ($\text{Na}$), magnesium ($\text{Mg}$), aluminium ($\text{Al}$), silicon ($\text{Si}$), phosphorus ($\text{P}$), sulfur ($\text{S}$), chlorine ($\text{Cl}$), and argon ($\text{Ar}$). Identify: first, the element with the largest atomic radius; second, the element with the highest electronegativity; third, the element with the highest first ionization energy; and fourth, the element that forms the most basic oxide. Explain the physical reasons for your selections.
Exercise 2: Arrange the following chemical species in order of increasing ionic radius, providing theoretical justification based on nuclear charge and electron count: $\text{K}^+, \text{Cl}^-, \text{Ca}^{2+}, \text{S}^{2-}$.
Exercise 3: Explain why the second ionization energy of sodium is substantially higher than its first ionization energy, whereas for magnesium, the second ionization energy is only moderately higher than its first ionization energy.
Solutions and Explanations
Solution 1: In Period 3: First, sodium ($\text{Na}$) has the largest atomic radius because atomic radius decreases from left to right across a period as effective nuclear charge ($Z_{\text{eff}}$) increases without the addition of new shells. Second, chlorine ($\text{Cl}$) has the highest electronegativity (excluding the noble gas argon, which does not form standard covalent bonds) because it has the highest effective nuclear charge and smallest covalent radius in the period, giving it the strongest pull on shared bonding pairs. Third, argon ($\text{Ar}$) has the highest first ionization energy because it possesses a completely filled, stable valence octet ($3s^2 3p^6$) held firmly by eighteen nuclear protons, requiring significant energy to remove an electron. Fourth, sodium ($\text{Na}$) forms the most basic oxide ($\text{Na}_2\text{O}$) because sodium is the most electropositive metal in the period; it readily donates electrons to oxygen to form an ionic oxide that hydrolyzes in water to yield a strongly alkaline sodium hydroxide solution ($\text{NaOH}$).
Solution 2: The species $\text{S}^{2-}, \text{Cl}^-, \text{K}^+,$ and $\text{Ca}^{2+}$ constitute an isoelectronic series: each ion possesses eighteen electrons with the electron configuration of argon ($2, 8, 8$). In an isoelectronic series, all ions have the same shielding constant from eighteen electrons, so ionic size is governed by nuclear charge ($Z$). A higher number of positive nuclear protons pulls the eighteen orbiting electrons inward more tightly, reducing ionic radius. The nuclear charges are: sulfur $Z = 16$; chlorine $Z = 17$; potassium $Z = 19$; and calcium $Z = 20$. Arranging in order of increasing ionic radius (smallest to largest) yields: $\text{Ca}^{2+} (100\text{ pm}) < \text{K}^+ (138\text{ pm}) < \text{Cl}^- (181\text{ pm}) < \text{S}^{2-} (184\text{ pm})$.
Solution 3: Sodium ($Z = 11$) has an electron configuration of $2, 8, 1$. Its first ionization energy removes the single valence electron from the $3s$ subshell, requiring $496\text{ kJ/mol}$ and leaving behind a stable neon core ($2, 8$). The second ionization energy requires removing an electron from this complete, tightly bound $2p^6$ noble gas octet, which is closer to the nucleus and experiences a higher effective nuclear charge without the screening of the $3s$ shell. Consequently, sodium's second ionization energy jumps to $4562\text{ kJ/mol}$—nearly ten times the first. In contrast, magnesium ($Z = 12$) has an electron configuration of $2, 8, 2$. Its first ionization energy removes one $3s$ electron ($738\text{ kJ/mol}$), leaving a $3s^1$ configuration ($2, 8, 1$). Its second ionization energy removes the second $3s$ electron from the same principal shell ($1451\text{ kJ/mol}$). While the second ionization energy is higher than the first due to increased effective nuclear charge, it does not disrupt an inner noble gas core. Consequently, magnesium's second ionization energy is only approximately double its first, allowing magnesium to readily form divalent $\text{Mg}^{2+}$ compounds.