Periodic Trends

Elements in groups exhibit similar properties as a result of their similar valence shell electron configurations. Trends emerge that allows us to predict, qualitatively, different properties of elements.

Effective Nuclear Charge

The effective nuclear charge (Zeff) is the central concept underlying all periodic trends. Atomic radius, ionization energy, electron affinity, and electronegativity all follow from how Zeff varies across the periodic table.

Shielding

Consider sodium (Z = 11). The nucleus contains 11 protons, but the lone 3s valence electron does not experience the pull of all 11 positive charges. The 10 inner electrons (1s22s22p6) form a cloud of negative charge between the nucleus and the valence electron, partially canceling the nuclear attraction. This is shielding (or screening).

The effective nuclear charge is the net positive charge an electron experiences after accounting for shielding:

\[Z_{\mathrm{eff}} = Z - \sigma\]

where Z is the atomic number and σ is the shielding constant. For sodium’s 3s electron, Zeff ≈ 2.5. The valence electron experiences roughly the pull of 2.5 protons, not 11.

Shielding in Sodium (Na, Z = 11) +11 Core cloud 1s² 2s² 2p⁶ (10 e⁻) Valence cloud 3s¹ (1 e⁻) Nucleus 11 protons The core electron cloud shields the valence electron from the full nuclear charge Nuclear charge: +11 Shielding (σ): −8.5 Effective charge: +2.5 Valence electron feels only +2.5 Zeff = Z − σ = 11 − 8.5 ≈ 2.5

Penetration

Not all electrons shield equally. Shielding effectiveness depends on penetration, how close an electron’s probability distribution gets to the nucleus.

From atomic orbitals: s orbitals have electron density at the nucleus, while p, d, and f orbitals have nodes there. The consequences:

  • s electrons penetrate deeply and are poorly shielded by other electrons in the same shell
  • p electrons penetrate less and are more effectively shielded
  • d and f electrons penetrate even less

Within the same shell, s orbitals experience higher Zeff than p orbitals, which experience higher Zeff than d orbitals. This explains why subshells within a shell have different energies in multi-electron atoms, unlike hydrogen where 2s and 2p are degenerate.

Shielding effectiveness follows the order: 1s > 2s > 2p > 3s > 3p > 3d > …

Core electrons (complete inner shells) shield effectively. Electrons in the same subshell shield each other poorly. This asymmetry drives periodic trends.

A common question: if 2s and 3s orbitals penetrate toward the nucleus (as radial probability plots show), why don’t they shield the 1s electrons?

Penetration ≠ shielding of inner electrons. For a 2s electron to shield a 1s electron, it would need to be between the 1s and the nucleus, meaning closer to the nucleus than the 1s on average. But penetration is relative: the 2s penetrates, but the 1s penetrates more. The 1s electron cloud is still closest to the nucleus on average.

Think of it this way: a 2s electron occasionally visits the region near the nucleus, but it spends most of its time outside the 1s cloud. Shielding depends on average position, not occasional proximity. So penetration explains why outer electrons experience less shielding (they get inside some of the shielding cloud), not why they shield inner electrons.

What does shield the 1s? Only the other 1s electron. Electrons in the same subshell shield each other poorly (~0.3 per Slater’s rules), which is why 1s Zeff is slightly less than Z. For krypton (Z = 36), the 1s electrons feel Zeff ≈ 35.2, not 36.

Zeff by Orbital

The chart below shows Zeff values calculated by Clementi and Raimondi using self-consistent field methods. Each line represents a different orbital type.

Click chart to open full size with zoom controls

Data source: Clementi, E. & Raimondi, D.L. (1963, 1967) J. Chem. Phys.

Several patterns emerge:

  • Zeff increases with atomic number for all orbitals. Each added proton increases the nuclear charge, and shielding does not fully compensate.

  • Core orbitals experience much higher Zeff than valence orbitals. In krypton (Z = 36), the 1s electrons feel Zeff ≈ 35, almost the full nuclear charge. Only the other 1s electron provides any shielding. The 4p valence electrons feel only Zeff ≈ 9.

  • Within a shell, Zeff follows s > p > d. At any element, compare 3s, 3p, and 3d. The 3s always experiences the highest effective charge due to greater penetration.

  • The lines are roughly parallel. Adding one proton increases Zeff for all orbitals by roughly the same amount, slightly less than 1 due to imperfect shielding by the added electron.

Atomic radius

Atoms have no hard boundary. The electron cloud extends indefinitely, though probability density drops off rapidly. Several operational definitions exist:

  • Covalent radius: Half the distance between two bonded identical atoms (e.g., half the Cl-Cl bond length in Cl2)
  • Van der Waals radius: Half the distance between nuclei of identical atoms in adjacent molecules (non-bonded contact)
  • Metallic radius: Half the distance between adjacent nuclei in a metallic crystal

The covalent radius is most commonly used for comparing atomic sizes across the periodic table.

Exceptions: The d-Block and f-Block Contractions

d-Block contraction (scandide contraction)

Transition metals (d-block) show much smaller size decreases across a period than main group elements. From Sc to Zn, atomic radii decrease only slightly and can even increase in places.

Why? The 3d electrons being added shield the 4s valence electrons effectively enough to partially offset the increasing nuclear charge. The 3d subshell lies relatively close to the nucleus, providing substantial shielding for the outer 4s electrons. The result: Zeff for the valence shell increases slowly across the d-block, and atomic radii remain roughly constant.

Consequence: Ga (Z = 31) is nearly the same size as Al (Z = 13), even though Ga has 18 more protons. The intervening d-electrons in Ga provide enough shielding to compensate.

Lanthanide contraction

The lanthanides (4f elements, Z = 57 to 71) show a gradual size decrease as 4f electrons are added. The 4f orbitals have poor radial penetration and shield very ineffectively. As protons are added, Zeff increases substantially, and atomic radii contract steadily.

Consequence: By the time the 4f subshell is filled, the lanthanide contraction has shrunk atoms so much that 6th-period transition metals (Hf to Au) are nearly the same size as their 5th-period counterparts (Zr to Ag). Zirconium and hafnium have almost identical radii despite Hf having 32 more protons.

This contraction affects chemistry: the similar sizes of 4d and 5d transition metals in the same group lead to similar chemical properties. Separating Zr from Hf, or Nb from Ta, is notoriously difficult.


Ionic radius

Ionic radius depends on the number of electrons relative to protons.

Cations are smaller than their parent atoms. Removing electrons reduces electron-electron repulsion and increases the effective nuclear charge experienced by the remaining electrons. Na+ (95 pm) is much smaller than Na (186 pm). When a cation loses its entire valence shell (like Na+ or Mg2+), the radius shrinks dramatically because the outermost electrons now occupy a lower shell.

Anions are larger than their parent atoms. Adding electrons increases electron-electron repulsion and distributes the same nuclear charge over more electrons, reducing Zeff per electron. Cl− (181 pm) is larger than Cl (99 pm).

Isoelectronic series illustrate these effects clearly. Consider species with 10 electrons: N3−, O2−, F−, Ne, Na+, Mg2+, Al3+. All have the same electron configuration, but different nuclear charges. As Z increases from 7 (N) to 13 (Al), the electrons are pulled progressively closer. N3− is the largest; Al3+ is the smallest.

Lattice enthalpy

The lattice enthalpy (ΔlatticeH) is the energy required to completely separate one mole of a solid ionic compound into gaseous ions:

\[\mathrm{NaCl(s)} \longrightarrow \mathrm{Na^+(g)} + \mathrm{Cl^-(g)} \quad \Delta_{\mathrm{lattice}}H = +786~\mathrm{kJ~mol^{-1}}\]

Lattice enthalpy is always positive (endothermic) and is a direct measure of ionic bond strength: the energy required to break the electrostatic interactions holding the lattice together. A larger lattice enthalpy means a stronger ionic bond.

The reverse process, gaseous ions combining to form the solid lattice, releases the same amount of energy:

\[\mathrm{Na^+(g)} + \mathrm{Cl^-(g)} \longrightarrow \mathrm{NaCl(s)} \quad \Delta H = -786~\mathrm{kJ~mol^{-1}}\]

Lattice enthalpy has no official IUPAC definition, and two conventions exist. Some sources define it as the energy released when the lattice forms (negative values); others define it as the energy required to break the lattice apart (positive values). The CRC Handbook and many university texts use positive values. When consulting other references, check the direction of the reaction to determine which convention is used.

Ionic bond strength can be estimated using Coulomb’s law, which describes the electrostatic attraction between oppositely charged ions:

\[E = \dfrac{k~q_1~q_2}{r}\]

where E is the potential energy between two charges, k is Coulomb’s constant, q1 and q2 are the charges of the ions, and r is the distance between ionic centers.

Coulomb’s law shows that stronger ionic bonds result from higher ion charges and shorter distances between ions.

Ionic bond strength vs distance

Ionic Bond Distance and Lattice Energy Constant cation: Na⁺ with varying anions Larger anion → longer bond → weaker lattice Na⁺ F⁻ Na⁺ Cl⁻ Na⁺ Br⁻ Na⁺ I⁻ 2.31 Å 2.81 Å 2.98 Å 3.23 Å 923 kJ/mol 786 kJ/mol 747 kJ/mol 704 kJ/mol Constant anion: Cl⁻ with varying cations Larger cation → longer bond → weaker lattice Li⁺ Cl⁻ Na⁺ Cl⁻ K⁺ Cl⁻ Rb⁺ Cl⁻ 2.57 Å 2.81 Å 3.14 Å 3.27 Å 853 kJ/mol 786 kJ/mol 701 kJ/mol 689 kJ/mol Lattice energy ∝ 1/d — shorter distance means stronger electrostatic attraction

Ionic bond strength vs ion charge difference

Ionic Bond Strength and Ion Charges Effect of ion charge: +1/−1 vs +2/−2 Higher charges → dramatically stronger lattice Na⁺ Cl⁻ +1 / −1 ×4.9 Mg²⁺ O²⁻ +2 / −2 2.81 Å 2.11 Å 786 kJ/mol 3,850 kJ/mol NaCl MgO Size still matters at same charge: +2/−2 compounds Larger ions → longer distance → lower energy (even with same charges) Mg²⁺ O²⁻ smaller cation Ca²⁺ O²⁻ larger cation 2.11 Å 2.40 Å 3,850 kJ/mol 3,461 kJ/mol MgO CaO Lattice energy ∝ (q₁ × q₂) / d — higher charges and shorter distances strengthen the lattice

Ionization energy

The ionization energy (IE in kJ mol−1) is the energy required to remove an electron from an atom or ion in the gas phase:

\[\mathrm{X(g)} \longrightarrow \mathrm{X^+(g)} + e^-\]

Higher ionization energy means the electron is more tightly bound.

Ionization enthalpy (ΔionH) is the enthalpy change for the ionization process at 298 K:

\[\mathrm{X(g)} \longrightarrow \mathrm{X^+(g)} + e^- \qquad \Delta_{\mathrm{ion}}H\]

Both IE and ΔionH are positive (endothermic). The relationship:

\[\Delta_{\mathrm{ion}}H = \mathrm{IE} + \frac{5}{2}RT\]

The (5/2)RT term (~6 kJ mol−1 at 298 K) accounts for the translational energy of the released electron. IE is defined at 0 K; ΔionH at 298 K. Since typical ionization energies are hundreds to thousands of kJ mol−1, this difference is negligible for most purposes.

Most data tables report IE values, and the terms are often used interchangeably.

Successive Ionization Energies

Each successive ionization requires more energy. Removing an electron from an already positive ion means pulling against a higher effective nuclear charge (fewer electrons shielding the same number of protons).

For carbon:

Successive Ionization Energies of Carbon 0 10,000 20,000 30,000 40,000 50,000 IE (kJ mol⁻¹) IE₁ 1,086 IE₂ 2,352 IE₃ 4,620 IE₄ 6,223 IE₅ 37,831 IE₆ 47,277 ×6.1 Valence electrons (2s²2p²) Core electrons (1s²) Removing core electrons requires dramatically more energy

Notice the jump between IE4 and IE5. Carbon has four valence electrons (2s22p2). The first four ionizations remove valence electrons. The fifth ionization breaks into the 1s core, where electrons experience Zeff close to the full nuclear charge. These core electrons are held far more tightly.

This pattern appears for all elements: ionization energies increase steadily until a core electron must be removed, then jump dramatically.

Explore successive ionization energies interactively:

Exceptions to the Trend

The general trend has notable exceptions that reveal the importance of electron configuration.

Group 13 vs Group 2 (B < Be, Al < Mg)

Boron (800 kJ/mol) has a lower IE1 than beryllium (900 kJ/mol), even though B has higher Zeff. Why?

Be: 1s22s2 (removing a 2s electron) B: 1s22s22p1 (removing a 2p electron)

The 2p electron in boron is higher in energy and easier to remove than the 2s electron in beryllium. The same pattern appears with Al < Mg.

Group 16 vs Group 15 (O < N, S < P)

Oxygen (1314 kJ/mol) has a lower IE1 than nitrogen (1402 kJ/mol).

N: 1s22s22p3 (half-filled 2p, one electron per orbital) O: 1s22s22p4 (one 2p orbital has paired electrons)

In oxygen, the fourth 2p electron must pair with an existing electron in one of the 2p orbitals. Electron-electron repulsion in this paired orbital makes that electron easier to remove. Nitrogen’s half-filled 2p subshell, with one electron per orbital and no pairing, is more stable. The same pattern appears with S < P.

Transition metals have nearly constant IE1

Across the d-block, first ionization energies remain relatively flat rather than increasing steadily like main group elements. From Sc to Zn, IE1 ranges only from about 630 to 906 kJ mol−1.

Why? Electrons are being added to inner 3d orbitals, not the outermost 4s. The 3d electrons shield the 4s electrons effectively, so Zeff for the 4s electrons increases slowly. Since ionization removes a 4s electron (in most cases), the energy required stays roughly constant.

This mirrors the d-block contraction in atomic radius: both properties remain nearly constant because the 3d electrons being added provide effective shielding.

Second Ionization Energies

H He Li Be B C N O F Ne Na Mg Al Si P S Cl Ar K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe Cs Ba Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn Fr Ra Rf Db Sg Bh Hs Mt Ds Rg Cn Nh Fl Mc Lv Ts Og 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 57-71 89-103 5250.5 7298.1 1757.1 2427.1 2352.6 2856 3388.3 3374.2 3952.3 4562 1450.7 1816.7 1577.1 1907 2252 2298 2665.8 3052 1145.4 1235 1309.8 1414 1590.6 1509 1561.9 1648 1753 1957.9 1733.3 1979.3 1537.5 1798 2045 2103 2350.4 2633 1064.2 1180 1270 1380 1560 1470 1620 1740 1870 2070 1631.4 1820.7 1411.8 1594.9 1790 1845.9 2046.4 2234.3 965.2 1440 1500 1700 1260 1600 1600 1791 1980 1810 1971 1450.5 1610 979 1 1 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 6 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 1067 1050 1020 1040 1050 1070 1085 1170 1110 1130 1140 1150 1160 1174.8 1340 1170 1110 1420 S e c o n d I o n i z a t i o n E n e r g y ( k J m o l ) 2000 4000 6000

Click to open full size with zoom controls | View in 3D

Third Ionization Energies

H He Li Be B C N O F Ne Na Mg Al Si P S Cl Ar K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe Cs Ba Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn Fr Ra Rf Db Sg Bh Hs Mt Ds Rg Cn Nh Fl Mc Lv Ts Og 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 57-71 89-103 11815 14848.7 3659.7 4620.5 4578.1 5300.5 6050.4 6122 6910.3 7732.7 2744.8 3231.6 2914.1 3357 3822 3931 4420 4912.4 2388.6 2652.5 2830 2987 3248 2957 3232 3395 3555 3833 2963 3302.1 2735 2973.7 3470 3565 3860 4138 1980 2218 2416 2618 2850 2747 2997 3177 3361 3616 2704 2943 2440 2698 3180 3099.4 3400 3600 2250 2510 3300 2878 3081.5 2466 1 1 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 6 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 1850.3 1949 2086 2130 2150 2260 2404 1990 2114 2200 2204 2194 2285 2417 2022.3 1930 T h i r d I o n i z a t i o n E n e r g y ( k J m o l ) 5000 10000

Click to open full size with zoom controls | View in 3D


Electron affinity

The electron affinity (Eea) is the minimum energy required to remove an electron from an isolated gaseous anion:

\[\mathrm{X^-(g)} \longrightarrow \mathrm{X(g)} + e^- \qquad E_{\mathrm{ea}}\]

Think of Eea as answering: “How hard is it to rip an electron off the anion?”

  • High Eea (large positive value): The anion holds its electron tightly. It takes a lot of energy to remove it. The anion is stable. Example: Cl− with Eea = 349 kJ mol−1.

  • Low Eea (small positive value): The anion holds its electron weakly. The anion is only modestly stable. Example: Na− with Eea ≈ 53 kJ mol−1.

  • Eea ≈ 0 or negative: The anion is unstable. An isolated anion would spontaneously eject its extra electron (or never form in the first place). Many databases report “0” for these elements because the anion cannot be studied experimentally. Noble gases, Group 2 elements, nitrogen, and Group 12 elements fall into this category.

Reading the Periodic Table

The periodic table below shows Eea values. The color gradient indicates anion stability:

  • Deep purple: High Eea, very stable anion
  • Orange/salmon: Moderate Eea
  • Pale yellow: Eea ≈ 0, barely stable or unstable anion

When you look at fluorine (F) on this table, you see deep purple and Eea ≈ 328 kJ mol−1. This describes F−, not neutral F. The color and value tell you: F− is a stable anion because removing its extra electron requires 328 kJ per mole.

H He Li Be B C N O F Ne Na Mg Al Si P S Cl Ar K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe Cs Ba Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn Fr Ra Rf Db Sg Bh Hs Mt Ds Rg Cn Nh Fl Mc Lv Ts Og 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 57-71 89-103 72.8 0 59.6 0 26.7 153.9 0 141 328 0 52.8 0 42.5 133.6 71 200 349 0 48.4 2.37 18.1 7.6 50.6 64.3 0 15.7 63.7 112 118.4 0 28.9 119 78 195 324.6 0 46.9 5.03 29.6 41.1 86.1 71.9 53 101.3 109.7 53.7 125.6 0 28.9 107.3 103.2 190.2 295.2 0 45.5 13.95 0 31 78.6 14.5 106.1 151 205.3 222.8 0 19.2 35.1 91.2 183.3 270.1 0 1 1 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 6 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 48 50 50 50 50 50 50 50 50 50 50 50 50 50 50 E l e c t r o n Affinity ( k J m o l ) 0 100 200 300

Click to open full size with zoom controls | View in 3D

Are all anions more stable than their neutral atoms?

If Eea > 0, then yes: the anion X− is more stable than the separated X + e−. Energy must be added to pull the electron off.

For elements with Eea ≈ 0 or negative (pale yellow on the table), the anion is not stable. Noble gases, Group 2 elements, and nitrogen fall into this category.

Important caveat: Positive Eea means the anion is more stable than the neutral atom plus a separated electron, but it doesn’t mean the anion is the most stable form of that element. Sodium has Eea ≈ 53 kJ mol−1, so Na− is technically more stable than Na + e−. Yet sodium forms Na+ in compounds, not Na−. Transferring sodium’s electron to chlorine (where the electron is held much more tightly) and forming an ionic lattice is far more favorable.

Exceptions

The zigzag pattern across a period

Eea does not increase smoothly across a period. Anion stability follows a zigzag pattern due to subshell structure:

  • Group 1 → 2: Eea drops. In Group 2 anions (Be−, Mg−), the extra electron occupies a higher-energy p subshell. These anions are unstable.

  • Group 2 → 13: Eea remains low. Group 13 anions (B−, Al−) hold their extra electron in the p subshell with moderate stability.

  • Group 13 → 14: Eea increases. Group 14 anions (C−, Si−) are more stable because the extra electron occupies a singly-occupied p orbital without severe repulsion.

  • Group 14 → 15: Eea drops sharply. Group 15 anions (N−, P−) require forcing an electron pair into the half-filled p subshell. The pairing repulsion destabilizes the anion.

  • Group 15 → 16 → 17: Eea increases steadily. Group 16 and 17 anions already have paired electrons in their neutral forms, so the additional pairing cost is less significant. Halide anions (F−, Cl−) have closed-shell configurations and are very stable.

Group 15: Why only nitrogen has Eea ≈ 0

All Group 15 anions have a paired electron in their p subshell. Yet N− is unique in being barely stable:

The difference is orbital size. Anion stability depends on two competing effects:

  1. Attraction: Zeff pulls the extra electron toward the nucleus, stabilizing the anion
  2. Repulsion: Paired electrons in the same orbital repel each other, destabilizing the anion

In N−, the 2p orbitals are exceptionally compact. The electron-electron repulsion from pairing in such a small space nearly cancels the stabilizing effect of Zeff. N− barely holds together, giving Eea ≈ 0.

In P− and heavier Group 15 anions, the p orbitals are larger. Paired electrons have more room, reducing repulsion. The attraction from Zeff dominates, and the anion is stable (positive Eea).

This is the same principle explaining why O− and F− are less stable than S− and Cl−: second-period anions have uniquely compact orbitals where electron-electron repulsion is maximized.

Sulfur has the highest electron affinity in Group 16

Among O, S, Se, Te, sulfur has the highest Eea:

Why S− > O−: In O−, the 2p orbitals are compact. Electron-electron repulsion is severe despite the high Zeff. S− has larger 3p orbitals where electrons have more room, reducing repulsion and making the anion more stable.

Why S− > Se−: Below sulfur, Zeff per unit volume decreases as orbitals become more diffuse. The nucleus holds the extra electron less tightly. S− hits the optimum balance: orbitals large enough to minimize repulsion, but compact enough for strong Zeff.

This mirrors the halogen pattern (F− < Cl− > Br− > I−), where Cl− is the most stable.

Chloride is more stable than fluoride

Cl− has higher Eea (349 kJ mol−1) than F− (328 kJ mol−1), despite F having higher Zeff.

In F−, the compact 2p orbitals force electrons close together. The resulting repulsion partially offsets the strong nuclear attraction. In Cl−, the larger 3p orbitals give electrons more space, and the anion holds its extra electron more tightly.

TipWhy doesn’t the most electronegative element have the highest electron affinity?

Fluorine is the most electronegative element, yet chlorine has a higher electron affinity. This seems contradictory until you recognize what each property measures:

  • Electronegativity describes how strongly an atom attracts shared electrons in a chemical bond. It depends on both nuclear attraction and bond distance (which depends on atomic radius).

  • Electron affinity measures the energy released when an isolated atom gains a complete electron. Here, electron-electron repulsion within the atom matters significantly.

Fluorine’s small size makes it excellent at pulling on shared electrons across a bond (high electronegativity), but that same small size creates severe electron repulsion when accepting a full electron into its compact 2p orbitals (lower EA than Cl).

Doubly-charged anions are inherently unstable

Removing an electron from X2− releases energy (the anion wants to lose that electron). Consider oxide:

  • O− → O + e−: Eea = +141 kJ mol−1 (O− is stable; costs energy to remove e−)
  • O2− → O− + e−: Eea = −744 kJ mol−1 (O2− is unstable; releases energy when e− leaves)

An isolated O2− ion spontaneously ejects an electron. Oxide ions exist in ionic compounds only because lattice energy stabilizes them.

Electronegativity

Electronegativity (χ) measures an atom’s ability to attract electrons toward itself in a chemical bond. Unlike ionization energy and electron affinity, which describe isolated atoms, electronegativity describes behavior in molecules.

Electronegativity Scales

Several scales exist:

Pauling scale (most common): Linus Pauling derived electronegativity values from bond dissociation energies. The difference in electronegativity between two bonded atoms correlates with the ionic character of the bond. Fluorine, the most electronegative element, is assigned χ = 4.0.

Mulliken scale: Averages ionization energy and electron affinity:

\[\chi_{\mathrm{Mulliken}} = \frac{\mathrm{IE} + E_{\mathrm{ea}}}{2}\]

This definition connects electronegativity directly to the atomic properties we’ve discussed. An element with high ionization energy (holds its electrons tightly) and favorable electron affinity (attracts additional electrons) will be highly electronegative.

Allred-Rochow scale: Based on the electrostatic force between the nucleus and valence electrons. Uses Zeff and covalent radius directly.

Electronegativity and Bond Polarity

The electronegativity difference between bonded atoms determines bond polarity:

  • Δχ ≈ 0: Nonpolar covalent bond. Electrons shared equally. (H2, Cl2)
  • 0 < Δχ < 1.7: Polar covalent bond. Electrons shifted toward more electronegative atom. (HCl, CO)
  • Δχ > 1.7: Ionic bond. Electrons essentially transferred. (NaCl, MgO)

These boundaries are approximate. Some compounds with Δχ > 1.7 are better described as polar covalent, and vice versa.

Exceptions

Transition metals have similar electronegativities

Across the d-block, electronegativity values cluster between 1.3 and 2.0, with little systematic increase. This parallels the relatively constant IE1 and atomic radius across the d-block: the 3d electrons shield effectively, so Zeff at the bonding surface increases slowly.

Gallium and germanium are more electronegative than expected

After the first d-block, Ga (χ = 1.81) and Ge (χ = 2.01) have higher electronegativities than Al (χ = 1.61) and Si (χ = 1.90). The d-block contraction leaves Ga and Ge with higher Zeff and smaller radii than simple periodic trends would predict.

Gold has unusually high electronegativity

Gold (χ = 2.54) is more electronegative than most metals and comparable to some nonmetals. Relativistic effects contract the 6s orbital, increasing Zeff experienced by valence electrons. This contributes to gold’s nobility and its ability to form auride anions (Au−) with highly electropositive metals like cesium.

Metallic character

Metallic character describes how readily an element exhibits typical metallic properties: electrical conductivity, malleability, ductility, luster, and the tendency to lose electrons and form cations.

Metallic character depends on how easily valence electrons can be removed or delocalized. Elements with low ionization energy release electrons easily, allowing them to move freely through a metallic lattice.

The Metal-Nonmetal Divide

The periodic table shows a diagonal boundary between metals and nonmetals, running roughly from boron to astatine. Elements near this boundary (B, Si, Ge, As, Sb, Te) are metalloids with intermediate properties.

Why diagonal? Moving right decreases metallic character (higher Zeff). Moving down increases it (larger radius). These effects partially offset along the diagonal, creating a transition zone rather than a sharp vertical or horizontal line.

Summary

Periodic trends follow from effective nuclear charge and orbital size.

Trend Summary Table

Grouping by Direction

The trends fall into two groups based on their direction across a period:

Increase across (→): Ionization energy, electron affinity, electronegativity

These properties reflect how tightly electrons are held. Higher Zeff → tighter hold → harder to remove electrons, more stable anions, stronger pull on bonding electrons.

Decrease across (←): Atomic radius, ionic radius, metallic character

These properties reflect size or ease of electron loss. Higher Zeff → smaller size, electrons harder to give up.

Down a group, all trends reverse because the increasing shell size (n) dominates over the modest increase in Zeff.

Zeff Explains the Patterns

The valence Zeff chart at the beginning of this chapter shows a sawtooth pattern (rising across each period, dropping at each new shell) that explains every trend:

  • Across a period: Zeff increases because added electrons shield poorly. Atoms shrink, hold electrons tighter, become more electronegative.

  • At new periods: A complete inner shell now shields effectively. Zeff drops, and trends reset.

  • Down groups: Zeff increases modestly, but electrons occupy larger orbitals farther from the nucleus. The distance effect dominates.

One principle, six trends.