Periodic Trends — Atomic Radii, Ionic Radii, Ionization Energy, Electron Affinity, and Electronegativity

Atomic Radii Trends

• Definition
  • Atomic radius (bonding atomic radius) describes the size of an atom in a particular context (often comparison within a period or group).
  • 1 Å = 10^{-10} m.
  • When discussing trends, consider shielding and effective nuclear charge (ENC).
• General trends across the periodic table
  • Within each group (vertical column): bonding atomic radius tends to increase from top to bottom.
  • Within each period (horizontal row): bonding atomic radius tends to decrease from left to right.
  • Shielding decreases going up the periodic table; ENC increases moving left to right across a period.
  • Small summary: large radius in the lower-left; small radius in the upper-right.
• Key concepts
  • Shielding: inner electron shells shield outer electrons from the full nuclear charge.
  • ENC (effective nuclear charge): effective positive pull felt by valence electrons after accounting for shielding.
  • As you move down a group, additional electron shells increase shielding, but nuclear charge increases only slightly relative to shielding, so radius grows.
  • As you move across a period, electrons experience a stronger effective nuclear charge with little additional shielding, so radius shrinks.
• Quick practice question (from transcript)
  • Question: Rank the following atoms in terms of decreasing atomic radius: Na, N, O, Mg, F?
  • Answer: d) Na, Mg, N, O, F
  • Rationale: radius is largest in the lower-left and smallest in the upper-right; Na (lower-left) is largest; F (upper-right) is smallest; among Na and Mg, Na is larger than Mg due to its position further left and lower.
• Practical implications and connections
  • Radius trends help predict chemical reactivity and bond lengths: larger atoms typically form bonds with longer bond lengths; smaller atoms tend to hold electrons tighter.
  • ENC and shielding underpin many other periodic properties (e.g., ionization energy, electronegativity).

Ionic Radii Trends

• What determines ionic size?
  • The size of an ion depends on:
  • Its nuclear charge (Z)
  • The number of electrons it possesses (electron count)
• General rules
  • Cations (positively charged) are smaller than their parent atoms.
  • Anions (negatively charged) are larger than their parent atoms.
• Isoelectronic series
  • Isoelectronic series: a group of ions that all contain the same number of electrons.
  • In an isoelectronic series, the more positively charged the species, the smaller the radius (because the same electron cloud is pulled tighter by a larger nuclear charge).
• Quick practice question (from transcript)
  • Question: Rank Li+, Be^{2+}, He, H^−, B^{3+} in order of decreasing size.
  • Answer: H^− > He > Li^+ > Be^{2+} > B^{3+}
  • Rationale: these species are isoelectronic (2 electrons) except for their differing nuclear charges; the larger the nuclear charge, the smaller the radius for a fixed electron count.
• Practical implications
  • Ion size affects lattice energies, lattice stability, and ionic bonding characteristics.
  • In biological systems and materials science, ionic radii influence solubility, diffusion, and conductivity.

Ionization Energy (Ionization Energies)

• Definition
  • Ionization energy (IE) is the minimum energy required to remove an electron from the valence shell in the ground state (gas phase).
  • First ionization energy (I1): energy to remove the first electron.
  • Second ionization energy (I2): energy to remove a second electron after the first has been removed, and so on.
  • Notation examples:
  • ext{Na}(g)
    ightarrow ext{Na}^+(g) + e^- ext{ with energy } I_1
  • ext{Na}^+(g)
    ightarrow ext{Na}^{2+}(g) + e^- ext{ with energy } I_2
• General trends
  • I1 < I2 < I3 < …
  • Across a period (left to right), ionization energies generally increase (harder to remove electrons as ENC increases).
  • The transition metals show only a slow gradual increase from left to right across a period.
  • The f-block elements also show only small variation in I1 values.
• Sharp rises in IE
  • A sharp increase occurs when an inner-shell (core) electron is removed, because those electrons are more tightly bound.
• Conceptual notes
  • Higher IE means greater difficulty in removing an electron; chemistry becomes less electropositive.
  • IE values relate to chemical reactivity, particularly in determining which elements form cations readily.
• Practical example (interpretation from transcript)
  • The progression from removing a valence electron (low IE) to removing a core electron (high IE) reflects increasing stability of filled shells.
• Connections and implications
  • IEs underpin redox chemistry and electrochemical series.
  • Trends help rationalize periodic reactivity patterns across groups and periods.

Electron Affinity

• Definition
  • Electron affinity (EA) is the change in energy when an electron is added to the valence shell of a neutral atom.
  • For most atoms, energy is released when an electron is added (negative EA indicates exothermic process).
• Trends
  • The trend is less obvious than ionization energy.
  • Electron affinities do not change greatly as you move down a group.
  • There is a slight decrease in EA downs a group, attributed to the enlargement of the atom (valence shell farther from the nucleus), which weakens the attraction for an added electron.
• Practical note
  • EA helps explain tendencies to form anions and the strength of bonding in compounds.
• Conceptual recap
  • IE measures the ease of removing electrons; EA measures the tendency to gain electrons.
• Transcript practice context
  • A demonstration question contrasted IE and EA to identify valence shell behavior and trends across the periodic table.

Electronegativity

• Definition
  • Electronegativity is the ability of an atom in a molecule to attract electrons toward itself.
• Scale
  • The most widely used scale is the Pauling scale, developed by Linus Pauling.
• General trends
  • Electronegativity increases from left to right across a period.
  • Electronegativity decreases with increasing atomic number down a group.
• Practice question (from transcript)
  • Rank the following in decreasing electronegativity: N, P, Sb, Bi
  • Answer: N > P > Sb > Bi
• Quantitative comparison
  • Example question: What is the difference in electronegativity between N and F atoms?
  • Typical answer (Pauling scale): χ(F) ≈ 3.98, χ(N) ≈ 3.04, so
  • ig| riangle ext{EN}ig| = | ext{χ}(F) - ext{χ}(N)| \, ext{approximately } 0.94.
• Significance
  • EN differences explain bond polarity and the nature of chemical bonds (ionic, covalent, polar covalent).
• Connections
  • EN correlates with dipole moments, bond strength, and reaction energetics in organic and inorganic chemistry.

Summary of Key Concepts and Connections

• Shielding and ENC drive periodic trends in atomic size and reactivity.
• Atomic radii increase down a group and decrease across a period; ionic radii follow related patterns with charge (cations smaller, anions larger).
• Ionization energies generally rise across a period and show a pronounced jump when core electrons are involved.
• Electron affinity trends are subtler but generally become less favorable down a group due to increased distance from the nucleus.
• Electronegativity rises across a period and falls down a group, influencing bond type and molecular polarity.
• Practical implications span reactivity, bonding, materials properties, and biological processes; understanding these trends aids in predicting compound formation and behavior.

Practice Problems (summary answers)

• Atomic radii ranking (decreasing): Na > Mg > N > O > F
• Ionic radii (decreasing size) in isoelectronic series for 2 electrons: H^- > He > Li^+ > Be^{2+} > B^{3+}
• Electron affinities and their trends: generally small downward trend down a group; energy release when adding an electron is common but varies by element.
• Electronegativity ranking: N > P > Sb > Bi
• Difference in EN between N and F: roughly 0.94 (χ(F) ≈ 3.98, χ(N) ≈ 3.04)