Atomic Radius, Ionic Radius, and Ionization Enthalpy

Trends in Atomic and Ionic Radii

• Atomic radius generally decreases across a period from left to right.
• The variation of atomic radius with atomic number can be observed in specific groups such as alkali metals and halogens. For example, specific values observed include:
  • $F(72)$
  • $Cl(99)$
  • $Br(114)$
  • $I(133)$
• Ionic radii represent the size of ions and can be estimated by measuring the distances between cations and anions within ionic crystals.
• In general, the trends for ionic radii follow the same patterns as the trends for atomic radii across the periodic table.

Formation and Size of Cations

• A cation is formed when an electron is removed from an atom.
• A cation is always smaller than its parent atom.
• This size difference occurs because a cation has fewer electrons than the parent atom while the nuclear charge remains the same.
• As there are fewer electrons being pulled by the same number of protons, the nucleus pulls the remaining electrons even closer to the center.
• Example of Sodium ($Na$):
  • The atomic radius of sodium ($Na$) is $186\,pm$.
  • The ionic radius of the sodium cation ($Na^{+}$) is $95\,pm$.
  • The $Na^{+}$ ion possesses $11$ protons but only $10$ electrons, leading to a stronger nuclear pull on the smaller electron cloud.

Formation and Size of Anions

• An anion is formed when one or more electrons are added to an atom.
• The size of an anion is always larger than that of its parent atom.
• The addition of electrons results in increased repulsion among the electrons.
• Furthermore, the addition of electrons causes a decrease in the effective nuclear charge, leading to an expansion in size.
• Example of Fluorine ($F$):
  • The atomic radius of fluorine ($F$) is only $64\,pm$.
  • The ionic radius of the fluoride ion ($F^{-}$) is $136\,pm$.

Isoelectronic Species

• Isoelectronic species are atoms and ions that contain the same total number of electrons.
• A more technical definition characterizes isoelectronic species as two or more species with the same number of atoms, the same number of valence electrons, and the same structure, regardless of the nature of the elements involved.
• Examples of isoelectronic species containing $10$ electrons include:
  • $O^{2-}$
  • $F^{-}$
  • $Na^{+}$
  • $Mg^{2+}$
• Despite having the same number of electrons, these species have different radii because they possess different nuclear charges (different numbers of protons).
• Size principles for isoelectronic species:
  • Cations with a greater positive charge will have a smaller radius because of the greater attraction of the electrons to the nucleus.
  • Anions with a greater negative charge will have a larger radius because the net repulsion of the electrons outweighs the nuclear charge, causing the ion to expand.

Comparative Analysis of Species Size

• When comparing species such as $Mg$, $Mg^{2+}$, $Al$, and $Al^{3+}$, the following rules apply:
  1. Atomic radii decrease across a period (making $Mg$ larger than $Al$).
  2. Cations are smaller than their parent atoms ($Mg^{2+}$ is smaller than $Mg$, and $Al^{3+}$ is smaller than $Al$).
  3. Among isoelectronic species (like $Mg^{2+}$ and $Al^{3+}$, both having $10$ electrons), the species with the larger positive nuclear charge has the smaller radius.
• As a result of these rules:
  • The largest species in this set is $Mg$.
  • The smallest species in this set is $Al^{3+}$.

Ionization Enthalpy

• Ionization enthalpy provides a quantitative measure of the tendency of an element to lose an electron.
• It is defined as the energy required to remove an electron from an isolated gaseous atom ($X$) in its ground state.
• The process can be represented as the formation of a cation: $X(g) \rightarrow X^{+}(g) + e^{-}$.