(a) Atomic Radius

Defining the size of an atom is complex due to the diffuse nature of its electron cloud. Atomic radius is generally estimated based on the distance between atoms in a combined state:

• Covalent Radius: Half the distance between two atoms bonded by a single bond in a covalent molecule (e.g., Cl-Cl bond in Cl₂ is 198 pm, so atomic radius of Cl is 99 pm).
• Metallic Radius: Half the internuclear distance between adjacent metal cores in a metallic crystal (e.g., Cu-Cu distance in solid Cu is 256 pm, so metallic radius of Cu is 128 pm).

Trends:

• Across a Period (Left to Right): Decreases. This is due to increasing effective nuclear charge (Z_eff). The outer electrons are in the same valence shell, but the increasing nuclear charge pulls them more tightly towards the nucleus.
• Down a Group (Top to Bottom): Increases. This is due to the increase in principal quantum number (n), meaning valence electrons are in higher energy shells, further from the nucleus. Inner electrons also provide increased shielding, reducing the pull of the nucleus on the outer electrons.
• Noble Gases: Not considered here with covalent radii, as they are monoatomic. Their van der Waals radii are much larger, which is a different measure.

(b) Ionic Radius

Ionic radii exhibit similar trends to atomic radii, but with key differences depending on whether an ion is a cation or an anion.

• Cation ($X^+$): Always smaller than its parent atom (X). This is because the cation has fewer electrons, but the same nuclear charge, leading to a stronger pull on the remaining electrons. Example: Na (186 pm) vs Na$^+$ (95 pm).
• Anion ($X^-$): Always larger than its parent atom (X). This is due to the addition of one or more electrons, increasing electron-electron repulsion and decreasing the effective nuclear charge felt by the valence electrons, causing the electron cloud to expand. Example: F (64 pm) vs F$^-$ (136 pm).
• Isoelectronic Species: Atoms or ions with the same number of electrons (e.g., O²⁻, F⁻, Na⁺, Mg²⁺ all have 10 electrons). For isoelectronic species, the radius decreases with increasing positive nuclear charge. The greater the nuclear charge, the stronger the attraction for the same number of electrons, leading to a smaller size.
  Order of size: O²⁻ > F⁻ > Na⁺ > Mg²⁺ (due to Z: 8, 9, 11, 12 respectively).

(c) Ionization Enthalpy ($\Delta_i H$)

Ionization enthalpy is the energy required to remove an electron from an isolated gaseous atom in its ground state. It is always positive (energy is absorbed).

$\text{X(g)} \rightarrow \text{X}^+\text{(g)} + \text{e}^-$ (First Ionization Enthalpy, $\Delta_i H_1$)

$\text{X}^+\text{(g)} \rightarrow \text{X}^{2+}\text{(g)} + \text{e}^-$ (Second Ionization Enthalpy, $\Delta_i H_2$)

Successive ionization enthalpies are always higher (e.g., $\Delta_i H_2 > \Delta_i H_1$) because it’s harder to remove an electron from a positively charged ion.

Factors Affecting Ionization Enthalpy:

• Effective Nuclear Charge (Z_eff): Higher Z_eff means electrons are held more tightly, requiring more energy to remove.
• Atomic Size: Larger atomic size means valence electrons are further from the nucleus, experiencing less attraction, thus easier to remove (lower IE).
• Shielding/Screening Effect: Inner core electrons shield valence electrons from the full nuclear charge. Greater shielding leads to lower IE.
• Penetration Effect of Orbitals: For the same principal quantum number, the order of penetration is s > p > d > f. More penetrating orbitals are closer to the nucleus and held more tightly, so s-electrons are harder to remove than p-electrons from the same shell.
• Stability of Half-filled/Completely Filled Orbitals: Atoms with exactly half-filled or completely filled subshells exhibit extra stability, requiring more energy to remove an electron.

Trends:

• Across a Period (Left to Right): Generally Increases. Increasing Z_eff and decreasing atomic size lead to stronger attraction for valence electrons.
  • Exceptions:
  • IE of B is less than Be: Be has $1s^22s^2$, electron removed is from stable 2s orbital. B has $1s^22s^22p^1$, electron removed is from 2p orbital. Due to better penetration of 2s over 2p, 2s electron is held more tightly.
  • IE of O is less than N: N has $1s^22s^22p^3$ (half-filled p-subshell, stable). O has $1s^22s^22p^4$. Removing an electron from O (one paired p-electron) is easier due to increased electron-electron repulsion, overcoming the effect of increased nuclear charge.
• Down a Group (Top to Bottom): Generally Decreases. Increasing atomic size and shielding effect outweigh the increasing nuclear charge, making it easier to remove the outermost electron.

(d) Electron Gain Enthalpy ($\Delta_{eg} H$)

Electron gain enthalpy is the enthalpy change when an electron is added to a neutral gaseous atom to form a negative ion.

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

This process can be exothermic ($\Delta_{eg}H$ is negative, energy released) or endothermic ($\Delta_{eg}H$ is positive, energy absorbed).

• Exothermic: Group 17 elements (halogens) have highly negative $\Delta_{eg}H$ values because they achieve a stable noble gas configuration by gaining an electron.
• Endothermic: Noble gases have large positive $\Delta_{eg}H$ values because adding an electron requires it to enter a higher, unstable energy level.

Trends:

• Across a Period (Left to Right): Generally becomes more negative. Effective nuclear charge increases, making it easier for an atom to attract an additional electron.
• Down a Group (Top to Bottom): Generally becomes less negative. Atomic size increases, meaning the added electron is further from the nucleus and experiences less attraction.
• Anomalies:
  • Electron gain enthalpy of O or F is less negative than that of S or Cl, respectively. This is because O (2p) and F (2p) are very small, and the incoming electron experiences significant repulsion from existing electrons in the small 2p orbitals. For S (3p) and Cl (3p), the larger atomic size means less electron-electron repulsion for the incoming electron. Thus, S and Cl have more negative electron gain enthalpies than O and F.

(e) Electronegativity

Electronegativity is a qualitative measure of the ability of an atom in a chemical compound to attract shared electrons to itself. Unlike IE and EGE, it is not a directly measurable quantity, but scales (like the Pauling scale, where Fluorine is assigned 4.0) have been developed.

Trends:

• Across a Period (Left to Right): Increases. As atomic radius decreases and effective nuclear charge increases, the attraction for shared electrons becomes stronger.
• Down a Group (Top to Bottom): Decreases. As atomic radius increases, the valence electrons are further from the nucleus, and the attraction for shared electrons weakens.

Relationship with Metallic/Non-metallic Character:

• Electronegativity is directly related to non-metallic properties (strong tendency to gain electrons).
• Electronegativity is inversely related to metallic properties.
• Thus, increasing electronegativity across a period is accompanied by an increase in non-metallic properties (and decrease in metallic properties).
• Decreasing electronegativity down a group is accompanied by a decrease in non-metallic properties (and increase in metallic properties).