Effective Nuclear Charge

$Z_{eff} = Z - \sigma$ where $Z$ = atomic number, $\sigma$ = shielding constant (Slater's rules)

Atomic Radius Trend

$r \propto \frac{n}{Z_{eff}}$

Across a period: $Z_{eff} \uparrow,\ n = \text{const} \Rightarrow r \downarrow$

Down a group: $n \uparrow \Rightarrow r \uparrow$ (dominates over Zeff increase)

Isoelectronic Radius

For species with same electron count: $r \propto \frac{1}{Z}$ (More protons → smaller radius)

Ionization Enthalpy (IE)

$\text{M}(g) \xrightarrow{+\Delta H_{IE}} \text{M}^+(g) + e^-$

Always endothermic ($\Delta H > 0$)

Key values (Period 2):

Electron Gain Enthalpy (EGE)

$\text{X}(g) + e^- \xrightarrow{\Delta H_{EGE}} \text{X}^-(g)$

Mostly exothermic for non-metals ($\Delta H < 0$)

Key values (Halogens): $\Delta H_{EGE}(\text{Cl}) = -349\ \text{kJ/mol} < \Delta H_{EGE}(\text{F}) = -328\ \text{kJ/mol}$

Diagonal Relationship Reactions

Li–Mg (both form normal oxide, not peroxide): $4\text{Li} + \text{O}_2 \rightarrow 2\text{Li}_2\text{O}$ $2\text{Mg} + \text{O}_2 \rightarrow 2\text{MgO}$

Be–Al (both dissolve in NaOH — amphoteric): $\text{Be} + 2\text{NaOH} \rightarrow \text{Na}_2\text{BeO}_2 + \text{H}_2\uparrow$ $2\text{Al} + 2\text{NaOH} + 2\text{H}_2\text{O} \rightarrow 2\text{NaAlO}_2 + 3\text{H}_2\uparrow$

B–Si (both chlorides hydrolyzed by water): $\text{BCl}_3 + 3\text{H}_2\text{O} \rightarrow \text{B(OH)}_3 + 3\text{HCl}$ $\text{SiCl}_4 + 4\text{H}_2\text{O} \rightarrow \text{Si(OH)}_4 + 4\text{HCl}$

Anomalous Behavior — First Element in Group

• Cannot expand octet beyond 4 bonds (no d-orbitals in n=2)
• Example: N (max covalency = 4), O (max covalency = 3 in $\text{H}_3\text{O}^+$)