Main-Group Electron Configurations, Valence Electrons, and Core Electron Calculations

Principal Energy Levels, Valence Electrons, and Core Electrons

• The principal energy level (represented by the principal quantum number $n$) indicates the main energy shell of an electron and corresponds to the period/row number on the periodic table.

• Valence electrons are defined as the electrons located within the highest principal energy level ($n_{\text{max}}$).

• To determine the total number of valence electrons for a main-group element, electrons residing in all subshells (such as $s$ and $p$ subshells) belonging to the highest principal energy level must be added together.

• Core electrons (also referred to as inner electrons) consist of all electrons in principal energy levels below the highest occupied level ($n < n_{\text{max}}$).

• Core electrons occupy shells closer to the atomic nucleus and do not participate in chemical reactions or bond formation.

• Valency (or valence) represents the combining capacity of an atom with other atoms, defined as the number of chemical bonds an atom can establish or the number of electrons available for bonding.

• Main-group electron configurations follow regular filling rules, whereas transition metal elements exhibit specific electron configuration irregularities that fall outside the standard main-group framework.

Main-Group Valence Configurations and Group Trends

• Valence electrons are frequently abbreviated as $v.e.$

• For main-group elements, the Roman numeral group number on the periodic table directly corresponds to the number of valence electrons possessed by elements in that group.

• Progression of valence electron counts across subshell combinations:

  • Configuration $ns^2$ yields $2\,v.e.$

  • Configuration $ns^2 np^1$ yields $2 + 1 = 3\,v.e.$

  • Configuration $ns^2 np^2$ yields $2 + 2 = 4\,v.e.$

  • Configuration $ns^2 np^6$ yields $2 + 6 = 8\,v.e.$

• Noble gases possess filled $s$ and $p$ subshells ($ns^2 np^6$), totaling $8$ valence electrons.

• Based on chemical behavior, noble gases are frequently assigned a valency of $0$ due to their chemical inertness and unreactive nature. Both $8$ valence electrons and a valency of $0$ are valid representations depending on whether counting electrons or describing bonding behavior.

• Lewis structures function as an accounting system for chemical bonding, exclusively displaying valence electrons because core electrons do not participate in bonding.

Orbital Diagrams, Sublevels, and Hund's Rule

• Phosphorus ($\text{P}$, atomic number $Z = 15$):

  • Total electron count: $15$ electrons.

  • Abbreviated electron configuration using the Neon core ($[Ne]$ representing $10$ electrons):   $[Ne]\,3s^2\,3p^3$

  • Highest principal energy level: $n = 3$.

  • Highest energy sublevel: $3p$.

  • Orbital filling according to Hund's Rule: The three degenerate orbitals of the $3p$ sublevel ($3p_x$, $3p_y$, $3p_z$) each receive a single electron with parallel (same) spin before any orbital receives a second electron, maximizing the number of unpaired electrons.

• Selenium ($\text{Se}$, atomic number $Z = 34$):

  • Total electron count: $34$ electrons.

  • Abbreviated electron configuration:   $[Ar]\,4s^2\,3d^{10}\,4p^4$

  • Highest principal energy level: $n = 4$.

  • Highest energy sublevel: $4p$.

  • Orbital filling according to Hund's Rule: Place single electrons with parallel spin into each of the three $4p$ orbitals ($3$ electrons), and then pair the $4\text{th}$ electron in the first orbital with an opposite spin.

  • Physical significance: Orbital diagram configurations mimic and explain the observed magnetic properties of elements.

Quantitative Determination of Core and Valence Electrons

• Fundamental mathematical relationship for electron accounting:   $\text{Core Electrons} = \text{Total Electrons} - \text{Valence Electrons}$

• Carbon ($\text{C}$, atomic number $Z = 6$):

  • Electron configuration: $1s^2\,2s^2\,2p^2$.

  • Highest principal energy level: $n = 2$.

  • Valence electrons: $2 + 2 = 4\,v.e.$

  • Core electrons: $2$ core electrons (from the $1s^2$ shell).

  • Total verification: $4 + 2 = 6$ total electrons.

• Nitrogen ($\text{N}$, atomic number $Z = 7$):

  • Electron configuration: $1s^2\,2s^2\,2p^3$ or $[He]\,2s^2\,2p^3$.

  • Highest principal energy level: $n = 2$.

  • Valence electrons: $2 + 3 = 5\,v.e.$

  • Core electrons: $2$ core electrons ($[He]$ core).

  • Total verification: $5 + 2 = 7$ total electrons.

• Silicon ($\text{Si}$, atomic number $Z = 14$):

  • Abbreviated electron configuration: $[Ne]\,3s^2\,3p^2$.

  • Valence electrons: $2 + 2 = 4\,v.e.$

  • Core electrons: $10$ core electrons ($[Ne]$ core).

  • Total verification: $4 + 10 = 14$ total electrons.

• Oxygen ($\text{O}$, atomic number $Z = 8$):

  • Period: $2$.

  • Valence electrons: $6\,v.e.$

  • Core electrons: $2$ core electrons (corresponding to Helium in Period $1$).

• Fluorine ($\text{F}$, atomic number $Z = 9$):

  • Period: $2$.

  • Total electrons: $9$.

  • Valence electrons: $7\,v.e.$

  • Core electrons: $2$ core electrons ($[He]$ core).

• Influence of $d$ Subshells in Higher Periods:

  • Period $2$ elements have $2$ core electrons ($[He]$ core).

  • Period $3$ elements have $10$ core electrons ($[Ne]$ core).

  • For elements in Period $4$ and higher, filled $d$ subshells (such as the $10$ electrons in $3d^{10}$) are included in the core electron count. Subtracting valence electrons from total electrons avoids errors when counting core electrons in heavier elements.

• Antimony ($\text{Sb}$, atomic number $Z = 51$):

  • Total electrons: $51$.

  • Group $15$ (Group 5A) element with $5$ valence electrons.

  • Core electrons calculation:   $\text{Core Electrons} = 51 - 5 = 46$