Comprehensive Study Guide on Electron Configurations, Atomic Stability, and Electronegativity Trends

Principles of Atomic Structure and Electron Orbitals

• Bohr Model of the Atom

  • The atomic structure can be visualized using Bohr's planetary model, where electrons orbit the nucleus on distinct, concentric circular energy levels.

  • Each principal energy level or shell is designated by the principal quantum number $n$, where $n = 1, 2, 3, 4, \dots$.

• Subshells and Orbitals

  • Energy levels are subdivided into subshells designated as $s$, $p$, $d$, and $f$.

  • An orbital represents a specific region or cloud shape where electrons reside within a subshell.

  • Every individual orbital can hold a maximum of $2$ electrons.

  • The breakdown of subshell orbital counts and maximum electron capacities is as follows:

  • $s$ subshell:

    • Contains $1$ orbital (spherical cloud shape).

    • Holds a maximum of $2$ electrons ($1 \times 2 = 2$).

  • $p$ subshell:

    • Contains $3$ orbitals.

    • Holds a maximum of $6$ electrons ($3 \times 2 = 6$).

  • $d$ subshell:

    • Contains $5$ orbitals.

    • Holds a maximum of $10$ electrons ($5 \times 2 = 10$).

  • $f$ subshell:

    • Contains $7$ orbitals.

    • Holds a maximum of $14$ electrons ($7 \times 2 = 14$).

  • The number of orbitals per subshell follows the sequence of odd numbers: $1, 3, 5, 7$.

Periodic Table Blocks and Quantum Energy Level Rules

• Periodic Table Block Mapping

  • The periodic table is organized into distinct blocks corresponding to electron subshells:

  • $s$-block: Groups 1 and 2 (plus Helium).

  • $p$-block: Groups 13 through 18.

  • $d$-block: Transition metals (Groups 3 through 12).

  • $f$-block: Inner transition metals (Lanthanides and Actinides).

• Energy Level Rules by Block

  • $s$-block and $p$-block:

  • The value of $n$ equals the period (row) number directly.

  • Row 1 corresponds to $n = 1$, Row 2 to $n = 2$, Row 3 to $n = 3$, and Row 4 to $n = 4$

  • $d$-block Rule ($n - 1$):

  • For transition metals in period $n$, the principal quantum number for the $d$ subshell is $n - 1$

  • Reading across Period 4 ($n = 4$), the sequence moves from $4s$ into the $3d$ block ($4 - 1 = 3$), and then returns to $4p$.

  • $f$-block Rule ($n - 2$):

  • For inner transition metals inserted in period $n$, the principal quantum number for the $f$ subshell is $n - 2$

  • In Period 6 ($n = 6$), the $f$ block subshell corresponds to $4f$ ($6 - 2 = 4$), while the $d$ block corresponds to $5d$ ($6 - 1 = 5$).

Step-by-Step Electron Configurations and Examples

• Full Configuration Tracing (Left to Right)

  • Electron configurations are determined by traversing the periodic table sequentially from hydrogen ($1s^1$) to the target element, subtracting energy levels for $d$ and $f$ blocks as required.

• Example 1: Selenium ($Se$)

  • Selenium is located in Period 4 ($n = 4$), Group 16 ($p$-block).

  • Sequential block progression across the periodic table:

  • Period 1: $1s^2$

  • Period 2: $2s^2 2p^6$

  • Period 3: $3s^2 3p^6$

  • Period 4:

    • $s$-block: $4s^2$

    • $d$-block ($n - 1$): $3d^{10}$

    • $p$-block ($n$): $4p^4$

  • Complete full electron configuration: $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^4$

  • Abbreviated noble gas configuration using Argon ($Ar$):

  • Argon covers $1s^2 2s^2 2p^6 3s^2 3p^6$

  • Abbreviated notation: $[Ar] 4s^2 3d^{10} 4p^4$

• Example 2: Titanium ($Ti$)

  • Titanium has an atomic number of $22$ ($22$ total electrons) and sits in Period 4, Group 4 ($d$-block).

  • Configuration trajectory: $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^2$

  • Abbreviated configuration: $[Ar] 4s^2 3d^2$

• Example 3: Titanium Ion ($Ti^{2+}$)

  • Total electrons = $22 - 2 = 20$

  • When transition metals ionize, electrons are removed from the outer principal energy level ($n = 4$) first before removing electrons from the lower $3d$ level.

  • Removing $2$ electrons eliminates the $4s^2$ shell.

  • Configuration for $Ti^{2+}$: $1s^2 2s^2 2p^6 3s^2 3p^6 3d^2$ (or represented with explicit empty shell as $4s^0 3d^2$).

• Example 4: Strontium ($Sr$)

  • Strontium is in Period 5, Group 2 ($s$-block).

  • Full electron configuration: $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2$

• Example 5: Tungsten ($W$)

  • Tungsten sits in Period 6 ($n = 6$) in the $d$-block.

  • Progression includes the $f$-block insertion:

  • Starts with $6s^2$

  • Enters $f$-block ($n - 2 = 4$): $4f^{14}$

  • Enters $d$-block ($n - 1 = 5$): $5d^4$

  • Outermost segment path: $6s^2 4f^{14} 5d^4$

Hund's Rule, Orbital Stability, and Transition Metal Ionization

• Subshell Stability Preferences

  • Subshells exhibit maximum stability under specific filling states:

  • $p$ subshell: Most stable when completely filled ($p^6$) or exactly half-filled ($p^3$).

  • Configurations such as $p^4$ leave one paired orbital and two unpaired orbitals, creating an energetically unstable system.

  • $d$ subshell: Most stable when completely filled ($d^{10}$) or exactly half-filled ($d^5$).

• Electron Shifting in Transition Metals

  • Atoms redistribute electrons between adjacent $s$, $d$, and $p$ subshells to achieve more stable low-energy configurations.

  • Copper ($Cu$) Behavior:

  • Expected neutral configuration: $[Ar] 4s^2 3d^9$

  • An electron shifts from the $4s$ subshell to complete the $3d$ subshell, producing $[Ar] 4s^1 3d^{10}$.

• Copper Ion States ($Cu^+$ and $Cu^{2+}$):

  • $Cu^+$ ($+1$ charge state):

  • Loses the single $4s^1$ electron.

  • Configuration: $4s^0 3d^{10}$

  • Highly stable due to a completely filled $3d$ orbital set.

  • $Cu^{2+}$ ($+2$ charge state):

  • Loses two electrons from the neutral ground state ($4s^2$ electrons).

  • Configuration: $4s^0 3d^9$

• Energy Level Dynamics and Orbital Notation

  • An energy level of $n = 3$ represents a lower energy state than $n = 4$. Electrons naturally favor residing in lower energy orbitals because less energy is required to exist there.

  • When writing shorthand orbital representations for ionized transition metals, explicitly retain the empty $4s$ orbital (e.g., $4s^0$ or a blank line) preceding the $3d$ block to verify that the $4s$ electrons were removed rather than overlooked.

Electronegativity Trends across the Periodic Table

• Definition of Electronegativity

  • Electronegativity measures an atom's ability or tendency to attract shared bonding electrons toward its nucleus.

  • High electronegativity indicates a powerful pull on electrons.

  • Low electronegativity indicates a weak pull, where the atom readily yields electrons.

• Noble Gas Exclusion

  • Noble gases (Group 18) are generally excluded from standard electronegativity trends because their valence shells are fully filled and highly stable, giving them negligible tendency to attract additional electrons.

• Periodic Trends

  • Electronegativity increases moving from left to right across a period.

  • Electronegativity increases moving from bottom to top up a group.

• Extreme Ends of the Trend

  • Francium ($Fr$): Lowest electronegativity on the periodic table.

  • Located at the bottom-left corner.

  • Contains $1$ valence electron in a high principal energy level ($7s^1$).

  • Large atomic radius places valence electrons far from the positive nucleus, making the attraction force extremely weak and causing the atom to lose electrons easily.

  • Fluorine ($F$): Highest electronegativity on the periodic table.

  • Located at the top-right corner (excluding noble gases).

  • Contains $7$ valence electrons and requires only $1$ electron to complete its octet.

  • Extremely small atomic radius keeps outer energy levels close to the nucleus, allowing protons to exert a powerful pull on incoming electrons.

Chemical Bonding, Molecular Polarity, and Lewis Structures

• Bond Polarity and Vector Representations

  • When two atoms with different electronegativities form a bond, the more electronegative atom pulls shared electrons closer to itself.

  • In a Lewis structure, this pull is represented as a directional bond dipole vector pointing toward the more electronegative atom.

  • Water ($H_2O$) Example:

  • Oxygen ($O$) has $6$ valence electrons; Hydrogen ($H$) has $1$ valence electron each.

  • Oxygen is significantly more electronegative than Hydrogen.

  • Dipole vectors point from each Hydrogen atom upward toward the central Oxygen atom.

  • Adding the two vector components yields a net overall upward dipole vector, making water a polar molecule.

• Electronegativity Difference ($\Delta EN$) Classification

  • The difference in electronegativity between two bonded atoms determines the nature of the bond:

  • Nonpolar Covalent Bond: $\Delta EN < 0.5$

    • Electrons are shared relatively equally.

  • Polar Covalent Bond: $0.5 \le \Delta EN \le 1.0$

    • Electrons are shared unequally, creating fractional charges and molecular dipoles.

  • Ionic Bond: $\Delta EN > 1.0$

    • Electronegativity difference is so severe that the more electronegative atom completely strips the electron away from the less electronegative atom rather than sharing it.

• Ionic Bonding Mechanisms and Representation

  • Sodium Chloride ($NaCl$) Example:

  • Sodium ($Na$) has very low electronegativity; Chlorine ($Cl$) has very high electronegativity.

  • Chlorine completely removes the single valence electron from Sodium, resulting in a positively charged sodium cation ($Na^+$) and a negatively charged chloride anion ($Cl^-$).

  • When dissolved in water, it forms aqueous ions: $NaCl_{(aq)} \rightarrow Na^+_{(aq)} + Cl^-_{(aq)}$.

  • Lewis Structure Formatting for Ionic Compounds:

  • Covalent bonding lines must not be drawn between ions because no electrons are shared.

  • Ionic compounds are drawn as isolated ions with formal charges and brackets around the full octet of the anion: $Na^+$ and $[:\ddot{Cl}:]^-$.