Comprehensive Study Guide on Atomic Structure, Subshells, and Electron Configurations

Periodic Table Groups and Chemical Reactivity Trends

• Group 1 (alkali metals) and Group 2 (alkaline earth metals) elements form ions by losing outer electrons to achieve a positive charge; for example, Group 1 elements readily lose $1$ electron to form a $+1$ cation.

• Groups 3 through 12 comprise the transition metals, which possess more complex electron structures; main-group charge rules do not apply directly to these elements (e.g., elements in Group 3 do not simply lose $3$ electrons in the same straightforward manner as Group 1 or 2 elements).

• Group 13 and Group 14 contain p-block elements with varied metallic and non-metallic properties.

• Group 15 elements belong to the nitrogen group, which includes elements such as Nitrogen ($N$) and Phosphorus ($P$).

• Group 16 elements belong to the chalcogen group, which includes elements such as Oxygen ($O$) and Sulfur ($S$).

• Group 17 elements belong to the halogen group, which includes elements such as Fluorine ($F$) and Chlorine ($Cl$).

• Group 18 elements are the noble gases, which possess completely filled valence shell electron configurations, resulting in extremely similar low chemical reactivity.

• Elements positioned in the same periodic table group exhibit similar valence electron configurations and, consequently, share similar chemical reactivity.

Principal Electron Shells and Energy Levels

• Electrons move around the atomic nucleus in structured, organized layers designated as principal energy shells, identified by the integer $n$.

• Shells are numbered sequentially outward from the nucleus: $n = 1, 2, 3, 4, 5, 6, 7$. Across known elements, the maximum principal shell number observed is $7$ (with standard configurations typically focusing on the first $3$, $4$, or $5$ shells).

• Distance from the atomic nucleus correlates directly with the shell energy level:

  • The shell closest to the nucleus ($n = 1$) possesses the lowest energy level.

  • As the shell number increases and electrons reside further from the nucleus, the energy level (potential energy) increases.

  • This behavior is analogous to gravitational potential energy increasing as an object is moved further from the center of the Earth against gravitational attraction.

• Each principal shell has a maximum electron capacity governed by the formula:   $\text{Maximum Electrons} = 2n^2$

• Electron capacity per principal shell:

  • Shell 1 ($n = 1$): $2(1)^2 = 2$ electrons maximum.

  • Shell 2 ($n = 2$): $2(2)^2 = 8$ electrons maximum.

  • Shell 3 ($n = 3$): $2(3)^2 = 18$ electrons maximum.

  • Shell 4 ($n = 4$): $2(4)^2 = 32$ electrons maximum.

  • Shell 5 ($n = 5$): $2(5)^2 = 50$ electrons maximum.

Subshells and Orbital Electron Capacity

• Each principal electron shell is divided into subshells, which define the spatial shape of the electron clouds/orbitals.

• There are four primary subshell types, listed in order of increasing energy level: $s$, $p$, $d$, and $f$.

• Subshell energy increases sequentially according to:   $s < p < d < f$

• An atomic orbital is a subregion capable of accommodating a maximum of $2$ electrons.

• The total number of orbitals and maximum electron capacity for each subshell type are:

  • $s$ subshell: Contains $1$ orbital, accommodating a maximum of $2$ electrons ($1 \times 2 = 2$).

  • $p$ subshell: Contains $3$ orbitals, accommodating a maximum of $6$ electrons ($3 \times 2 = 6$).

  • $d$ subshell: Contains $5$ orbitals, accommodating a maximum of $10$ electrons ($5 \times 2 = 10$).

  • $f$ subshell: Contains $7$ orbitals, accommodating a maximum of $14$ electrons ($7 \times 2 = 14$).

• The orbital sequence across subshells follows the odd number series: $1, 3, 5, 7$

• The subshell maximum electron capacity sequence follows: $2, 6, 10, 14$

Subshell Energy Hierarchy and Filling Order

• Subshell notation combines the principal shell number and the subshell letter in the form $\text{Shell}\text{Subshell}$ (e.g., $1s$ denotes shell $1$, subshell $s$).

• Subshell composition across shells:

  • Shell 1 ($n = 1$): Contains only the $1s$ subshell ($2$ electrons maximum). Total capacity = $2$

  • Shell 2 ($n = 2$): Contains $2s$ ($2$ electrons) and $2p$ ($6$ electrons) subshells. Total capacity = $8$

  • Shell 3 ($n = 3$): Contains $3s$ ($2$ electrons), $3p$ ($6$ electrons), and $3d$ ($10$ electrons) subshells. Total capacity = $18$

• Relative Energy Anomaly between $4s$ and $3d$:

  • Although principal shell numbers generally dictate energy levels, the $4s$ subshell is slightly lower in energy than the $3d$ subshell.

  • Therefore, electrons fill the $4s$ subshell prior to filling the $3d$ subshell.

  • This energy inversion pattern recurs in higher principal shells (e.g., $5s$ fills before $4d$, $6s$ fills before $5d$).

• Standard filling sequence by increasing energy:   $1s \rightarrow 2s \rightarrow 2p \rightarrow 3s \rightarrow 3p \rightarrow 4s \rightarrow 3d \rightarrow 4p \rightarrow 5s$

Fundamental Rules Governing Electron Configuration

• Aufbau Principle (Lowest Energy First):

  • Electrons occupy the available orbital with the lowest energy level first before moving to higher energy orbitals.

  • Filling proceeds sequentially through subshells ($1s$, then $2s$, then $2p$, then $3s$, then $3p$, then $4s$, then $3d$) until all electrons of an atom are assigned.

• Pauli Exclusion Principle and Spin Pairing:

  • Each orbital box/state can hold a maximum of $2$ electrons.

  • Two electrons occupying the same orbital must possess opposite spin states, depicted in diagrammatic representations as one upward arrow (spin up) and one downward arrow (spin down).

  • Co-occupancy of an orbital by two electrons with parallel spins (e.g., two upward arrows in a single orbital) is forbidden.

• Hund's Rule (Degenerate Orbital Filling):

  • When filling orbitals of equal energy (degenerate orbitals, such as the $3$ orbitals of a $p$ subshell), electrons enter orbitals individually with parallel spins until each orbital is half-filled.

  • Single occupancy of all degenerate orbitals in a subshell must occur before any orbital receives a second electron to pair up.

  • Because degenerate orbitals share identical energy levels, it does not matter which specific degenerate box receives the initial single electron or the subsequent pairing electron.

Configuration Methods and Representative Examples

• Standard Subshell Notation:

  • Represented as $\text{Shell}\text{Subshell}^{\text{Electrons}}$, where the superscript indicates the total electron count in that subshell.

  • Hydrogen ($H$, atomic number $1$): $1s^1$

  • Helium ($He$, atomic number $2$): $1s^2$

  • Lithium ($Li$, atomic number $3$):

  • Total electrons = $3$

  • First $2$ electrons fill the $1s$ subshell ($1s^2$).

  • Remaining $1$ electron enters the $2s$ subshell ($2s^1$).

  • Configuration: $1s^2\,2s^1$

  • Atom with $8$ electrons (Oxygen):

  • Configuration: $1s^2\,2s^2\,2p^4$

  • Sodium ($Na$, atomic number $11$):

  • Total electrons = $11$

  • Configuration: $1s^2\,2s^2\,2p^6\,3s^1$

• Abbreviated (Noble Gas Core) Notation:

  • Full inner electron shells corresponding to a completed noble gas core are replaced with the noble gas element symbol enclosed in square brackets ($[\text{Noble Gas}]$).

  • Helium ($He$) represents the completed inner core of Shell 1 ($1s^2$).

  • Abbreviated configuration for Lithium ($Li$): $[He]\,2s^1$

  • Abbreviated configuration for Sodium ($Na$): $[Ne]\,3s^1$

Transition Metal Configuration Exceptions and Ionization Rules

• Specific transition metal groups deviate from standard Aufbau filling rules to achieve lower energy states associated with half-filled or fully filled subshells.

• Group 6 Exceptions (e.g., Chromium and Molybdenum):

  • Group 6 elements adopt a half-filled $d$ subshell ($d^5$) and a half-filled $s$ subshell ($s^1$) rather than a filled $s$ subshell and a $d^4$ subshell.

  • Chromium ($Cr$, atomic number $24$):

  • Standard predicted configuration: $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^2\,3d^4$ (or $[Ar]\,4s^2\,3d^4$).

  • Actual correct configuration: $1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^5\,4s^1$ (or $[Ar]\,3d^5\,4s^1$).

  • Molybdenum ($Mo$): Follows the identical exception pattern in shell 5, yielding [Kr]\,4d^5\,5s^1$.\n* Group 11 Exceptions (e.g., Copper):\n * Group 11 elements adopt a completely filled d$subshell ($d^{10}$) and a half-filled$s$subshell ($s^1).\n * Copper (Cu$, atomic number$29):\n * Standard predicted configuration: [Ar]\,4s^2\,3d^9\n * Actual correct configuration: [Ar]\,3d^{10}\,4s^1\n* Ionization and Electron Loss Sequence:\n * When an atom loses electrons to form a positive ion (cation), electrons are always removed from the outermost shell (highest principal quantum number n) first.\n * In transition metals containing both 4s$and$3d$electrons, the$4s$electrons ($n = 4$) reside in the outermost shell and are removed prior to removing any$3d$electrons ($n = 3).\n * Example: Removing 1$electron from a neutral transition metal atom removes a$4s$electron first; removing a second electron removes the remaining$4s$electron before any$3d$$ electrons are lost.