Electron Configuration and Atomic Orbital Theory

Atomic Structure and Electron Energy Levels

• The study begins by examining how atoms produce light via changes in the energy levels of their electrons. The focus is specifically on how electrons are arranged within an atom and the resulting effects.
• Gold ($Au$) contains $79$ electrons. This is determined by its atomic number, which expresses the number of protons. Because an atom like gold is electrically neutral, it must possess an equal number of electrons, thus it has $79$ electrons.

The Shift from Bohr Orbits to Orbitals

• The Bohr model, which depicts electrons as planets orbiting a solar system, is fundamentally incorrect. Electrons do not move in fixed orbits.
• Instead, electrons exist in "orbitals," which are three-dimensional regions of space. Describing an orbital requires two primary pieces of information:
• 1. Principal Quantum Number ($n$): This is the numerical value derived from the Bohr model (e.g., $n = 1$, $n = 2$, $n = 3$).
• 2. Letter Code (Shape): This code identifies the specific geometry of the orbital.
• Orbital shapes discussed in this course include:
  • $s$ orbitals: These are spherical.
  • $p$ orbitals: These resemble small dumbbells.
  • $d$ orbitals: These look like small clovers.

Nature of the Orbital and Uncertainty

• Orbitals are often represented as "fuzzy" images rather than defined lines. This is not due to low resolution but because the quantum level is probabilistic.
• A darker region in an orbital diagram indicates where an electron is more likely to be found, while lighter regions indicate lower probability.
• The standard representation of an orbital shows only the $90\%$ probability region of space; the electron could theoretically exist elsewhere.
• This stems from the fact that one cannot determine the exact position and velocity of an electron simultaneously. There is an inherent uncertainty in the physical world.
• For all orbitals, the nucleus of the atom sits at the center of the sphere or shape.

Fundamental Rules for Electron Configuration

Three main principles dictate how electrons are placed into orbitals:

• 1. Aufbau Principle: Electrons always fill the lowest energy orbital first. This determines the order of subshells (e.g., filling $1s$ before $2s$).
• 2. Pauli Exclusion Principle: A single orbital can hold a maximum of two electrons. These electrons must be paired with opposing spins. In diagrams, they are represented as an up arrow ($\uparrow$) and a down arrow ($\downarrow$).
• 3. Hund’s Rule: When dealing with degenerate orbitals (orbitals of equal energy), electrons do not pair up until every orbital in that subshell has at least one electron. Electrons stay unpaired for as long as possible.

Shells, Subshells, and Degeneracy

• Shell: Refers to the broad principal quantum level ($n$).
• Subshell: Refers to the specific type of orbital within a shell (e.g., $s$, $p$, or $d$).
• Individual Orbitals: The specific spaces where electrons reside.

Shells and Subshell Components:

• Shell $n = 1$: Contains a single orbital called the $1s$ orbital ($1s$).
• Shell $n = 2$: Contains the $2s$ orbital and the $2p$ subshell. The $2s$ is higher in energy than the $1s$. The $2p$ subshell consists of three separate orbitals: $p_z$ (oriented on the z-axis), $p_x$ (x-axis), and $p_y$ (y-axis).
• Degenerate Orbitals: These are orbitals with the same energy level. For example, the three orbitals in a $p$ subshell are degenerate. In diagrams, they are drawn side-by-side without spaces.
• Shell $n = 3$: Contains the $3s$ orbital, the $3p$ subshell (three orbitals), and the $3d$ subshell (five degenerate orbitals). The $3s$ is a larger sphere surrounding the $2s$ sphere.
• Shell $n = 4$: Contains the $4s$, $4p$, $4d$, and $4f$ subshells. The $f$ subshell is related to Lanthanides and Actinides and contains seven degenerate orbitals.

Systematic Patterns in Orbital Counts

• The number of subshells in a shell is equal to the principal quantum number ($n$). Shell $1$ has one, Shell $5$ has five, etc.
• The number of orbitals in a subshell type increases by two at each step:
  • $s$ subshell: $1$ orbital ($2$ electrons max).
  • $p$ subshell: $3$ orbitals ($6$ electrons max).
  • $d$ subshell: $5$ orbitals ($10$ electrons max).
  • $f$ subshell: $7$ orbitals ($14$ electrons max).
• Every atom contains every subshell; the identity of the atom simply determines which subshells are full and which are empty.

The Diagonal Method and Ground State

• Ground State refers to the configuration where electrons occupy the lowest possible energy orbitals available.
• To follow the Aufbau principle, one uses the diagonal filling method. This demonstrates that the $4s$ orbital is lower in energy than the $3d$ orbital, even though $3d$ has a lower principal quantum number.
• Order of filling: $1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s \dots$

Periodic Table Blocks

• $s$-block: Groups 1 (Alkali metals) and 2 (Alkaline earth metals). The period number corresponds to the shell.
• $p$-block: Located on the right side of the periodic table. The period number corresponds to the shell.
• $d$-block (Transition Metals): The subshell number is one less than the period ($n-1$). If you are in period $4$, you are filling the $3d$ subshell.
• $f$-block: Lanthanides and Actinides.

Configuration Examples

• Hydrogen ($H$): Has $1$ electron. Configuration: $1s^1$.
• Helium ($He$): Has $2$ electrons. Configuration: $1s^2$.
• Lithium ($Li$): Has $3$ electrons. Configuration: $1s^2 2s^1$.
• Beryllium ($Be$): Has $4$ electrons. Configuration: $1s^2 2s^2$.
• Scandium ($Sc$): Has $21$ electrons. Terminates in the $3d$ subshell. Configuration: $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^1$.
• Rhodium ($Rh$): Has $45$ electrons. Terminates in the $4d$ subshell. Configuration: $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^7$.

Classes of Electrons and Noble Gas Shorthand

• Valence Electrons: Electrons in the outermost shell. These are most susceptible to chemical change.
• Core Electrons: Lower energy electrons tucked away in inner shells; these do not participate in chemical reactions.
• Noble Gas Configuration: A shorthand method utilizing the previous noble gas (in brackets) to represent core electrons. For Magnesium ($Mg$), instead of $1s^2 2s^2 2p^6 3s^2$, we write $[Ne] 3s^2$ (the configuration of Neon plus valence electrons).

Excited States and Ions

• Excited State: Formed when energy (like electricity) is added to an atom, jumping one electron from the highest energy orbital to a higher shell. This atom is denoted with a star ($*$). For Helium ($He^*$), the excited configuration is $1s^1 2s^1$. Unpaired electrons in an excited state typically maintain the same spin direction.
• Ions: Ions are formed by changing the number of electrons.
  • Carbon ($C$) to Carbon $2+$ ($C^{2+}$): Carbon starts with $6$ electrons. As a $+2$ ion, it has $4$ electrons. Electrons are lost from the highest energy subshell first ($2p$), resulting in $1s^2 2s^2$.
  • General Rule: Always lose electrons from the highest energy/outermost subshell first.

Stability Exceptions in Transition Metals

• In transition metals, electronic stability can result in unexpected configurations.
• For an ion like $Fe^{2+}$ (atomic number $26$, minus $2$ electrons = $24$ total), the expected configuration might be $[Ar] 4s^2 3d^4$.
• However, it is more electronically stable to have two half-full subshells rather than one full and one partially full. Therefore, the configuration adjusts to $[Ar] 4s^1 3d^5$.
• Stability gains primarily occur when you can create a full shell, a full subshell, or a set of half-full subshells.

Questions & Discussion

• Do empty subshells exist? Yes, all atoms possess all subshells (e.g., hydrogen technically has a $4f$ subshell), but they are usually empty and too high in energy for electrons to reside there under normal conditions.
• Direction of Arrow in Orbital Diagrams: If an orbital has only one electron, it is conventionally drawn as an up arrow, though this is just a standardized notation decided upon by the scientific community.
• Memorizing the Periodic Table: The lecturer suggests it is silly to memorize the table; it is much more important to understand how to use the table to extract information. A periodic table with names is typically provided during exams.