Atomic Structure, Electron Configurations, and Periodic Trends

Principal Energy Levels and Sublevel Structure

• Orbital Shapes and f Sublevels: In the discussion of orbital diagrams, the focus is on the distinct shapes of different orbital types. An $f$ sublevel specifically contains $7$ distinct $f$ orbitals.

• Principal Energy Level $n=1$: This is the first level of energy for electrons. In the $n=1$ level, the only available location for an electron is an $s$ sublevel. This sublevel consists of a single $s$ orbital, which possesses a spherical shape.

• Principal Energy Level $n=2$: In the second level, electrons have two sublevel options:

  • One $s$ sublevel (containing one $s$ orbital).

  • One $p$ sublevel, which consists of three $p$ orbitals. These orbitals are oriented periperpendicularly, lying at $90\text{ degrees}$ to $100$.

• Principal Energy Level $n=3$: The third level expands to include three sublevel options:

  • The $s$ sublevel.

  • The $p$ sublevel.

  • The $d$ sublevel, which consists of five distinct $d$-shaped orbitals.

• Principal Energy Level $n=4$: The fourth level includes four sublevel options:

  • The $s$ sublevel.

  • The $p$ sublevel.

  • The $d$ sublevel.

  • The $f$ sublevel, consisting of seven $f$ orbitals.

• Levels $n=5, 6, 7$: Beyond the fourth principal energy level, the availability of sublevels remains the same as in $n=4$. All four types—$s, p, d,$ and $f$—are available as options for electrons at these higher levels.

• Numerical Designations: The number appearing in front of a sublevel (e.g., the $1$ in $1s$ or the $2$ in $2p$) does not indicate quantity; rather, it indicates which principal energy level the electrons are occupying.

Quantum Mechanics, Energy, and Orbital Definitions

• Quantized Energy States: Research into the line spectrum of light revealed that electrons cannot possess any arbitrary energy value; only specific, "allowed" energies are possible. These energy values are fundamentally tied to the wavelength and frequency of light. In the visible realm, these specific energies appear as distinct bands of color.

• Definition of an Orbital: An orbital is defined as a three-dimensional region or area where an electron is most likely to be found. It does not define an exact path but a high-probability location.

• Quantum Number Analogy: Quantum numbers act as a way to narrow down the probable location of an electron, similar to an address.

  • Scenario: If someone were looking for a student on a Monday or Wednesday between $4:30$ and $7:30$, they would narrow the search down by:

    1. County: Butler County.

    2. Township: Penn Township.

    3. Address: College Drive.

    4. Specific Building.

    5. Specific Floor.

    6. Specific Classroom.

  • Probability vs. Certainty: Just as the student might not be in that classroom $100\text{\%}$ of the time, an orbital represents where the probability of finding an electron goes up significantly during a specific state, though it is not a absolute certainty.

• Electron Repulsion: Electrons possess a negative charge of $-1$ and naturally repel one another. Because "like charges repel," they try to spread out as far as possible within a confined space.

  • Volume and Space: In smaller volumes, such as the first principal energy level, there is only room for one $s$ orbital. Larger volumes (higher $n$ levels) can accommodate more types and quantities of orbitals, much like a large laboratory building with many rooms vs. a one-room schoolhouse.

Rules and Principles of Orbital Diagrams

• Orbital Diagram Notation: An orbital is represented graphically by a box. Electrons are represented by up and down arrows within those boxes.

• The Energy Axis: Orbital diagrams are typically drawn with a vertical axis where height corresponds to energy; as you move up the axis, energy increases.

• The Hydrogen Atom Exception: In a hydrogen atom (which only has one electron), all sublevels within the same principal energy level (e.g., $2s$ and $2p$) share the same energy.

• Multi-electron Atoms: In atoms with more than one electron, sublevels within the same principal energy level have different energies. The general order of increasing energy is:     s < p < d < f

• The Aufbau Principle: Electrons must occupy the lowest energy orbital available first before moving to higher energy levels (e.g., filling $1s$ before $2s$).

• The Pauli Exclusion Principle: A maximum of two electrons can occupy any single orbital. To occupy the same orbital, they must have opposite spins, represented by one arrow pointing up and one arrow pointing down.

  • Spin Logic: Like the Earth spinning on its axis while orbiting the sun, electrons spin on their own axis. Opposite spins (clockwise and counter-clockwise) are required for two electrons to occupy the same orbital space due to energy considerations.

• Hund’s Rule: When electrons occupy orbitals of identical energy (the same sublevel), they will half-fill each orbital with parallel spins (all arrows pointing up) before any orbital receives a second electron.

  • Kindergarten Analogy: To lower the "energy" in a classroom where children are biting or pinching each other, a teacher separates them into different areas. Similarly, electrons prefer to be in separate orbitals of the same energy to minimize repulsion.

Electron Configuration and the Diagonal Rule

• Configuration Notation: This is a simplified form of an orbital diagram that eliminates boxes and arrows. It uses superscripts to denote the number of electrons in a sublevel (e.g., $1s^2$).

• The Diagonal Rule (Page 280 in Textbook): To determine the filling order, one can list sublevels and follow diagonal paths:

  1. $1s$

  2. $2s$

  3. $2p, 3s$

  4. $3p, 4s$

  5. $3d, 4p, 5s$

  6. $4d, 5p, 6s$

  7. $4f, 5d, 6p, 7s$

  • Energy Considerations: The $4s$ orbital is slightly lower in energy than the $3d$ orbital. Therefore, the $4s$ fills before the $3d$ despite being in a higher principal energy level.

• Example: Carbon ($C$):

  • Atomic Number: $6$ ($6$ protons, $6$ electrons).

  • Configuration: $1s^2 2s^2 2p^2$.

  • In the $2p$ sublevel, the two electrons occupy two separate boxes (orbitals) with parallel spins according to Hund's Rule.

• Example: Silicon ($Si$):

  • Atomic Number: $14$ ($14$ electrons).

  • Configuration: $1s^2 2s^2 2p^6 3s^2 3p^2$.

Geography of the Periodic Table

• Block Divisions:

  • $s$-block: Two elements wide (Groups $1a$ and $2a$), representing the $2$ electrons that fill an $s$ sublevel. Helium ($He$) is functionally part of this block for configuration purposes.

  • $p$-block: Six elements wide, representing the $6$ electrons that fill a $p$ sublevel ($3$ orbitals $\times 2$ electrons).

  • $d$-block: Ten elements wide (transition metals), representing the $10$ electrons that fill a $d$ sublevel ($5$ orbitals $\times 2$ electrons).

  • $f$-block: Fourteen elements wide (lanthanides and actinides), representing the $14$ electrons that fill an $f$ sublevel ($7$ orbitals $\times 2$ electrons).

• Example: Bromine ($Br$):

  • To find the configuration, work through the table until reaching Bromine (Atomic Number $35$):

  • $1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 4s^2, 3d^{10}, 4p^5$.

  • Rule for d-block: When entering the $d$-block, fall back one principal energy level ($n-1$). After the $d$-block, revert back to the original level for the $p$-block.

• Example: Manganese ($Mn$):

  • Atomic Number: $25$.

  • Configuration: $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^5$.

• Abbreviated (Noble Gas) Configuration: Locate the previous noble gas, place its symbol in brackets, and write the remaining configuration.

  • Iron ($Fe$): Previous noble gas is Argon ($Ar$). Abbreviated form: $[Ar] 4s^2 3d^6$.

Valence Electrons and Ion Formation

• Definition: Valence electrons are those in the highest principal energy level ($n$ level) that is farthest from the nucleus. These are chemically important and drive reactions and ion formation.

• Core (Inner) Electrons: All electrons not categorized as valence electrons.

• Valence Trends: For $-a$ group elements, the Roman numeral of the group matches the number of valence electrons.

  • Bromine (Group $7a$): $7$ valence electrons ($4s^2$ and $4p^5$).

  • Lead ($Pb$ in Group $4a$): $4$ valence electrons.

  • Alkali Metals (Group $1a$): $1$ valence electron.

• Ion Stability (Octet Rule): Atoms lose or gain electrons to achieve the same electron configuration as the nearest noble gas (usually having $8$ valence electrons). This state is isoelectronic with the noble gas.

  • Cations: Group $1a$ loses $1$ electron to become $+1$. Group $2a$ loses $2$ to become $+2$.

  • Anions: Group $7a$ (halogens) gain $1$ electron (becoming $p^6$) to reach a $-1$ charge.

  • Isoelectronic Example: The Sodium cation ($Na^+$) and the Oxide anion ($O^{2-}$) both have the configuration $1s^2 2s^2 2p^6$, which is identical to Neon ($Ne$).

Periodic Trends

• Reactivity of Metals: Historically defined by how easily a metal loses its valence electrons.

  • Trend: Reactivity increases as you move down a group.

  • Reasoning: For Potassium ($K$) compared to Sodium ($Na$), the valence electron is in the $n=4$ level rather than $n=3$. Being farther from the nucleus and shielded by more inner core electrons ($18$ for $K$ vs $10$ for $Na$), the nucleus has less control, allowing the electron to be removed more easily.

• Ionization Energy (IE): The quantity of energy required to remove a valence electron from an atom in its ground state.

  • Trend: Ionization Energy decreases as you move down a group.

  • Parent/Child Analogy: A parent (nucleus) has more control over a child (electron) if they live in the same town. If the child lives $3,000\text{ miles}$ away, the parent's influence is much weaker.

• Atomic Size/Radius: Measured as the distance from the center of the nucleus to the boundary of the electron cloud. Trends and horizontal period changes will be discussed in further detail at the next session.

Questions & Discussion

• Wednesday Lab Notice: Students should bring their textbooks (physical or e-book) for the Lewis Lab on Wednesday. Tables in Chapter 8 are essential for the Lewis dot structure exercises.

• Exam Review:

  • Scores: The instructor inquired if students achieved their desired scores.

  • Study Habits: A student noted they should have read questions more carefully to avoid errors on known material.

  • Homework Correlation: Students confirmed that doing the end-of-chapter homework for Chapters 1 and 2 was helpful, as the test questions mirrored the homework, though with fewer math problems.

• Future Schedule: Chapter 7 will be finalized on Wednesday, and a significant portion of Chapter 8 will be covered during the lab. A test on Chapters 8 and 16 is expected soon after, followed by the midterm exam.