Understanding Quantum Mechanics and Periodic Trends

Announcements on Test Number Three

  • Lewis Structures:

    • Lewis structure will not be on Test Number Three due to insufficient coverage in class.

    • If there were plans to include it, students need to be aware it will not be assessed.

Quantum Numbers

  • Quantum Numbers Overview:

    • The quantum number is crucial for specifying the properties of orbitals.

    • Abbreviated as n, l, ml, and ms.

  • Four Quantum Numbers Explained:

    1. n (Principal Quantum Number):

      • Must be a positive integer: $n
        eq 0$

      • Possible values: 1, 2, 3, 4, 5, …

      • Indicates the energy level and average distance of electrons from the nucleus.

    2. l (Azimuthal Quantum Number):

      • Must satisfy: $0 ext{ to } (n-1)$

      • Indicates the subshell or shape of the orbital.

      • Possible values depend upon n (e.g., if $n=2$, then $l=0 ext{ or } 1$).

    3. m_l (Magnetic Quantum Number):

      • Can have values: $-l ext{ to } +l$

      • Determines orientation of the orbital.

    4. m_s (Spin Quantum Number):

      • Possible values: $+ rac{1}{2}$ or $- rac{1}{2}$

      • Indicates the spin direction of the electron.

      • Note: m_s is often easiest to identify.

Rules of Quantum Mechanics

  • Key Rules for Quantum Numbers:

    • No two electrons in an atom may have the same set of four quantum numbers (Pauli exclusion principle).

    • Make sure to include commas between quantum numbers in notation.

Electron Configuration

  • Notation for Last Electron Added:

    • Example: For sulfur with 16 electrons, the last electron is in the 3p orbital.

    • Sulfur's Electron Configuration: 1s² 2s² 2p⁶ 3s² 3p⁴

    • Total: Ensure to track all contributions to electron configuration through periodic table.

Energy of Orbitals

  • Order of Filling Orbitals:

    • Orbitals filled based on energy levels, using the Aufbau principle.

    • Filling Order:

      • 1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d …

      • Note: 4s is filled before 3d despite 3d being a lower number.

Heisenberg's Uncertainty Principle

  • Stated that it is impossible to know simultaneously both the exact position and momentum of a particle; thus, the position and velocity cannot be accurately known.

Hund's Rule

  • Each orbital in a given subshell must be singly occupied before any orbital is doubly occupied, to minimize electron repulsion.

Pauli Exclusion Principle

  • No two electrons in an atom can have the same four quantum numbers.

Electron and Ion Behaviors

  • Ionization Process:

    • During ion formation, the outermost electrons (farthest from the nucleus) are removed first.

    • Metals tend to lose electrons, forming cations; conversely, nonmetals typically gain electrons, becoming anions.

Periodic Trends Related to Radii and Ionization Energy

Atomic and Ionic Radius

  • Atomic Radius: Increases down a group and decreases across a period.

  • Ionic Radius:

    • Anions are larger than their neutral atoms (due to added electron shielding).

    • Cations are smaller than their neutral atoms (due to loss of electrons).

Ionization Energy

  • Definition: The amount of energy required to remove an electron from an atom.

  • Observations:

    • Ionization energy increases across a period and decreases down a group.

    • Noble gases exhibit the highest ionization energies due to stable electron configurations.

Electronegativity

  • Electronegativity is a measure of the tendency of an atom to attract a bonding pair of electrons.

  • Most electronegative elements are found in the upper right of the periodic table (e.g., F, O, N, and Cl).

Diagrams and Electron Notation

  • Core vs. Valence Electrons:

    • Core Electrons: Electrons in inner shells, close to the nucleus.

    • Valence Electrons: Electrons in the outermost shell, important for bonding and chemical behavior.

  • SPDF Notation Example:

    • Carbon: 1s² 2s² 2p² or abbreviated as [He] 2s² 2p².

    • Calcium: [Ar] 4s².

Review and Assessments

Common Assessment Focus for Exam:

  • SPDF Notation for elements (short form preferably).

  • Ability to calculate electron configurations upon ion formation.

  • Practice Problems: Course materials suggest performing exercises to enhance understanding of valence electrons and trends in ionization energy.

  • Create note cards for quick quizzes and definitions to aid review between classes.

  • Be aware of core and valence distinctions as they are pivotal for Lewis structures, expected in future assessments.

  • Final Study Notes: Revision sheets and previous quizzes available for student review before exams.