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Quantum Numbers and Atomic Orbitals Overview

Oct 20, 2024

Lecture on Quantum Numbers and Atomic Orbitals

Introduction

  • Topics: Atomic orbitals and quantum numbers.
  • Focus on s, p, d orbitals, and briefly on f orbitals.
  • Wave functions as solutions to the Schrödinger equation.
  • Four quantum numbers: n, l, m<sub>l</sub>, m<sub>s</sub>
  • Quantum numbers describe an electron's address in an atom.

Atomic Orbitals

  • S Orbitals: Spherical shape.
  • P Orbitals: Dumbbell-shaped, three-dimensional.
  • D Orbitals: Four-leaf clover or toroidal shapes.
    • Types: d<sub>xy</sub>, d<sub>xz</sub>, d<sub>yz</sub>, d<sub>x²-y²</sub>, d<sub>z²</sub>.
  • F Orbitals: Complex shapes, typically not illustrated.
  • Orbital Capacity: Each orbital can hold a maximum of 2 electrons.

Orbital Shapes and Nodes

  • Orbitals are solutions to 3D mathematical equations (wave functions).
  • Higher shell orbitals (2s, 3s, etc.) have nodes.
  • S orbitals: First shell, P orbitals: Second shell, D orbitals: Third shell.
  • Higher shells add complexity (e.g., radial nodes).

Schrödinger Equation

  • Describes 3D orbitals, unlike Bohr’s 2D orbits.
  • Electrons exhibit wave-like properties.

Quantum Numbers

  • Principal Quantum Number (n)
    • Indicates shell number (1st, 2nd, etc.).
    • Range: 1 to infinity.
  • Azimuthal Quantum Number (l)
    • Indicates subshell type (s, p, d, f).
    • Values: 0 (s), 1 (p), 2 (d), 3 (f).
    • Range: 0 to n-1.
  • Magnetic Quantum Number (m<sub>l</sub>)
    • Specifies orbital within a subshell.
    • Range: -l to +l.
  • Spin Quantum Number (m<sub>s</sub>)
    • Describes electron spin.
    • Values: +1/2 or -1/2.

Electron Configuration and Quantum Numbers

  • n, l, m<sub>l</sub>, m<sub>s</sub> describe an electron’s location.
  • Pauli Exclusion Principle: No two electrons can have the same set of quantum numbers.

Orbital Filling Diagram

  • Lowest energy orbital: 1s.
  • Higher shells (2s, 3p, 3d, etc.) represent increasing energy levels.
  • Multi-electron systems have split energy levels within shells.

Applications and Problem-Solving

  • Identifying possible quantum number sets for given orbitals.
  • Evaluating quantum number validity in multiple-choice questions.

Conclusion

  • Quantum numbers provide a code for electron locations.
  • Upcoming lessons will explore electron configurations.
  • Additional resources available for general chemistry practice.

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