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Survey of the Hydrogenic Atomic Orbitals | OpenStax Chemistry 2e 6.3

Overview of Atomic Orbitals

  • The video surveys atomic orbitals of the hydrogen atom.

  • Focus on the shapes of orbitals and their relative energies.

  • Establish a scaffold for understanding heavy atoms' atomic orbitals.

Quantum Numbers in Atomic Orbitals

Description of Atomic Orbitals

  • Solutions to the Schrödinger equation for hydrogen described using quantum numbers.

Principal Quantum Number (n)

  • Similar to energy levels in the Bohr model; represents the shell of the electron.

  • Values: n = 1, 2, 3, etc.

Shells and Subshells

  • Shells are represented by circular orbits (Bohr model) highlighted in blue.

  • Within each shell, multiple containers (subshells) exist for electrons.

Metaphors for Understanding

  • Onion Metaphor: Layers of an atom where electrons occupy various quantum levels.

  • Building Metaphor: A building where each floor represents a shell with different rooms (subshells).

Quantum Numbers and Electron Organization

Angular Momentum Quantum Number (l)

  • Represents the shape of the probability distribution in a shell.

  • Determines the subshell shape: s, p, d, f, etc.

Magnetic Quantum Number (m_l)

  • Describes the orientation of subshells in space.

  • Depends on the value of l; allows for various orientations in a given subshell.

Spin Quantum Number (m_s)

  • Represents the intrinsic spin of electrons (either spin up or spin down).

  • Important for understanding magnetic properties.

Atomic Orbitals: S, P, D, and F Orbitals

S Orbitals

  • Defined by l = 0; represented as ns (colors indicate wave function signs).

  • Spherical shape; regions where the electron is likely to be found.

  • Number of radial nodes depends on the principal quantum number:

    • 1s: zero nodes

    • 2s: one node

    • 3s: two nodes

  • General formula for nodes: Number of Radial Nodes = n - l - 1.

P Orbitals

  • Found in n = 2 shell and higher (l = 1).

  • Directional dumbbell shape; three orbitals per subshell (m_l values: -1, 0, +1).

D Orbitals

  • More complex with l = 2; five orbitals per subshell (m_l values: -2, -1, 0, +1, +2).

  • Cloverleaf shapes with two-dimensional characteristics.

F Orbitals

  • Even more complex shapes not detailed in the transcript.

Summary

  • Quantum numbers provide a comprehensive address for electrons in atoms.

  • Each electron is described using a set of four quantum numbers (n, l, m_l, m_s).

  • Shells and subshells of the atom can be visualized through metaphors, enhancing understanding of atomic structure.