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.