Atomic Orbitals and Electron Configurations

Posted on Nov 30, 2024 in Chemistry

1. Atomic Orbitals and Quantum Numbers

Quantum Mechanical Model of the Atom

The quantum mechanical model describes the atom based on fundamental quantum mechanics principles. A key consequence of the uncertainty principle is the impossibility of precisely defining an electron’s trajectory.

Atomic Orbitals and Quantum Numbers

Each atomic orbital is characterized by three quantum numbers and possesses a specific energy level derived from the Schrödinger equation. Placing electrons in these orbitals generates the electron configuration.

Quantum Numbers: n, l, and ml are derived from the wave equation, while ms was introduced later to explain anomalies in the hydrogen spectrum. Each unique combination of these quantum numbers describes a single atomic orbital.

  • Principal Quantum Number (n): Indicates the electron’s energy level (n = 1, 2, 3, 4…). It relates to the electron’s distance from the nucleus and the orbital size. Higher n values correspond to greater distances and larger orbitals.
  • Angular Momentum Quantum Number (l): Indicates the orbital shape and the number and types of sublevels within an energy level (l = 0, 1, 2…). l = 0 corresponds to s orbitals, l = 1 to p orbitals, l = 2 to d orbitals, and l = 3 to f orbitals.
  • Magnetic Quantum Number (ml): Indicates the spatial orientations of an orbital. The allowed values range from –l to +l, indicating the number of orbitals of a specific type within a sublevel (2l + 1 orbitals).
  • Spin Magnetic Quantum Number (ms): Indicates the two possible spin orientations of an electron (ms = -1/2 or +1/2). Electrons behave like tiny magnets.

2. Atomic Orbital Types and Distribution

Each electron shell (energy level) contains sublevels or orbital types (s, p, d, and f). Each value of l determines the number of orbitals of a given type. Each energy level has the same sublevels as the previous level, plus a new type.

Form of Atomic Orbitals

Orbitals lack defined boundaries. However, they are conveniently represented by geometric shapes. S orbitals are spherical, while p, d, and f orbitals have lobes. The orbital’s geometric center coincides with the nucleus. The orbital shape depends on l, while the size depends on n.

  1. Orbital energy and instability increase with n + l.
  2. Orbitals with the same n + l value have the same energy and are called degenerate orbitals. This degeneracy is broken in a magnetic field (Zeeman effect), leading to new energy levels and additional lines in the atomic spectrum.

3. Electron Configurations

An electron configuration describes the distribution of electrons within an atom or ion’s orbitals. The ground state represents the lowest energy configuration. The outermost energy level is the valence shell.

Pauli Exclusion Principle

No two electrons in an atom can have identical sets of four quantum numbers. This means each orbital holds a maximum of two electrons with opposite spins.

Orbital Occupation Diagram

This diagram helps determine the ground-state electron configuration. Hund’s rule states that electrons occupy available orbitals singly with parallel spins before pairing up.

Electron Configurations of Ions

For ions, electrons are added (anions) or removed (cations) based on the charge. For example, O2- has two additional electrons compared to the neutral oxygen atom.

4. Magnetic Properties and Aufbau Principle

Diamagnetism and Paramagnetism

Paramagnetic substances are weakly attracted to magnets, while diamagnetic substances are not.

Aufbau Principle

As you move across the periodic table, each new element adds a proton and an electron, filling orbitals in a specific order. This principle has exceptions, often related to the stability of half-filled or fully filled sublevels.

5. Periodic Table Development

Early Element Groupings

Dobereiner (1829) grouped elements into triads, while Newlands (1866) proposed the Law of Octaves, arranging elements by increasing atomic weight and noting similarities every eighth element.

Periodic Properties

Outer electrons are attracted to the nucleus by electrostatic forces. The strength of these forces depends on the nuclear charge and the distance between the nucleus and the electron.

Atomic and Ionic Radii

Atomic radius is half the distance between adjacent nuclei in a solid metal or molecule. Ionic radius considers the size of ions.

  1. Within a group, the radius increases down due to increasing electron shells.
  2. Within a period, the radius generally decreases to the right due to increasing effective nuclear charge.

Ionization Energy

Ionization energy is the minimum energy needed to remove an electron from a neutral gaseous atom in its ground state. It’s expressed in kJ/mol.

  1. Within a group, ionization energy increases upward.
  2. Within a period, ionization energy generally increases to the right.