Electron Configurations and Quantum Theory: Study Notes

Electron Configurations and Quantum Theory

Quantum Theory Summary

Quantum theory describes the behavior of matter and energy at the atomic and subatomic levels. It introduces concepts that differ significantly from classical physics.

• Quantization of Energy: Energy is absorbed or emitted by atoms only in discrete, quantized amounts, not in a continuous flow.

• Wave-Particle Duality: Particles such as electrons exhibit both wave-like and particle-like properties, especially at the molecular, atomic, and subatomic scales.

• Probabilistic Nature: The properties of particles at these scales are described using probabilities rather than certainties, reflecting the inherent uncertainty in quantum systems.

Electron Orbitals

Electrons in atoms occupy regions of space called orbitals, which are defined by mathematical functions that describe the probability of finding an electron in a particular region around the nucleus.

• Principal Level (Shell): Indicates the relative distance of the orbital from the nucleus and its relative energy. Denoted by the principal quantum number n (e.g., n = 1, 2, 3...).

• Sublevel (Subshell): Refers to the shape of the orbital, designated as s, p, d, or f.

• Number of Orbitals: Each sublevel contains a specific number of orbitals:

  • s: 1 orbital

  • p: 3 orbitals

  • d: 5 orbitals

  • f: 7 orbitals

Example: The 2p sublevel contains three orbitals (2px, 2py, 2pz), each capable of holding two electrons.

Quantum Numbers

Quantum numbers uniquely identify the state of an electron in an atom. The spin quantum number (ms) designates the spin of the electron.

• Spin Quantum Number (ms): Can have values of $+\frac{1}{2}$ or $-\frac{1}{2}$, representing the two possible spin orientations of an electron.

Additional info: Other quantum numbers include the principal quantum number (n), angular momentum quantum number (l), and magnetic quantum number (ml).

Pauli Exclusion Principle

The Pauli Exclusion Principle is a fundamental rule in quantum mechanics that governs the arrangement of electrons in atoms.

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

• A maximum of two electrons can occupy a given orbital.

• If two electrons occupy the same orbital, they must have opposite spins (one with $+\frac{1}{2}$, one with $-\frac{1}{2}$).

Electron Configurations

Electron configuration describes the arrangement of electrons in an atom's orbitals. Electrons fill orbitals in order of increasing energy, following the Aufbau principle.

• Order of Filling: Orbitals are filled in the order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, etc.

• Example Table: Order of Orbital Filling

Energy Level	Sublevels
1	1s
2	2s, 2p
3	3s, 3p, 3d
4	4s, 4p, 4d, 4f

Example: The electron configuration of boron (B, atomic number 5) is $1s^2 2s^2 2p^1$.

Examples of Electron Configurations

• Boron (B): $1s^2 2s^2 2p^1$

• Oxygen (O): $1s^2 2s^2 2p^4$

Additional info: The superscripts indicate the number of electrons in each sublevel.

Orbital Diagrams and Hund's Rule

Orbital diagrams visually represent the arrangement of electrons in orbitals. Hund's Rule states that electrons occupy degenerate orbitals singly before pairing up, maximizing total electron spin in the ground state.

• Example: For oxygen (O), the 2p orbitals are filled as follows: one electron in each of the three 2p orbitals before any pairing occurs, then the fourth electron pairs up in one of the 2p orbitals.

Unpaired Electrons

The number of unpaired electrons in an atom can be determined from its electron configuration and orbital diagram.

• Chlorine (Cl): $1s^2 2s^2 2p^6 3s^2 3p^5$ → 1 unpaired electron in the 3p sublevel.

• Carbon (C): $1s^2 2s^2 2p^2$ → 2 unpaired electrons in the 2p sublevel.

Abbreviated Electron Configurations (Noble-Gas Notation)

To simplify electron configurations, the configuration of the nearest noble gas is used as a starting point, followed by the remaining electrons.

• Example: Sodium (Na, atomic number 11): [Ne] $3s^1$

• Alkali Metals: All have a single electron in an s orbital beyond the noble gas core.

• Alkaline-Earth Metals: All have two electrons in an s orbital beyond the noble gas core.

• Halogens: All have five electrons in the p sublevel beyond the noble gas core.

• Chalcogens: All have four electrons in the p sublevel beyond the noble gas core.

Element	Abbreviated Configuration
Na	[Ne] $3s^1$
Mg	[Ne] $3s^2$
Cl	[Ne] $3s^2 3p^5$
O	[He] $2s^2 2p^4$

Valence Electrons

Valence electrons are the outermost electrons of an atom and are important in determining chemical reactivity and bonding.

• Example: Sulfur (S, atomic number 16): $1s^2 2s^2 2p^6 3s^2 3p^4$ → 6 valence electrons (those in the 3s and 3p sublevels).

• Bromine (Br, atomic number 35): $[Ar] 4s^2 3d^{10} 4p^5$ → 7 valence electrons (those in the 4s and 4p sublevels).

Diamagnetism and Paramagnetism

Atoms or ions are classified as diamagnetic if all electrons are paired, and paramagnetic if they have one or more unpaired electrons.

• Example: Cobalt (Co, atomic number 27): $[Ar] 4s^2 3d^7$ → Paramagnetic (has unpaired electrons in the 3d sublevel).

Summary Table: Electron Configuration and Properties

Element	Electron Configuration	Unpaired Electrons	Valence Electrons	Magnetism
C	$1s^2 2s^2 2p^2$	2	4	Paramagnetic
O	$1s^2 2s^2 2p^4$	2	6	Paramagnetic
Cl	$1s^2 2s^2 2p^6 3s^2 3p^5$	1	7	Paramagnetic
Na	$1s^2 2s^2 2p^6 3s^1$	1	1	Paramagnetic
Mg	$1s^2 2s^2 2p^6 3s^2$	0	2	Diamagnetic

Additional info: The above tables and explanations provide a comprehensive overview of electron configurations, quantum numbers, and related properties, suitable for exam preparation in General Chemistry.