In-Depth Notes on Orbitals, Electron Configurations, and Periodic Properties

Orbitals

• Definition: Electrons occupy orbitals, which are regions of space where they're likely to be found.
• Wavefunctions: Each orbital has a unique wavefunction affecting its size, shape, and orientation.
• Principal Quantum Number (n): Indicates the size of the orbital; larger n means larger size.
  • n = 1: 1 type of orbital - s
  • n = 2: 2 types of orbitals - s and p
  • n = 3: 3 types of orbitals - s, p, and d
  • n = 4: 4 types of orbitals - s, p, d, and f

Probability Densities

• Radial Probability: The probability of being at a distance r from the nucleus decreases exponentially.
• Surface Area Growth: Surface area of a sphere grows as r^2 .
• 1s Maximum: Occurs at 52.9 pm, equivalent to the radius of the n=1 Bohr orbit.

Nodes

• Definition: Nodes are regions where the wavefunction changes sign, leading to zero probability of finding the electron.
• 1s Max: 52.9 pm | 2s Max: 300 pm | 3s Max: 700 pm
• Orbital Characteristics: All orbitals except for 1s have nodes.

Phase of Orbitals

• Nodal Planes: Occur when the wavefunction sign changes.
• 1s Orbital: No nodes, always positive.
• 2p Orbitals: Have a nodal plane, demonstrating positive on one side and negative on the other.

p Orbitals

• Characteristics: Have a nodal plane through the nucleus; identical shape, differ in orientations (x, y, z).

d and f Orbitals

• d Orbitals: Varying subtypes (e.g., d{xy}, d{yz} ).
• f Orbitals: More complex arrangements, including types like f{x^3-3xy^2}, f{y^3-3x^2} .

Periodic Properties of Elements

• Influence of Quantum Mechanics: Electrons in atoms result in periodic chemical properties. Examples include Dobreiner's triads, Newlands' octaves, and Mendeleev's periodic table.

Electron Configurations

• Each atom's orbitals resemble hydrogen, conforming to the same quantum numbers.
• Ground state configurations vary; for example:
  • Hydrogen: 1s^1
  • Helium: 1s^2
  • Lithium: NOT 1s^3

Pauli Exclusion Principle

• No two electrons can have identical quantum numbers; each has a unique label.
• Max Capacity of Orbitals: Each can hold at most two electrons, with spins denoted as ms = +rac{1}{2} (up) or ms = -rac{1}{2} (down).

Energy Levels in Hydrogen Atom

• Energy mainly reliant on principal quantum number n ; all orbitals in a given shell have the same energy (degenerate).

Multi-electron Atom Orbital Energies

• Electron interactions influence subshell energies:
  • Energy order: 2s < 2p ; 3s < 3p < 3d .
• Degenerate orbitals (same subshell) remain at the same energy even if they differ in orientation.

Coulomb's Law

• Charged particles interact via Coulomb's Law: E = rac{1}{4 imes ext{pi} imes ext{epsilon} imes 0} rac{q1 q2}{r} .
• Repulsion/Attraction: Like charges repel; opposite charges attract. The system's energy becomes much more negative with proximity.

Shielding

• Electron probability densities concentrate within increasingly larger shells as n increases.
• Inner shell electrons shield outer ones from the full charge of the nucleus, allowing for effective nuclear charge calculations: Z_{ ext{eff}} = Z - s .

Effective Nuclear Charge (Z_eff)

• Inner shell electrons imperfectly shield outer shell electrons.
• Simplified shielding model: inner shells shield perfectly, same shell does not shield each other.
• Sample calculations:
  • Li: Z_{ ext{eff}} = 3 - 2 = 1
  • Be: Z_{ ext{eff}} = 4 - 2 = 2

Penetration

• s orbitals have better penetration towards the nucleus over p orbitals, leading to lower energy due to greater effective nuclear charge.

Filling Orbitals

• Filling Rule: Start filling from the lowest energy first, two opposite spins per orbital.
• Hund's Rule: For degenerate orbitals, each gets one electron with parallel spins before pairing.

Valence and Core Electrons

• Electrons are organized in shells (n); outermost shell is called the Valence Shell and inner shells are the Core.
• Valence electrons dictate chemical properties and are essential in bonding interactions.