Atomic Structure and Quantum Numbers

Atomic Structure

• Atoms consist of a nucleus containing protons (positive charge) and neutrons (neutral charge), surrounded by orbiting electrons (negative charge).

Models of the Atom

• Bohr Model (1913): Electrons orbit the nucleus in fixed orbits/shells with specific energy levels.
• Quantum Mechanical Model: Electrons exist in orbitals, which are regions of high probability around the nucleus.

Quantum Numbers

• Each electron is described by four quantum numbers.
• Principal Quantum Number (n): Indicates the energy level or shell.
• Azimuthal Quantum Number (l): Describes the shape of the orbital (s, p, d, f).
• Magnetic Quantum Number (ml): Specifies the orientation of the orbital in space.
• Spin Quantum Number (ms): Indicates the intrinsic angular momentum (+1/2 or -1/2).

Heisenberg Uncertainty Principle

• Position and momentum of a particle cannot both be precisely known.
• ΔxΔp ≥ ħ/2, where Δx is uncertainty in position, Δp is uncertainty in momentum, and ħ is the reduced Planck constant.

Wave-Particle Duality

• De Broglie Hypothesis (1924): Matter exhibits wave-like properties.
• Wavelength (λ) relates to momentum (p) by λ = h/p = h/mv, where h is Planck's constant, m is mass, and v is velocity.

Quantum Mechanics

• Schrödinger Equation: Describes how the quantum state of a system changes over time.
• Time-dependent Schrödinger equation: iħ ∂Ψ(r, t)/∂t = ĤΨ(r, t).
• Time-independent Schrödinger equation: EΨ(r) = ĤΨ(r), where Ψ is the wave function, Ĥ is the Hamiltonian operator, and E is the energy.

Quantum Numbers Table

Atomic Orbitals

• s orbitals: Spherical shape.
• p orbitals: Dumbbell shape.
• d orbitals: More complex shapes.
• f orbitals: Even more complex shapes.

Electron Configuration

• Arrangement of electrons in an atom's orbitals.
• Follows the Aufbau principle, Hund's rule, and the Pauli exclusion principle.