The Quantum mechanical Model

Describes atoms using principles of quantum mechanics rather than classical physics

• Electrons are described by wave functions (Ψ) that determine their probabilities of being found in various regions around the nucleus.
• Electrons occupy discrete energy levels or shells (n = 1, 2, 3, …).
• Orbitals, described by quantum numbers, are regions where electrons are likely to be found.
• Provides a framework for understanding electron configurations, periodic properties, and chemical bonding.

Heisenberg Uncertainty Principle

• States a fundamental limit in quantum mechanics regarding the precision with which certain pairs of physical properties of a particle can be known simultaneously

Key Points:

• It is impossible to simultaneously determine the exact position (Δx) and momentum (Δp) of a particle with arbitrary precision.
• Impacts our understanding of the wave-particle duality and the limitations of measurement in quantum systems.

Quantum Numbers

• Quantum numbers are used to describe the unique quantum state of each electron in an atom.

Quantum Numbers:

• Principal Quantum Number (n): Determines the energy level or shell of the electron.
• Angular Momentum Quantum Number (l): Specifies the shape of the orbital.
• Magnetic Quantum Number (ml): Describes the orientation of the orbital in space.
• Spin Quantum Number (ms): Represents the spin of the electron.

Roles:

• Define the size( energy ), shape, orientation, and energy of atomic orbitals. & spin of electron.

Shapes of Atomic Orbitals:

• Atomic orbitals are regions of space around the nucleus where electrons are likely to be found.

Types of Orbitals:

• s Orbital: Spherical in shape, centered around the nucleus.
• p Orbital: Dumbbell-shaped with three orientations (px, py, pz) perpendicular to each other.
• d Orbital: Complex shapes with five orientations (dxy, dxz, dyz, dx²-y², dz²).
• f Orbital: More complex shapes with seven orientations.

Determined by:

• Angular momentum quantum number (l) dictates the shape and number of orbitals within each subshell.

Generally

• The quantum mechanical model of the atom utilizes wave functions to describe electrons in discrete energy levels, governed by quantum numbers that define orbital shapes and orientations. The Heisenberg Uncertainty Principle imposes limits on the precision of measuring pairs of complementary properties. Quantum numbers (n, l, ml, ms) specify the quantum state of electrons, influencing their spatial distribution within atomic orbitals, each characterized by distinct shapes (s, p, d, f). Together, these concepts form the foundation of modern atomic theory, explaining the structure, behavior, and properties of atoms and molecules.