Untitled Quiz

Quantum Numbers

• Four quantum numbers describe electron movement and trajectories within an atom
• All electrons in an atom combined are described by a wave function that follows the Schrödinger equation
• Each electron in an atom has a unique set of quantum numbers (Pauli Exclusion Principle)

Atomic Orbitals

• Diagrams illustrate shapes and characteristics of atomic orbitals (1s, 2px, 2py, 2pz, 3d)
• Images of quantum numbers like 1s, 2px, 2py, 2pz, 3d, 4f, 15g,2po, 2px, etc
• Different orbitals have different shapes and energy levels (s, p, d, and f)

Schrödinger Equation

• Fundamental equation for quantum mechanics describing submicroscopic phenomena
• Wave equation describes the form of probability waves governing small particle motion
• Specifies how these waves are affected by external influences: ħ²/2m▽²ψ+V(x)=Εψ

Pauli Exclusion Principle

• In a single atom, no two electrons have the same set of quantum numbers (n, l, ml, ms)
• Only two electrons can occupy the same orbital
• These two electrons have opposite spins (antiparallel)

Quantum Numbers: Details

• Principal Quantum Number (n): Describes electron energy level and distance from nucleus (higher n, farther from nucleus, larger atom)
  • Can be any positive integer (n = 1, 2, 3, ...)
• Azimuthal Quantum Number (l): Describes orbital shape and angular momentum
  • Whole numbers from 0 to n-1 (l = 0, 1, 2, 3 ... n-1)
• Magnetic Quantum Number (ml): Describes orientation of orbital in space
  • Integer values from -l to +l, including 0 (ml = -l, -l+1, ..., 0, ..., l-1, l)
• Spin Quantum Number (ms): Describes electron spin
  • ±1/2 (ms = +1/2 or -1/2)

Specific Quantum Number Values

• n values correspond to the principal energy levels (shells)
• Possible values for l, ml, and ms depend on the principal quantum number (n)
• Different orbitals hold different numbers of electrons (s: 2, p: 6, d: 10, f: 14)
• Each subshell has a particular shape (s = sphere, p = dumbbell, d = more complex)
• ml values represent the number of different orbitals
• Subshells in each principal level (with specific letters (s, p, d, and f)
• Possible subshells in a given principal shell (n)

Electron Configurations

• Electron configurations arrangement of electrons in atomic orbitals (1s², 2s², 2p⁵)
• This method helps predict and explain an element's chemical behavior
• Standard configuration notation and orbital notation
• Diagrams show filling of quantum levels

Aufbau Principle

• Electrons occupy lower energy orbitals before higher energy orbitals
• Standard electron configuration rules based on diagrams of atom's energy level filling

Hund's Rule

• Electrons fill degenerate orbitals individually before pairing up
• Helps predict electron configurations for atoms with multiple electrons in the same subshell (e.g., p, d, or f orbitals)

Exceptions to Aufbau Principle

• Some transition metals and heavier elements have electron configurations that deviate from the predicted Aufbau pattern

Questions

• There are three subshells possible for n = 3 (3s, 3p, 3d)
• Number of electrons and orbitals in various subshells(2s, 3p, 4d, 6f)

Key Takeaway

• Quantum mechanics describes the relationship between electron motion and energy in atoms and molecules