Quantum Mechanics and Atomic Structure Fundamentals

Wave and Energy Fundamentals

• Wavelength (λ) = T (period)
• Frequency (f) = 1 ÷ T (Hz)
• Velocity (V) = S / T = λ / T = λ • f
• Energy of a photon (E) = h • f

Planck's Hypothesis

Energy absorbed or emitted by a body occurs in a discontinuous manner, in the form of tiny amounts of energy called "quanta."

• Quantum of energy: E = h • f
• Planck constant (h) = 6.67 • 10⁻³⁴ J·s
• Total energy (Et) = n • h • f

Bohr Model Postulates

• First Postulate: Electrons orbiting the nucleus are in stationary orbits; they do not emit or absorb energy while in these orbits.
• Second Postulate: Only specific orbits are possible, meeting the condition: L = n • h / 2π (angular momentum).
• Third Postulate: When an electron jumps from a higher to a lower orbital, it emits electromagnetic radiation, known as a photon.

Modern Quantum Mechanics

• De Broglie Hypothesis: Matter (elementary particles) has an associated wave, exhibiting dual nature (particle and wave), as highlighted in electron diffraction.
• Heisenberg Uncertainty Principle: It is impossible to simultaneously determine the exact speed and position of an electron. The product of the uncertainties in position and momentum is ≥ h / 4π.
• Schrödinger Wave Equation: This equation defines the wave energy associated with an electron moving around the nucleus, utilizing four quantum numbers.

Quantum Numbers

• Principal Quantum Number (n): Indicates the energy level (1 to 7).
• Azimuthal Quantum Number (l): Indicates the energy sublevel (0 to n-1). Sublevels: s², p⁶, d¹⁰, f¹⁴.
• Magnetic Quantum Number (m): Indicates the orbital orientation in a magnetic field (values from -l to +l).
• Spin Quantum Number (s): Indicates the direction of electron rotation (+½ or -½).

Atomic Rules

• Pauli Exclusion Principle: No two electrons within a single atom can have the same four quantum numbers.
• Hund's Rule of Maximum Multiplicity: Electrons in the same energy sublevel tend to remain unpaired as much as possible.

Periodic Properties

• Ionization Energy: Energy required to remove an electron from an atom in a gaseous state to form a cation. Increases up a group and to the right across a period.
• Electron Affinity: Energy released when an atom in a gaseous state captures an electron to become an anion (follows the same trend as ionization energy).
• Electronegativity: The tendency of an atom to attract shared electrons within a molecule. Follows the same periodic variation as the previous properties.