CHEM Chapter 7

Chapter 7: Quantum Theory and Atomic Structure

7.1 The Nature of Light

• Electromagnetic Radiation: Light is a type of electromagnetic radiation characterized by its wave properties.

  • Key Variables:

    • Frequency (ν): Measured in cycles per second.

    • Wavelength (λ): Distance a wave travels during one cycle.

    • Speed (c): Constant for light in a vacuum, c = 3.00 x 10^8 m/s.

    • Amplitude: Height of a wave crest or depth of a trough, affecting brightness.

  • Relationship: Frequency and wavelength have an inverse relationship (c = ν × λ).

7.2 Atomic Spectra

• Emission Spectrum: Created when electrically excited hydrogen atoms emit light, which is dispersed through a prism, producing a line spectrum.

• Hydrogen Spectrum:

  • Specific wavelengths correspond to features of hydrogen's atomic structure but can be generalized via the Rydberg equation.

  • Major wavelengths include: 434.1 nm, 410.1 nm, 486.1 nm, 656.3 nm.

• Bohr Model of Hydrogen Atom:

  • Posits quantized energy levels (stationary states) for electrons in defined orbits around the nucleus.

  • Electrons absorb/emitte photons to transition between these levels.

7.3 The Wave-Particle Duality of Matter and Energy

• Fundamental Concept: Matter and energy exhibit both wave-like and particle-like properties.

  • de Broglie Wavelength: The wavelength associated with a particle is given by λ = h / (mu), where h is Planck's constant, m is mass, and u is speed.

• Heisenberg’s Uncertainty Principle: It is impossible to simultaneously know the exact position and momentum of a particle.

7.4 The Quantum-Mechanical Model of the Atom

• Atomic Orbitals: Regions around the nucleus defined by quantum numbers, indicating the probability of finding an electron.

  • Quantum Numbers:

    • Principal Quantum Number (n): Positive integers representing energy levels.

    • Angular Momentum Quantum Number (ℓ): Defines orbital shape (s, p, d, f).

    • Magnetic Quantum Number (mℓ): Indicates spatial orientation of the orbital.

    • Spin Quantum Number (ms): Represents electron spin (± 1/2).

• Pauli’s Exclusion Principle: No two electrons in the same atom can have identical sets of quantum numbers; thus, an atomic orbital can hold up to two electrons with opposite spins.

Additional Concepts

• Energy Relationships:

  • Energy of a photon (E) is related to frequency (E = hν) and wavelength (E = hc/λ).

  • Changes in electron energy levels correspond to light emission or absorption at specific wavelengths.

Practice Calculations

• Practice with calculating frequency from given wavelengths and energy in Joules from photon counts.

• Use the mathematical relationships between wavelength, frequency, and energy to solve problems regarding electron transitions in atoms.

Summary of Quantum Numbers

• n: Principal quantum number, indicating energy and size.

• ℓ: Angular momentum quantum number, indicating shape.

• mℓ: Magnetic quantum number, indicating orientation.

• ms: Spin quantum number, indicating spin direction.