CHAPTER 7-3
Chapter 7: Quantum Theory and the Electronic Structure of Atoms
Atomic Structure
Atom Components:
Nucleus: Contains nucleons (Protons: +, Neutrons: 0)
Electron Cloud: Contains electrons (-)
Electromagnetic Radiation: Essential to understanding electronic structure.
Properties of Waves
Wavelength (λ):
Distance between adjacent minima or maxima.
Frequency (ν):
Number of waves passing a point per unit of time.
Relationship: Longer wavelength correlates with lower frequency; shorter wavelength with higher frequency.
Speed of Light (c): 3.00 x 10^8 m/s, described by equation c = λν.
Types of Electromagnetic Radiation
Gamma Rays: Shortest wavelength, highest frequency.
Radio Waves: Longest wavelength, lowest frequency.
Planck’s Quantum Theory: Energy (E) is proportional to frequency (ν). E = hν (h = Planck’s constant: 6.626 x 10^−34 J·s).
Work Function and Photon Energy
Work Function (W): Minimum energy needed to eject an electron from an atom.
Calculation for Lithium: W = 283 kJ/mol → Energy of one photon = 4.70 x 10^-19 J.
Minimum frequency to eject electron: ν = 7.09 x 10^14 s^-1.
Total Energy Equation: E = hν = W + KE (where KE is kinetic energy).
Bohr’s Theory of the Hydrogen Atom
Key Assumptions:
Electrons occupy specific orbits/energies.
Allowed energies are not radiated away.
Energy is absorbed/emitted only during transitions between allowed states (E = hν).
Energy levels in hydrogen: E_n = -RH (1/n²).
Quantum Series
Emission Spectrum: Unique fingerprint of emitted energy.
Rydberg Constant (RH): 2.18 x 10^-18 J.
Transition Series:
Lyman series: n_final = 1
Balmer series: n_final = 2
Paschen series: n_final = 3
Photon wavelength calculation example for transition in Balmer series yielding λ = 434 nm.
Wave Nature of Matter
Louis de Broglie Hypothesis: Matter exhibits wave properties, λ = h/mv.
Example Calculation: λ for electron at 68 m/s yields λ = 1.1 x 10^-5 m.
Uncertainty Principle
Heisenberg’s Principle: Uncertainty in position (Δx) and momentum (Δmv) is expressed as ΔxΔmv ≥ h/4π.
Example calculation for a honey bee: Δx ≥ 7.75 x 10^-31 m.
Quantum Mechanics
Wave Function (ψ): Describes statistical likelihood of an electron's position.
Solving the wave equation gives wave functions/orbitals characterized by quantum numbers.
Quantum Numbers
Principal Quantum Number (n): Indicates energy level.
Angular Momentum Quantum Number (l): Defines orbital shape.
Magnetic Quantum Number (ml): Describes orientation of orbital.
Spin Quantum Number (ms): Indicates the spin of electrons (+1/2 or -1/2).
Electron Configurations
Pauli Exclusion Principle: No two electrons may have identical quantum numbers;
Organization of electrons: lowest energy configuration is stable. Examples:
Lithium (Li): 1s² 2s¹
Carbon (C): 1s² 2s² 2p²
Notable exceptions: Chromium (Cr) and Copper (Cu) configurations.
Orbital Diagrams
Each box represents an orbital; half-arrows represent electrons and indicate spin direction.
Hund’s Rule: Maximize unpaired electrons in degenerate orbitals for lowest energy.
Aufbau Principle: Filling of orbitals starts from lowest energy to highest.
Example: Mn is paramagnetic (unpaired electrons) while Zn is diamagnetic (paired electrons).
Speed of Light: c = λν
Energy of a photon: E = hν (where h = Planck’s constant: 6.626 x 10^−34 J·s)
Work Function: W = 283 kJ/mol → Energy of one photon = 4.70 x 10^-19 J
Minimum frequency to eject electron: ν = 7.09 x 10^14 s^-1
Total Energy Equation: E = hν = W + KE
Energy levels in hydrogen: E_n = -RH (1/n²)
Rydberg Constant: RH = 2.18 x 10^-18 J
Wave Nature of Matter: λ = h/mv
Uncertainty Principle: ΔxΔmv ≥ h/4π
Principal Quantum Number: n
Angular Momentum Quantum Number: l
Magnetic Quantum Number: ml
Spin Quantum Number: ms