6: Quantum Mechanics and Bohr's Model

Lecture Announcements

• Lecture 6 topics: The Wave Nature of Light, Quantized Energy and Photons, Line Spectra and the Bohr Model, The Wave Behavior of Matter, Quantum Mechanics and Atomic Orbitals, Representation of Orbitals, Multielectron Atoms, Electron Configurations, Electron Configurations and the Periodic Table, Effective Nuclear Charge, Sizes of Atoms and Ions, Ionization Energy, Electron Affinity.
• Problem Set 5 due before Exercise 6.
• Problem Set 6 posted on Moodle; due before Exercise 7 next week.
• Study Center hours: Wednesdays 18:00-20:00 in ETA F 5
• Office Hours: Prof. Norris and Brisby, Thursdays 17:00-18:00 in LEE P 210.
• No office hours this week.
• Next week's topics: Basic Concepts of Chemical Bonding and Molecular Geometry and Bonding Theories (Brown Ch. 8 and 9).

Review

• In lecture 5, 2nd Law of Thermodynamics was introduced; spontaneous vs. nonspontaneous processes.
• Reversible, irreversible processes.
• Included isothermal processes, entropy and the 2nd Law of Thermodynamics.
• Boltzmann's equation and microstates.
• 3rd Law of Thermodynamics.
• The Gibbs Free Energy equation: G = H – TS.
• Gibbs Free Energy equation at constant T: ΔG = ΔH – TΔS.
• Standard Gibbs free energies.
• Role of temperature.

Importance of Temperature

• Determining spontaneity of a reaction depends on temperature.
  • ΔH , ΔS, -TAS and the reaction characteristics at specific temperatures.
• Examples of reactions sensitive to temperature changes (with favorable enthalpy and entropy, etc).

Electronic Structure

• Chemistry involves electrons that determine reactivity among atoms.
• Bonds hold atoms and build molecules.

Light

• Light consists of oscillating electromagnetic waves.
• Important parameters: wavelength (λ), frequency (ν), speed of light (c).
• The speed of light is constant at a value of 2.998x10⁸ m/s.
• Color depends on wavelength: 430 nm is blue, 530 nm is green, 630 nm is red.
• Light carries energy in discrete amounts known as photons.
• Energy of a photon (E) = hν where h is Planck's constant (6.626 x 10⁻³⁴ J⋅s). Alternatively = hc/λ.

Light Emitted from Hydrogen Atoms

• Light sources emit white light.
• Hydrogen atoms emit light at specific energies.

Mystery of Hydrogen

• Hydrogen atom emits photons at certain energies explained by an empirical formula called Rydberg Equation.
• Important entity in the Rydberg equation is the Rydberg constant (R) with a value of 1.097x10⁷ m⁻¹.

Bohr Model

• Atomic-scale solar system analogy.
• Electrons occupy specific orbits with quantized energies (En).
• Electrons move between orbits by absorbing or emitting photons with energy (Eph = hv).
  • Equation for change in energy (ΔE) between two electron levels.

Orbital Energies

• Energy levels (En) are calculated using relevant entities
• Electron transitions and photon energy calculations.

Limitations of Bohr Model

• Fails to explain stable orbits of electrons in atoms other than hydrogen.
• Quantum mechanics provides a model to address these limitations.
• Uncertainty principle: The uncertainty in position (Δx), and momentum (Δp), of an electron cannot be simultaneously known. ( Δx. Δp ≥ h/4π.)
• Orbit is fuzzy, thus, referring to the electron cloud model.

Quantum Mechanics

• Quantum mechanics resolves limitations of the Bohr model.
• Explains electron behavior using wavefunctions
• Explains probabilities of finding an electron.
• Describes orbitals by quantum numbers: n, l, ml, and ms

Quantum Numbers

• Orbitals are described by four quantum numbers: n principal quantum number; l angular momentum quantum number; m_l magnetic quantum number (between -l and l); m_s spin quantum number (+1/2 or -1/2).
• The range of values for l and m_l are given with respect to the principal quantum number n.

Summarizing Labels for Atomic Orbitals

• Table summarizing the relationships between n, l, and m_l for different electron shells (up to n = 4).

Visualizing Atomic Orbitals

• Graphical representations of orbitals (s, p, and d).
• Illustrate electron cloud concept and probabilities of finding electrons.

Energy of Atomic Orbitals in Hydrogen

• Hydrogen has one electron.
• Energy levels depend only on the value of n (the principal quantum number).
• Identical values of energy for similar subshells.
• Diagrams illustrating energy levels and orbitals

Last Quantum Number?

• Discusses the spin magnetic quantum number(m_s).
• It has one two values.
• It describes electron spin and its effect on magnetic fields.

Energy of Atomic Orbitals in Multielectron Atoms

• Multielectron atoms have more than one electron.
• Electrons in multielectron atoms fill atomic orbitals with particular quantum numbers according to their energy in order from lowest to highest.
• Pauli Exclusion Principle: No two electrons in the same atom can have the same set of quantum numbers.
• Electron repulsion between electrons within the same shell.
• Ordering of subshells using periodic table.

Order of Subshells

• Determining the order of filling subshells using the periodic table.

Electron Configurations

• Table summarizing electron configurations for lighter elements (Li, Be, B, C, N, and Ne).
• Illustrating Hund's rule for filling atomic orbitals with respect to electron spin.

Valence Electrons

• Valence electrons are those in the outermost electron shell.
• Noble gas core configuration and valence electron configuration.
• Determining electron configurations using periodic table.

Exceptions

• Exceptions to normal electronic configurations due to electron repulsions.

Screening

• Valence electrons feel less than the full nuclear charge due to repulsion from the core electrons.
• Effective nuclear charge (Z_eff) is lower than the nuclear charge (Z).
• Greater distance from the nucleus reduces repulsion, causing the influence of Z to decrease.

Atomic Size

• Methods for defining atomic sizes.
• Trends: increase down a group; decrease across a period.

Ionic Radii

• Estimating ionic sizes from bond lengths in ionic solids.
• Trends: cations smaller than neutral atoms; anions larger than neutral atoms.
• Trends with respect to charge of ion.

Ionization Energy

• Energy needed to remove an electron from an atom.
• Trends: increase across a period; decrease down a group.
• Values of 1st and subsequent ionization energy.

Electron Affinity

• Energy change when an atom gains an electron.
• Trends: generally increase across a period; decrease down a group (except for noble gases).

Summary of Key Concepts

• Key takeaways from the lecture.
• Next topic to be discussed.

Test your knowledge on quantum mechanics, focusing on the s subshell shapes, magnetic quantum numbers, and Bohr's model of the atom. This quiz covers essential concepts such as orbital size, the Rydberg constant, and electron transitions. Perfect for students studying advanced chemistry and physics.