Yours

9.5: The Quantum-Mechanical Model- Atoms with Orbitals

CHEM 114: Introductory Chemistry · LibreTexts

0%

Contents

    Text

    Size
    100%
    Theme
    Typeface
    Line length
    Spacing

    From LibreTexts, under CC BY-NC-SA 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    Chapter 1
    1. Chapter 1: The Chemical World
    2. 1.1: The Scope of Chemistry
    3. 1.2: Chemicals Compose Ordinary Things
    4. 1.3: Hypothesis, Theories, and Laws
    5. 1.4: The Scientific Method: How Chemists Think
    6. 1.5: A Beginning Chemist: How to Succeed
     •  Chapter 2
    1. Chapter 2: Measurement and Problem Solving
    2. 2.1: Taking Measurements
    3. 2.2: Scientific Notation: Writing Large and Small Numbers
    4. 2.3: Significant Figures: Writing Numbers to Reflect Precision
    5. 2.4: Significant Figures in Calculations
    6. 2.5: The Basic Units of Measurement
    7. 2.6: Problem Solving and Unit Conversions
    8. 2.7: Solving Multistep Conversion Problems
    9. 2.8: Units Raised to a Power
    10. 2.9: Density
    11. 2.10: Numerical Problem-Solving Strategies and the Solution Map
    12. 2.E: Measurement and Problem Solving (Exercises)
     •  Chapter 3
    1. Chapter 3: Matter and Energy
    2. 3.1: In Your Room
    3. 3.2: What is Matter?
    4. 3.3: Classifying Matter According to Its State: Solid, Liquid, and Gas
    5. 3.4: Classifying Matter According to Its Composition
    6. 3.5: Differences in Matter: Physical and Chemical Properties
    7. 3.6: Changes in Matter: Physical and Chemical Changes
    8. 3.7: Conservation of Mass: There is No New Matter
    9. 3.8: Energy
    10. 3.9: Energy and Chemical and Physical Change
    11. 3.10: Temperature: Random Motion of Molecules and Atoms
    12. 3.11: Temperature Changes: Heat Capacity
    13. 3.12: Energy and Heat Capacity Calculations
    14. 3.E: Exercises
     •  Chapter 4
    1. Chapter 4: Atoms and Elements
    2. 4.1: Experiencing Atoms at Tiburon
    3. 4.2: Indivisible: The Atomic Theory
    4. 4.3: The Nuclear Atom
    5. 4.4: The Properties of Protons, Neutrons, and Electrons
    6. 4.5: Elements: Defined by Their Numbers of Protons
    7. 4.6: Looking for Patterns: The Periodic Law and the Periodic Table
    8. 4.7: Ions: Losing and Gaining Electrons
    9. 4.8: Isotopes: When the Number of Neutrons Varies
    10. 4.9: Atomic Mass: The Average Mass of an Element’s Atoms
      •  Chapter 5
    1. Chapter 5: Molecules and Compounds
    2. 5.1: Sugar and Salt
    3. 5.2: Compounds Display Constant Composition
    4. 5.3: Chemical Formulas: How to Represent Compounds
    5. 5.4: A Molecular View of Elements and Compounds
    6. 5.5: Writing Formulas for Ionic Compounds
    7. 5.6: Nomenclature: Naming Compounds
    8. 5.7: Naming Ionic Compounds
    9. 5.8: Naming Molecular Compounds
    10. 5.9: Naming Acids
    11. 5.10: Nomenclature Summary
    12. 5.11: Formula Mass: The Mass of a Molecule or Formula Unit
      •  Chapter 6
    1. Chapter 6: Chemical Composition
    2. 6.1: How Much Sodium?
    3. 6.2: Counting Nails by the Pound
    4. 6.3: Counting Atoms by the Gram
    5. 6.4: Counting Molecules by the Gram
    6. 6.5: Chemical Formulas as Conversion Factors
    7. 6.6: Mass Percent Composition of Compounds
    8. 6.7: Mass Percent Composition from a Chemical Formula
    9. 6.8: Calculating Empirical Formulas for Compounds
    10. 6.9: Calculating Molecular Formulas for Compounds
      •  Chapter 7
    1. Chapter 7: Chemical Reactions
    2. 7.1: Grade School Volcanoes, Automobiles, and Laundry Detergents
    3. 7.2: Evidence of a Chemical Reaction
    4. 7.3: The Chemical Equation
    5. 7.4: How to Write Balanced Chemical Equations
    6. 7.5: Aqueous Solutions and Solubility: Compounds Dissolved in Water
    7. 7.6: Precipitation Reactions: Reactions in Aqueous Solution That Form a Solid
    8. 7.7: Writing Chemical Equations for Reactions in Solution: Molecular, Complete Ionic, and Net Ionic Equations
    9. 7.8: Acid–Base and Gas Evolution Reactions
    10. 7.9: Oxidation–Reduction Reactions
    11. 7.10: Classifying Chemical Reactions
    12. 7.11: The Activity Series
     •  Chapter 8
    1. Chapter 8: Quantities in Chemical Reactions
    2. 8.1: Climate Change: Too Much Carbon Dioxide
    3. 8.2: Stoichiometry
    4. 8.3: Making Molecules: Mole-to-Mole Conversions
    5. 8.4: Making Molecules: Mass-to-Mass Conversions
    6. 8.5: Limiting Reactant, Theoretical Yield, and Percent Yield
    7. 8.6: Limiting Reactant, Theoretical Yield, and Percent Yield from Initial Masses of Reactants
    8. 8.7: Enthalpy: A Measure of the Heat Evolved or Absorbed in a Reaction
    Chapter 9
    1. Chapter 9: Electrons in Atoms and the Periodic Table
    2. 9.1: Blimps, Balloons, and Models of the Atom
    3. 9.2: Light: Electromagnetic Radiation
    4. 9.3: The Electromagnetic Spectrum
    5. 9.4: The Bohr Model: Atoms with Orbits
    6. 9.5: The Quantum-Mechanical Model: Atoms with Orbitals
    7. 9.6: Quantum-Mechanical Orbitals and Electron Configurations
    8. 9.7: Electron Configurations and the Periodic Table
    9. 9.8: The Explanatory Power of the Quantum-Mechanical Model
    10. 9.9: Periodic Trends: Atomic Size, Ionization Energy, and Metallic Character
     •  Chapter 10
    1. Chapter 10: Chemical Bonding
    2. 10.1: Bonding Models and AIDS Drugs
    3. 10.2: Representing Valence Electrons with Dots
    4. 10.3: Lewis Structures of Ionic Compounds: Electrons Transferred
    5. 10.4: Covalent Lewis Structures: Electrons Shared
    6. 10.5: Writing Lewis Structures for Covalent Compounds
    7. 10.6: Resonance: Equivalent Lewis Structures for the Same Molecule
    8. 10.7: Predicting the Shapes of Molecules
    9. 10.8: Electronegativity and Polarity: Why Oil and Water Don’t Mix
     •  Chapter 11
    1. Chapter 11: Gases
    2. 11.1: Extra-Long Straws
    3. 11.2: Kinetic Molecular Theory: A Model for Gases
    4. 11.3: Pressure: The Result of Constant Molecular Collisions
    5. 11.4: Boyle’s Law: Pressure and Volume
    6. 11.5: Charles’s Law: Volume and Temperature
    7. 11.6: Gay-Lussac's Law: Temperature and Pressure
    8. 11.7: The Combined Gas Law: Pressure, Volume, and Temperature
    9. 11.8: Avogadro’s Law: Volume and Moles
    10. 11.9: The Ideal Gas Law: Pressure, Volume, Temperature, and Moles
    11. 11.10: Mixtures of Gases: Why Deep-Sea Divers Breathe a Mixture of Helium and Oxygen
    12. 11.11: Gases in Chemical Reactions
     •  Chapter 12
    1. Chapter 12: Liquids, Solids, and Intermolecular Forces
    2. 12.1: Interactions between Molecules
    3. 12.2: Properties of Liquids and Solids
    4. 12.3: Intermolecular Forces in Action: Surface Tension and Viscosity
    5. 12.4: Evaporation and Condensation
    6. 12.5: Melting, Freezing, and Sublimation
    7. 12.6: Types of Intermolecular Forces: Dispersion, Dipole–Dipole, Hydrogen Bonding, and Ion-Dipole
    8. 12.7: Types of Crystalline Solids: Molecular, Ionic, and Atomic
    9. 12.8: Water: A Remarkable Molecule
     •  Chapter 13
    1. Chapter 13: Solutions
    2. 13.1: Prelude - Tragedy in Cameroon
    3. 13.2: Solutions: Homogeneous Mixtures
    4. 13.3: Solutions of Solids Dissolved in Water: How to Make Rock Candy
    5. 13.4: Solutions of Gases in Water: How Soda Pop Gets Its Fizz
    6. 13.5: Solution Concentration: Mass Percent
    7. 13.6: Solution Concentration: Molarity
    8. 13.7: Solution Dilution
    9. 13.8: Solution Stoichiometry
    10. 13.9: Freezing Point Depression and Boiling Point Elevation: Making Water Freeze Colder and Boil Hotter
    11. 13.10: Osmosis: Why Drinking Salt Water Causes Dehydration
      •  Chapter 14
    1. Chapter 14: Acids and Bases
    2. 14.1: Sour Patch Kids and International Spy Movies
    3. 14.2: Acids: Properties and Examples
    4. 14.3: Bases: Properties and Examples
    5. 14.4: Molecular Definitions of Acids and Bases
    6. 14.5: Reactions of Acids and Bases
    7. 14.6: Acid–Base Titration: A Way to Quantify the Amount of Acid or Base in a Solution
    8. 14.7: Strong and Weak Acids and Bases
    9. 14.8: Water: Acid and Base in One
    10. 14.9: The pH and pOH Scales: Ways to Express Acidity and Basicity
    11. 14.10: Buffers: Solutions That Resist pH Change
     

    Template:HideTOC

    Learning Objectives
    • Define quantum mechanics
    • Differentiate between an orbit and an orbital.

    How do you study something that seemingly makes no sense? We talk about electrons being in orbits and it sounds like we can tell where that electron is at any moment. We can draw pictures of electrons in orbit, but the reality is that we don't know exactly where they are. We are going to take a look at an area of science that even leaves scientists puzzled. When asked about quantum mechanics, Niels Bohr (who proposed the Bohr model of the atom) said: "Anyone who is not shocked by quantum theory has not understood it". Richard Feynman (one of the founders of modern quantum theory) stated: "I think I can safely say that nobody understands quantum theory." So, let's take a short trip into a land that challenges our everyday world.

    Quantum Mechanics

    The study of motion of large objects such as baseballs is called mechanics, or more specifically, classical mechanics. Because of the quantum nature of the electron and other tiny particles moving at high speeds, classical mechanics is inadequate to accurately describe their motion. Quantum mechanics is the study of the motion of objects that are atomic or subatomic in size and thus demonstrate wave-particle duality. In classical mechanics, the size and mass of the objects involved effectively obscures any quantum effects, so that such objects appear to gain or lose energies in any amounts. Particles whose motion is described by quantum mechanics gain or lose energy in small pieces called quanta.

    One of the fundamental (and hardest to understand) principles of quantum mechanics is that the electron is both a particle and a wave. In the everyday macroscopic world of things we can see, something cannot be both. But this duality can exist in the quantum world of the submicroscopic on the atomic scale.

    At the heart of quantum mechanics is the idea that we cannot accurately specify the location of an electron. All we can say is that there is a probability that it exists within this certain volume of space. The scientist Erwin Schrödinger developed an equation that deals with these calculations, which we will not pursue at this time.

    A smiling man with glasses and curly hair, wearing a bow tie and a jacket, stands outdoors holding a small object.

    Erwin Schrödinger.

    Recall that in the Bohr model, the exact path of the electron was restricted to very well-defined circular orbits around the nucleus. An orbital is the quantum mechanical refinement of Bohr’s orbit. In contrast to his concept of a simple circular orbit with a fixed radius, orbitals are mathematically derived regions of space with different probabilities of having an electron.

    Summary

    Quantum mechanics involves the study of material at the atomic level. This field deals with probabilities, since we cannot definitely locate a particle. Orbitals are mathematically derived regions of space with different probabilities of having an electron.

    9.5: The Quantum-Mechanical Model- Atoms with Orbitals is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts.