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Introductory Chemistry - 1st Canadian Edition: Light

Introductory Chemistry - 1st Canadian Edition
Light
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table of contents
  1. Cover
  2. Title Page
  3. Copyright
  4. Table Of Contents
  5. Acknowledgments
  6. Dedication
  7. About BCcampus Open Education
  8. Chapter 1. What is Chemistry
    1. Some Basic Definitions
    2. Chemistry as a Science
  9. Chapter 2. Measurements
    1. Expressing Numbers
    2. Significant Figures
    3. Converting Units
    4. Other Units: Temperature and Density
    5. Expressing Units
    6. End-of-Chapter Material
  10. Chapter 3. Atoms, Molecules, and Ions
    1. Acids
    2. Ions and Ionic Compounds
    3. Masses of Atoms and Molecules
    4. Molecules and Chemical Nomenclature
    5. Atomic Theory
    6. End-of-Chapter Material
  11. Chapter 4. Chemical Reactions and Equations
    1. The Chemical Equation
    2. Types of Chemical Reactions: Single- and Double-Displacement Reactions
    3. Ionic Equations: A Closer Look
    4. Composition, Decomposition, and Combustion Reactions
    5. Oxidation-Reduction Reactions
    6. Neutralization Reactions
    7. End-of-Chapter Material
  12. Chapter 5. Stoichiometry and the Mole
    1. Stoichiometry
    2. The Mole
    3. Mole-Mass and Mass-Mass Calculations
    4. Limiting Reagents
    5. The Mole in Chemical Reactions
    6. Yields
    7. End-of-Chapter Material
  13. Chapter 6. Gases
    1. Pressure
    2. Gas Laws
    3. Other Gas Laws
    4. The Ideal Gas Law and Some Applications
    5. Gas Mixtures
    6. Kinetic Molecular Theory of Gases
    7. Molecular Effusion and Diffusion
    8. Real Gases
    9. End-of-Chapter Material
  14. Chapter 7. Energy and Chemistry
    1. Formation Reactions
    2. Energy
    3. Stoichiometry Calculations Using Enthalpy
    4. Enthalpy and Chemical Reactions
    5. Work and Heat
    6. Hess’s Law
    7. End-of-Chapter Material
  15. Chapter 8. Electronic Structure
    1. Light
    2. Quantum Numbers for Electrons
    3. Organization of Electrons in Atoms
    4. Electronic Structure and the Periodic Table
    5. Periodic Trends
    6. End-of-Chapter Material
  16. Chapter 9. Chemical Bonds
    1. Lewis Electron Dot Diagrams
    2. Electron Transfer: Ionic Bonds
    3. Covalent Bonds
    4. Other Aspects of Covalent Bonds
    5. Violations of the Octet Rule
    6. Molecular Shapes and Polarity
    7. Valence Bond Theory and Hybrid Orbitals
    8. Molecular Orbitals
    9. End-of-Chapter Material
  17. Chapter 10. Solids and Liquids
    1. Properties of Liquids
    2. Solids
    3. Phase Transitions: Melting, Boiling, and Subliming
    4. Intermolecular Forces
    5. End-of-Chapter Material
  18. Chapter 11. Solutions
    1. Colligative Properties of Solutions
    2. Concentrations as Conversion Factors
    3. Quantitative Units of Concentration
    4. Colligative Properties of Ionic Solutes
    5. Some Definitions
    6. Dilutions and Concentrations
    7. End-of-Chapter Material
  19. Chapter 12. Acids and Bases
    1. Acid-Base Titrations
    2. Strong and Weak Acids and Bases and Their Salts
    3. Brønsted-Lowry Acids and Bases
    4. Arrhenius Acids and Bases
    5. Autoionization of Water
    6. Buffers
    7. The pH Scale
    8. End-of-Chapter Material
  20. Chapter 13. Chemical Equilibrium
    1. Chemical Equilibrium
    2. The Equilibrium Constant
    3. Shifting Equilibria: Le Chatelier’s Principle
    4. Calculating Equilibrium Constant Values
    5. Some Special Types of Equilibria
    6. End-of-Chapter Material
  21. Chapter 14. Oxidation and Reduction
    1. Oxidation-Reduction Reactions
    2. Balancing Redox Reactions
    3. Applications of Redox Reactions: Voltaic Cells
    4. Electrolysis
    5. End-of-Chapter Material
  22. Chapter 15. Nuclear Chemistry
    1. Units of Radioactivity
    2. Uses of Radioactive Isotopes
    3. Half-Life
    4. Radioactivity
    5. Nuclear Energy
    6. End-of-Chapter Material
  23. Chapter 16. Organic Chemistry
    1. Hydrocarbons
    2. Branched Hydrocarbons
    3. Alkyl Halides and Alcohols
    4. Other Oxygen-Containing Functional Groups
    5. Other Functional Groups
    6. Polymers
    7. End-of-Chapter Material
  24. Chapter 17. Kinetics
    1. Factors that Affect the Rate of Reactions
    2. Reaction Rates
    3. Rate Laws
    4. Concentration–Time Relationships: Integrated Rate Laws
    5. Activation Energy and the Arrhenius Equation
    6. Reaction Mechanisms
    7. Catalysis
    8. End-of-Chapter Material
  25. Chapter 18. Chemical Thermodynamics
    1. Spontaneous Change
    2. Entropy and the Second Law of Thermodynamics
    3. Measuring Entropy and Entropy Changes
    4. Gibbs Free Energy
    5. Spontaneity: Free Energy and Temperature
    6. Free Energy under Nonstandard Conditions
    7. End-of-Chapter Material
  26. Appendix A: Periodic Table of the Elements
  27. Appendix B: Selected Acid Dissociation Constants at 25°C
  28. Appendix C: Solubility Constants for Compounds at 25°C
  29. Appendix D: Standard Thermodynamic Quantities for Chemical Substances at 25°C
  30. Appendix E: Standard Reduction Potentials by Value
  31. Glossary
  32. About the Authors
  33. Versioning History

Light

Learning Objectives

  1. Describe light with its frequency and wavelength.
  2. Describe light as a particle of energy.

What we know as light is more properly called electromagnetic radiation. We know from experiments that light acts as a wave. As such, it can be described as having a frequency and a wavelength. The wavelength of light is the distance between corresponding points in two adjacent light cycles, and the frequency of light is the number of cycles of light that pass a given point in one second. Wavelength is typically represented by λ, the lowercase Greek letter lambda, while frequency is represented by ν, the lowercase Greek letter nu (although it looks like a Roman “vee,” it is actually the Greek equivalent of the letter “en”). Wavelength has units of length (metres, centimetres, etc.), while frequency has units of per second, written as s−1 and sometimes called a hertz (Hz). Figure 8.01 “Characteristics of Light Waves” shows how these two characteristics are defined.

Diagrams of light waves. Long description needed.
Figure 8.01 “Characteristics of Light Waves.” Light acts as a wave and can be described by a wavelength λ and a frequency ν.

One property of waves is that their speed is equal to their wavelength times their frequency. That means we have:

\text{speed}=\lambda\nu

For light, however, speed is actually a universal constant when light is travelling through a vacuum (or, to a very good approximation, air). The measured speed of light (c) in a vacuum is 2.9979 × 108 m/s, or about 3.00 × 108 m/s. Thus, we have:

c=\lambda \nu

Because the speed of light is a constant, the wavelength and the frequency of light are related to each other: as one increases, the other decreases and vice versa. We can use this equation to calculate what one property of light has to be when given the other property.

Example 8.7

Problem

What is the frequency of light if its wavelength is 5.55 × 10−7 m?

Solution

We use the equation that relates the wavelength and frequency of light with its speed. We have:

3.00\times 10^8\text{ m/s}=(5.55\times 10^{-7}\text{ m})\nu

We divide both sides of the equation by 5.55 × 10−7 m and get:

\nu = 5.41\times 10^{14}\text{ s}^{-1}

Note how the m units cancel, leaving s in the denominator. A unit in a denominator is indicated by a −1 power — s−1 — and read as “per second.”

Test Yourself

What is the wavelength of light if its frequency is 1.55 × 1010 s−1?

Answer

0.0194 m, or 19.4 mm

Light also behaves like a package of energy. It turns out that for light, the energy of the “package” of energy is proportional to its frequency. (For most waves, energy is proportional to wave amplitude, or the height of the wave.) The mathematical equation that relates the energy (E) of light to its frequency is:

E=h\nu

Where ν is the frequency of the light, and h is a constant called Planck’s constant. Its value is 6.626 × 10−34 J·s — a very small number that is another fundamental constant of our universe, like the speed of light. The units on Planck’s constant may look unusual, but these units are required so that the algebra works out.

Example 8.8

Problem

What is the energy of light if its frequency is 1.55 × 1010 s−1?

Solution

Using the formula for the energy of light, we have:

E=(6.626\times 10^{-34}\text{ J}\cdot \text{s})(1.55\times 10^{10}\text{ s}^{-1})

Seconds are in the numerator and the denominator, so they cancel, leaving us with joules, the unit of energy. So:

E=1.03\times 10^{-23}\text{ J}

This is an extremely small amount of energy — but this is for only one light wave.

Test Yourself

What is the frequency of a light wave if its energy is 4.156 × 10−20 J?

Answer

6.27 × 1013 s−1

Because a light wave behaves like a little particle of energy, light waves have a particle-type name: the photon. It is not uncommon to hear light described as photons.

Wavelengths, frequencies, and energies of light span a wide range; the entire range of possible values for light is called the electromagnetic spectrum. We are mostly familiar with visible light, which is light having a wavelength range between about 400 nm and 700 nm. Light can have much longer and much shorter wavelengths than this, with corresponding variations in frequency and energy. Figure 8.02 “The Electromagnetic Spectrum” shows the entire electromagnetic spectrum and how certain regions of the spectrum are labelled. You may already be familiar with some of these regions; they are all light—with different frequencies, wavelengths, and energies.

The electromagnetic spectrum. Long description needed.
Figure 8.02 “The Electromagnetic Spectrum.” The electromagnetic spectrum, with its various regions labelled. The borders of each region are approximate.

Key Takeaways

  • Light acts like a wave, with a frequency and a wavelength.
  • The frequency and wavelength of light are related by the speed of light, a constant.
  • Light acts like a particle of energy, whose value is related to the frequency of light.

Exercises

Questions

  1. Describe the characteristics of a light wave.
  2. What is a characteristic of a particle of light?
  3. What is the frequency of light if its wavelength is 7.33 × 10−5 m?
  4. What is the frequency of light if its wavelength is 1.226 m?
  5. What is the frequency of light if its wavelength is 733 nm?
  6. What is the frequency of light if its wavelength is 8.528 cm?
  7. What is the wavelength of light if its frequency is 8.19 × 1014 s−1?
  8. What is the wavelength of light if its frequency is 3.66 × 106 s−1?
  9. What is the wavelength of light if its frequency is 1.009 × 106 Hz?
  10. What is the wavelength of light if its frequency is 3.79 × 10−3 Hz?
  11. What is the energy of a photon if its frequency is 5.55 × 1013 s−1?
  12. What is the energy of a photon if its frequency is 2.06 × 1018 s−1?
  13. What is the energy of a photon if its wavelength is 5.88 × 10−4 m?
  14. What is the energy of a photon if its wavelength is 1.888 × 102 m?

Answers

  1. Light has a wavelength and a frequency.
  1. 4.09 × 1012 s−1
  1. 4.09 × 1014 s−1
  1. 3.66 × 10−7 m
  1. 297 m
  1. 3.68 × 10−20 J
  1. 3.38 × 10−22 J

Media Attributions

  • “Characteristics of Light Waves” by David W. Ball © CC BY-NC-SA (Attribution-NonCommercial-ShareAlike)
  • “The Electromagnetic Spectrum” by David W. Ball © CC BY-NC-SA (Attribution-NonCommercial-ShareAlike)

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Copyright © 2014

                                by Jessie A. Key

            Introductory Chemistry - 1st Canadian Edition by Jessie A. Key is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.
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