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Astronomy

5.4 The Structure of the Atom

Astronomy5.4 The Structure of the Atom
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  1. Preface
  2. 1 Science and the Universe: A Brief Tour
    1. Introduction
    2. 1.1 The Nature of Astronomy
    3. 1.2 The Nature of Science
    4. 1.3 The Laws of Nature
    5. 1.4 Numbers in Astronomy
    6. 1.5 Consequences of Light Travel Time
    7. 1.6 A Tour of the Universe
    8. 1.7 The Universe on the Large Scale
    9. 1.8 The Universe of the Very Small
    10. 1.9 A Conclusion and a Beginning
    11. For Further Exploration
  3. 2 Observing the Sky: The Birth of Astronomy
    1. Thinking Ahead
    2. 2.1 The Sky Above
    3. 2.2 Ancient Astronomy
    4. 2.3 Astrology and Astronomy
    5. 2.4 The Birth of Modern Astronomy
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  4. 3 Orbits and Gravity
    1. Thinking Ahead
    2. 3.1 The Laws of Planetary Motion
    3. 3.2 Newton’s Great Synthesis
    4. 3.3 Newton’s Universal Law of Gravitation
    5. 3.4 Orbits in the Solar System
    6. 3.5 Motions of Satellites and Spacecraft
    7. 3.6 Gravity with More Than Two Bodies
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  5. 4 Earth, Moon, and Sky
    1. Thinking Ahead
    2. 4.1 Earth and Sky
    3. 4.2 The Seasons
    4. 4.3 Keeping Time
    5. 4.4 The Calendar
    6. 4.5 Phases and Motions of the Moon
    7. 4.6 Ocean Tides and the Moon
    8. 4.7 Eclipses of the Sun and Moon
    9. Key Terms
    10. Summary
    11. For Further Exploration
    12. Collaborative Group Activities
    13. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  6. 5 Radiation and Spectra
    1. Thinking Ahead
    2. 5.1 The Behavior of Light
    3. 5.2 The Electromagnetic Spectrum
    4. 5.3 Spectroscopy in Astronomy
    5. 5.4 The Structure of the Atom
    6. 5.5 Formation of Spectral Lines
    7. 5.6 The Doppler Effect
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  7. 6 Astronomical Instruments
    1. Thinking Ahead
    2. 6.1 Telescopes
    3. 6.2 Telescopes Today
    4. 6.3 Visible-Light Detectors and Instruments
    5. 6.4 Radio Telescopes
    6. 6.5 Observations outside Earth’s Atmosphere
    7. 6.6 The Future of Large Telescopes
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  8. 7 Other Worlds: An Introduction to the Solar System
    1. Thinking Ahead
    2. 7.1 Overview of Our Planetary System
    3. 7.2 Composition and Structure of Planets
    4. 7.3 Dating Planetary Surfaces
    5. 7.4 Origin of the Solar System
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  9. 8 Earth as a Planet
    1. Thinking Ahead
    2. 8.1 The Global Perspective
    3. 8.2 Earth’s Crust
    4. 8.3 Earth’s Atmosphere
    5. 8.4 Life, Chemical Evolution, and Climate Change
    6. 8.5 Cosmic Influences on the Evolution of Earth
    7. Key Terms
    8. Summary
    9. For Further Exploration
    10. Collaborative Group Activities
    11. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  10. 9 Cratered Worlds
    1. Thinking Ahead
    2. 9.1 General Properties of the Moon
    3. 9.2 The Lunar Surface
    4. 9.3 Impact Craters
    5. 9.4 The Origin of the Moon
    6. 9.5 Mercury
    7. Key Terms
    8. Summary
    9. For Further Exploration
    10. Collaborative Group Activities
    11. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  11. 10 Earthlike Planets: Venus and Mars
    1. Thinking Ahead
    2. 10.1 The Nearest Planets: An Overview
    3. 10.2 The Geology of Venus
    4. 10.3 The Massive Atmosphere of Venus
    5. 10.4 The Geology of Mars
    6. 10.5 Water and Life on Mars
    7. 10.6 Divergent Planetary Evolution
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  12. 11 The Giant Planets
    1. Thinking Ahead
    2. 11.1 Exploring the Outer Planets
    3. 11.2 The Giant Planets
    4. 11.3 Atmospheres of the Giant Planets
    5. Key Terms
    6. Summary
    7. For Further Exploration
    8. Collaborative Group Activities
    9. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  13. 12 Rings, Moons, and Pluto
    1. Thinking Ahead
    2. 12.1 Ring and Moon Systems Introduced
    3. 12.2 The Galilean Moons of Jupiter
    4. 12.3 Titan and Triton
    5. 12.4 Pluto and Charon
    6. 12.5 Planetary Rings
    7. Key Terms
    8. Summary
    9. For Further Exploration
    10. Collaborative Group Activities
    11. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  14. 13 Comets and Asteroids: Debris of the Solar System
    1. Thinking Ahead
    2. 13.1 Asteroids
    3. 13.2 Asteroids and Planetary Defense
    4. 13.3 The “Long-Haired” Comets
    5. 13.4 The Origin and Fate of Comets and Related Objects
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  15. 14 Cosmic Samples and the Origin of the Solar System
    1. Thinking Ahead
    2. 14.1 Meteors
    3. 14.2 Meteorites: Stones from Heaven
    4. 14.3 Formation of the Solar System
    5. 14.4 Comparison with Other Planetary Systems
    6. 14.5 Planetary Evolution
    7. Key Terms
    8. Summary
    9. For Further Exploration
    10. Collaborative Group Activities
    11. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  16. 15 The Sun: A Garden-Variety Star
    1. Thinking Ahead
    2. 15.1 The Structure and Composition of the Sun
    3. 15.2 The Solar Cycle
    4. 15.3 Solar Activity above the Photosphere
    5. 15.4 Space Weather
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  17. 16 The Sun: A Nuclear Powerhouse
    1. Thinking Ahead
    2. 16.1 Sources of Sunshine: Thermal and Gravitational Energy
    3. 16.2 Mass, Energy, and the Theory of Relativity
    4. 16.3 The Solar Interior: Theory
    5. 16.4 The Solar Interior: Observations
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  18. 17 Analyzing Starlight
    1. Thinking Ahead
    2. 17.1 The Brightness of Stars
    3. 17.2 Colors of Stars
    4. 17.3 The Spectra of Stars (and Brown Dwarfs)
    5. 17.4 Using Spectra to Measure Stellar Radius, Composition, and Motion
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  19. 18 The Stars: A Celestial Census
    1. Thinking Ahead
    2. 18.1 A Stellar Census
    3. 18.2 Measuring Stellar Masses
    4. 18.3 Diameters of Stars
    5. 18.4 The H–R Diagram
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  20. 19 Celestial Distances
    1. Thinking Ahead
    2. 19.1 Fundamental Units of Distance
    3. 19.2 Surveying the Stars
    4. 19.3 Variable Stars: One Key to Cosmic Distances
    5. 19.4 The H–R Diagram and Cosmic Distances
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  21. 20 Between the Stars: Gas and Dust in Space
    1. Thinking Ahead
    2. 20.1 The Interstellar Medium
    3. 20.2 Interstellar Gas
    4. 20.3 Cosmic Dust
    5. 20.4 Cosmic Rays
    6. 20.5 The Life Cycle of Cosmic Material
    7. 20.6 Interstellar Matter around the Sun
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  22. 21 The Birth of Stars and the Discovery of Planets outside the Solar System
    1. Thinking Ahead
    2. 21.1 Star Formation
    3. 21.2 The H–R Diagram and the Study of Stellar Evolution
    4. 21.3 Evidence That Planets Form around Other Stars
    5. 21.4 Planets beyond the Solar System: Search and Discovery
    6. 21.5 Exoplanets Everywhere: What We Are Learning
    7. 21.6 New Perspectives on Planet Formation
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  23. 22 Stars from Adolescence to Old Age
    1. Thinking Ahead
    2. 22.1 Evolution from the Main Sequence to Red Giants
    3. 22.2 Star Clusters
    4. 22.3 Checking Out the Theory
    5. 22.4 Further Evolution of Stars
    6. 22.5 The Evolution of More Massive Stars
    7. Key Terms
    8. Summary
    9. For Further Exploration
    10. Collaborative Group Activities
    11. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  24. 23 The Death of Stars
    1. Thinking Ahead
    2. 23.1 The Death of Low-Mass Stars
    3. 23.2 Evolution of Massive Stars: An Explosive Finish
    4. 23.3 Supernova Observations
    5. 23.4 Pulsars and the Discovery of Neutron Stars
    6. 23.5 The Evolution of Binary Star Systems
    7. 23.6 The Mystery of the Gamma-Ray Bursts
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  25. 24 Black Holes and Curved Spacetime
    1. Thinking Ahead
    2. 24.1 Introducing General Relativity
    3. 24.2 Spacetime and Gravity
    4. 24.3 Tests of General Relativity
    5. 24.4 Time in General Relativity
    6. 24.5 Black Holes
    7. 24.6 Evidence for Black Holes
    8. 24.7 Gravitational Wave Astronomy
    9. Key Terms
    10. Summary
    11. For Further Exploration
    12. Collaborative Group Activities
    13. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  26. 25 The Milky Way Galaxy
    1. Thinking Ahead
    2. 25.1 The Architecture of the Galaxy
    3. 25.2 Spiral Structure
    4. 25.3 The Mass of the Galaxy
    5. 25.4 The Center of the Galaxy
    6. 25.5 Stellar Populations in the Galaxy
    7. 25.6 The Formation of the Galaxy
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  27. 26 Galaxies
    1. Thinking Ahead
    2. 26.1 The Discovery of Galaxies
    3. 26.2 Types of Galaxies
    4. 26.3 Properties of Galaxies
    5. 26.4 The Extragalactic Distance Scale
    6. 26.5 The Expanding Universe
    7. Key Terms
    8. Summary
    9. For Further Exploration
    10. Collaborative Group Activities
    11. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  28. 27 Active Galaxies, Quasars, and Supermassive Black Holes
    1. Thinking Ahead
    2. 27.1 Quasars
    3. 27.2 Supermassive Black Holes: What Quasars Really Are
    4. 27.3 Quasars as Probes of Evolution in the Universe
    5. Key Terms
    6. Summary
    7. For Further Exploration
    8. Collaborative Group Activities
    9. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  29. 28 The Evolution and Distribution of Galaxies
    1. Thinking Ahead
    2. 28.1 Observations of Distant Galaxies
    3. 28.2 Galaxy Mergers and Active Galactic Nuclei
    4. 28.3 The Distribution of Galaxies in Space
    5. 28.4 The Challenge of Dark Matter
    6. 28.5 The Formation and Evolution of Galaxies and Structure in the Universe
    7. Key Terms
    8. Summary
    9. For Further Exploration
    10. Collaborative Group Activities
    11. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  30. 29 The Big Bang
    1. Thinking Ahead
    2. 29.1 The Age of the Universe
    3. 29.2 A Model of the Universe
    4. 29.3 The Beginning of the Universe
    5. 29.4 The Cosmic Microwave Background
    6. 29.5 What Is the Universe Really Made Of?
    7. 29.6 The Inflationary Universe
    8. 29.7 The Anthropic Principle
    9. Key Terms
    10. Summary
    11. For Further Exploration
    12. Collaborative Group Activities
    13. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  31. 30 Life in the Universe
    1. Thinking Ahead
    2. 30.1 The Cosmic Context for Life
    3. 30.2 Astrobiology
    4. 30.3 Searching for Life beyond Earth
    5. 30.4 The Search for Extraterrestrial Intelligence
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  32. A | How to Study for an Introductory Astronomy Class
  33. B | Astronomy Websites, Images, and Apps
  34. C | Scientific Notation
  35. D | Units Used in Science
  36. E | Some Useful Constants for Astronomy
  37. F | Physical and Orbital Data for the Planets
  38. G | Selected Moons of the Planets
  39. H | Future Total Eclipses
  40. I | The Nearest Stars, Brown Dwarfs, and White Dwarfs
  41. J | The Brightest Twenty Stars
  42. K | The Chemical Elements
  43. L | The Constellations
  44. M | Star Chart and Sky Event Resources
  45. Index

Learning Objectives

By the end of this section, you will be able to:

  • Describe the structure of atoms and the components of nuclei
  • Explain the behavior of electrons within atoms and how electrons interact with light to move among energy levels

The idea that matter is composed of tiny particles called atoms is at least 25 centuries old. It took until the twentieth century, however, for scientists to invent instruments that permitted them to probe inside an atom and find that it is not, as had been thought, hard and indivisible. Instead, the atom is a complex structure composed of still smaller particles.

Probing the Atom

The first of these smaller particles was discovered by British physicist James (J. J.) Thomson in 1897. Named the electron, this particle is negatively charged. (It is the flow of these particles that produces currents of electricity, whether in lightning bolts or in the wires leading to your lamp.) Because an atom in its normal state is electrically neutral, each electron in an atom must be balanced by the same amount of positive charge.

The next step was to determine where in the atom the positive and negative charges are located. In 1911, British physicist Ernest Rutherford devised an experiment that provided part of the answer to this question. He bombarded an extremely thin piece of gold foil, only about 400 atoms thick, with a beam of alpha particles (Figure 5.14). Alpha particles (α particles) are helium atoms that have lost their electrons and thus are positively charged. Most of these particles passed though the gold foil just as if it and the atoms in it were nearly empty space. About 1 in 8000 of the alpha particles, however, completely reversed direction and bounced backward from the foil. Rutherford wrote, “It was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.”

Rutherford’s Experiment. This figure presents a schematic representation of the experimental apparatus, and a model of an atom. In (a), on the left, is a box which is the source of the α-particles. The beam of particles leaves the source in a straight line to a thin gold foil. The gold foil is nearly completely surrounded by a circular screen which detects α-particles. Most of the beam passes straight though the foil, but a few are slightly deflected to the left or right of the foil. Even fewer are reflected nearly straight back to the emitter. Part (b) shows a simplified model of an atom. It shows a nucleus of protons and neutrons, surrounded by three orbiting electrons, each in a different circular orbit around the nucleus.
Figure 5.14 Rutherford’s Experiment. (a) When Rutherford allowed α particles from a radioactive source to strike a target of gold foil, he found that, although most of them went straight through, some rebounded back in the direction from which they came. (b) From this experiment, he concluded that the atom must be constructed like a miniature solar system, with the positive charge concentrated in the nucleus and the negative charge orbiting in the large volume around the nucleus. Note that this drawing is not to scale; the electron orbits are much larger relative to the size of the nucleus.

The only way to account for the particles that reversed direction when they hit the gold foil was to assume that nearly all of the mass, as well as all of the positive charge in each individual gold atom, is concentrated in a tiny center or nucleus. When a positively charged alpha particle strikes a nucleus, it reverses direction, much as a cue ball reverses direction when it strikes another billiard ball. Rutherford’s model placed the other type of charge—the negative electrons—in orbit around this nucleus.

Rutherford’s model required that the electrons be in motion. Positive and negative charges attract each other, so stationary electrons would fall into the positive nucleus. Also, because both the electrons and the nucleus are extremely small, most of the atom is empty, which is why nearly all of Rutherford’s particles were able to pass right through the gold foil without colliding with anything. Rutherford’s model was a very successful explanation of the experiments he conducted, although eventually scientists would discover that even the nucleus itself has structure.

The Atomic Nucleus

The simplest possible atom (and the most common one in the Sun and stars) is hydrogen. The nucleus of ordinary hydrogen contains a single proton. Moving around this proton is a single electron. The mass of an electron is nearly 2000 times smaller than the mass of a proton; the electron carries an amount of charge exactly equal to that of the proton but opposite in sign (Figure 5.15). Opposite charges attract each other, so it is an electromagnetic force that holds the proton and electron together, just as gravity is the force that keeps planets in orbit around the Sun.

Model of the Hydrogen Atom. In the center of a circle is a small dot labeled “proton”, and has a “+” sign on the dot. On the perimeter of the circle is another dot labeled “electron”, with a “-“ sign on the dot. The circle represents the orbit of the electron around the proton.
Figure 5.15 Hydrogen Atom. This is a schematic diagram of a hydrogen atom in its lowest energy state, also called the ground state. The proton and electron have equal but opposite charges, which exert an electromagnetic force that binds the hydrogen atom together. In the illustration, the size of the particles is exaggerated so that you can see them; they are not to scale. They are also shown much closer than they would actually be as it would take more than an entire page to show their actual distance to scale.

There are many other types of atoms in nature. Helium, for example, is the second-most abundant element in the Sun. Helium has two protons in its nucleus instead of the single proton that characterizes hydrogen. In addition, the helium nucleus contains two neutrons, particles with a mass comparable to that of the proton but with no electric charge. Moving around this nucleus are two electrons, so the total net charge of the helium atom is also zero (Figure 5.16).

Model of the Helium Atom. In the center of a circle are 4 dots representing the nucleus, 2 labeled “proton”, and 2 labeled “neutron”. The protons have “+” signs. On the perimeter of the circle are 2 dots labeled “electron”, and have “-“ signs. A distance from the nucleus to the orbit of the electrons is depicted, and given as 10-10 meters.
Figure 5.16 Helium Atom. Here we see a schematic diagram of a helium atom in its lowest energy state. Two protons are present in the nucleus of all helium atoms. In the most common variety of helium, the nucleus also contains two neutrons, which have nearly the same mass as the proton but carry no charge. Two electrons orbit the nucleus.

From this description of hydrogen and helium, perhaps you have guessed the pattern for building up all the elements (different types of atoms) that we find in the universe. The type of element is determined by the number of protons in the nucleus of the atom. For example, any atom with six protons is the element carbon, with eight protons is oxygen, with 26 is iron, and with 92 is uranium. On Earth, a typical atom has the same number of electrons as protons, and these electrons follow complex orbital patterns around the nucleus. Deep inside stars, however, it is so hot that the electrons get loose from the nucleus and (as we shall see) lead separate yet productive lives.

The ratio of neutrons to protons increases as the number of protons increases, but each element is unique. The number of neutrons is not necessarily the same for all atoms of a given element. For example, most hydrogen atoms contain no neutrons at all. There are, however, hydrogen atoms that contain one proton and one neutron, and others that contain one proton and two neutrons. The various types of hydrogen nuclei with different numbers of neutrons are called isotopes of hydrogen (Figure 5.17), and all other elements have isotopes as well. You can think of isotopes as siblings in the same element “family”—closely related but with different characteristics and behaviors.

Isotopes of Hydrogen. This figure depicts three isotopes of hydrogen. Each is a circle of the same size with one dot and a “-“ sign on the perimeter representing the electron. From the left we see hydrogen with mass no. 1 with a single proton, “+”, at the center of the circle. In the middle is hydrogen with mass no. 2 (deuterium), having one proton, “+”, and one neutron in the center. On the right is hydrogen with mass no. 3 (tritium), having one proton, “+”, and two neutrons in the center.
Figure 5.17 Isotopes of Hydrogen. A single proton in the nucleus defines the atom to be hydrogen, but there may be zero, one, or two neutrons. The most common isotope of hydrogen is the one with only a single proton and no neutrons.

The Bohr Atom

Rutherford’s model for atoms has one serious problem. Maxwell’s theory of electromagnetic radiation says that when electrons change either speed or the direction of motion, they must emit energy. Orbiting electrons constantly change their direction of motion, so they should emit a constant stream of energy. Applying Maxwell’s theory to Rutherford’s model, all electrons should spiral into the nucleus of the atom as they lose energy, and this collapse should happen very quickly—in about 10–16 seconds.

It was Danish physicist Niels Bohr (1885–1962) who solved the mystery of how electrons remain in orbit. He was trying to develop a model of the atom that would also explain certain regularities observed in the spectrum of hydrogen. He suggested that the spectrum of hydrogen can be understood if we assume that orbits of only certain sizes are possible for the electron. Bohr further assumed that as long as the electron moves in only one of these allowed orbits, it radiates no energy: its energy would change only if it moved from one orbit to another.

This suggestion, in the words of science historian Abraham Pais, was “one of the most audacious hypotheses ever introduced in physics.” If something equivalent were at work in the everyday world, you might find that, as you went for a walk after astronomy class, nature permitted you to walk two steps per minute, five steps per minute, and 12 steps per minute, but no speeds in between. No matter how you tried to move your legs, only certain walking speeds would be permitted. To make things more bizarre, it would take no effort to walk at any one of the allowed speeds, but it would be difficult to change from one speed to another. Luckily, no such rules apply at the level of human behavior. But at the microscopic level of the atom, experiment after experiment has confirmed the validity of Bohr’s strange idea. Bohr’s suggestions became one of the foundations of the new (and much more sophisticated) model of the subatomic world called quantum mechanics.

In Bohr’s model, if the electron moves from one orbit to another closer to the atomic nucleus, it must give up some energy in the form of electromagnetic radiation. If the electron goes from an inner orbit to one farther from the nucleus, however, it requires some additional energy. One way to obtain the necessary energy is to absorb electromagnetic radiation that may be streaming past the atom from an outside source.

A key feature of Bohr’s model is that each of the permitted electron orbits around a given atom has a certain energy value; we therefore can think of each orbit as an energy level. To move from one orbit to another (which will have its own specific energy value) requires a change in the electron’s energy—a change determined by the difference between the two energy values. If the electron goes to a lower level, the energy difference will be given off; if the electron goes to a higher level, the energy difference must be obtained from somewhere else. Each jump (or transition) to a different level has a fixed and definite energy change associated with it.

A crude analogy for this situation might be life in a tower of luxury apartments where the rent is determined by the quality of the view. Such a building has certain, definite numbered levels or floors on which apartments are located. No one can live on floor 5.37 or 22.5. In addition, the rent gets higher as you go up to higher floors. If you want to exchange an apartment on the twentieth floor for one on the second floor, you will not owe as much rent. However, if you want to move from the third floor to the twenty-fifth floor, your rent will increase. In an atom, too, the “cheapest” place for an electron to live is the lowest possible level, and energy is required to move to a higher level.

Here we have one of the situations where it is easier to think of electromagnetic radiation as particles (photons) rather than as waves. As electrons move from one level to another, they give off or absorb little packets of energy. When an electron moves to a higher level, it absorbs a photon of just the right energy (provided one is available). When it moves to a lower level, it emits a photon with the exact amount of energy it no longer needs in its “lower-cost living situation.”

The photon and wave perspectives must be equivalent: light is light, no matter how we look at it. Thus, each photon carries a certain amount of energy that is proportional to the frequency (f) of the wave it represents. The value of its energy (E) is given by the formula

E=hfE=hf

where the constant of proportionality, h, is called Planck’s constant.

The constant is named for Max Planck, the German physicist who was one of the originators of the quantum theory (Figure 5.18). If metric units are used (that is, if energy is measured in joules and frequency in hertz), then Planck’s constant has the value h = 6.626 × 10–34 joule-seconds (J-s). Higher-energy photons correspond to higher-frequency waves (which have a shorter wavelength); lower-energy photons are waves of lower frequency.

Image A is of Niels Bohr. Image B is of Max Planck.
Figure 5.18 Niels Bohr (1885–1962) and Max Planck (1858–1947). (a) Bohr, shown at his desk in this 1935 photograph, and (b) Planck helped us understand the energy behavior of photons.

To take a specific example, consider a calcium atom inside the Sun’s atmosphere in which an electron jumps from a lower level to a higher level. To do this, it needs about 5 × 10–19 joules of energy, which it can conveniently obtain by absorbing a passing photon of that energy coming from deeper inside the Sun. This photon is equivalent to a wave of light whose frequency is about 7.5 × 1014 hertz and whose wavelength is about 3.9 × 10–7 meters (393 nanometers), in the deep violet part of the visible light spectrum. Although it may seem strange at first to switch from picturing light as a photon (or energy packet) to picturing it as a wave, such switching has become second nature to astronomers and can be a handy tool for doing calculations about spectra.

Example 5.5

The Energy of a Photon Now that we know how to calculate the wavelength and frequency of a photon, we can use this information, along with Planck’s constant, to determine how much energy each photon carries. How much energy does a red photon of wavelength 630 nm have?

Solution First, as we learned earlier, we can find the frequency of the photon:

f=cλ=3×108m/s630×10–9m=4.8×1014Hzf=cλ=3×108m/s630×10–9m=4.8×1014Hz

Next, we can use Planck’s constant to determine the energy (remember that a Hz is the same as 1/s):

E=hf=(6.626×10–34J-s)(4.8×1014Hz(1/s))=3.2×10–19JE=hf=(6.626×10–34J-s)(4.8×1014Hz(1/s))=3.2×10–19J

Check Your Learning What is the energy of a yellow photon with a frequency of 5.5 × 1014 Hz?

Answer:

E=hf=(6.626×10–34J-s)(5.5×1014Hz)=3.6×10–19JE=hf=(6.626×10–34J-s)(5.5×1014Hz)=3.6×10–19J

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