1. Unit 3 Atomic Structure Part 2
Electrons In Atoms
Revising the Atomic Model
Electron Arrangement in Atoms
Atomic Emission Spectra and
the Quantum Mechanical Model
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2. Limitations of Rutherford’s Atomic Model
Energy Levels in Atoms
Limitations of Rutherford’s Atomic Model
It explained only a few simple properties of atoms.
It could not explain the chemical properties of elements.
For example, Rutherford’s model could not explain why an object such as the iron scroll shown here first glows dull red, then yellow, and then white when heated to higher and higher temperatures.
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3. Energy Levels in Atoms
The Bohr Model
In 1913, Niels Bohr (1885–1962), a young Danish physicist and a student of Rutherford, developed a new atomic model.
He changed Rutherford’s model to incorporate newer discoveries about how the energy of an atom changes when the atom absorbs or emits light.
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4. Energy Levels in Atoms
The Bohr Model
Bohr proposed that an electron is found only in specific circular paths, or orbits, around the nucleus.
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5. Each possible electron orbit in Bohr’s model has a fixed energy.
Energy Levels in Atoms
The Bohr Model
Each possible electron orbit in Bohr’s model has a fixed energy.
The fixed energies an electron can have are called energy levels.
A quantum of energy is the amount of energy required to move an electron from one energy level to another energy level.
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6. Energy Levels in Atoms
The Bohr Model
The rungs on this ladder are somewhat like the energy levels in Bohr’s model of the atom.
A person on a ladder cannot stand between the rungs. Similarly, the electrons in an atom cannot exist between energy levels.
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7. Energy Levels in Atoms
The Bohr Model
The rungs on this ladder are somewhat like the energy levels in Bohr’s model of the atom.
The energy levels in atoms are unequally spaced, like the rungs in this unusual ladder. The higher energy levels are closer together.
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8. How does the Bohr model improve upon the Rutherford model?
The Rutherford model could not explain why elements that have been heated to higher and higher temperatures give off different colors of light. The Bohr model explains how the energy levels of electrons in an atom change when the atom emits light.
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9. The Quantum Mechanical Model
Austrian physicist Erwin Schrödinger (1887–1961) used new theoretical calculations and experimental results to devise and solve a mathematical equation describing the behavior of the electron in a hydrogen atom.
The modern description of the electrons in atoms, the quantum mechanical model, came from the mathematical solutions to the Schrödinger equation.
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10. The Quantum Mechanical Model
Like the Bohr model, the quantum mechanical model of the atom restricts the energy of electrons to certain values.
Unlike the Bohr model, however, the quantum mechanical model does not specify an exact path the electron takes around the nucleus.
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11. The Quantum Mechanical Model
The quantum mechanical model determines the allowed energies an electron can have and how likely it is to find the electron in various locations around the nucleus of an atom.
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12. The Quantum Mechanical Model
Probability describes how likely it is to find an electron in a particular location around the nucleus of an atom.
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13. The Quantum Mechanical Model
In the quantum mechanical model, the probability of finding an electron within a certain volume of space surrounding the nucleus can be represented as a fuzzy cloudlike region.
The cloud is more dense where the probability of finding the electron is high.
Electron cloud
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14. How are the quantum mechanical model and the Bohr model alike
How are the quantum mechanical model and the Bohr model alike? How are they different?
Like the Bohr model, the quantum mechanical model restricts the energy of electrons to certain values. Unlike the Bohr model, the quantum mechanical model does not specify an exact path the electron takes around the nucleus.
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15. Atomic Orbitals
Solutions to the Schrödinger equation give the energies, or energy levels, an electron can have.
For each energy level, the Schrödinger equation also leads to a mathematical expression, called an atomic orbital.
An atomic orbital is represented pictorially as a region of space in which there is a high probability of finding an electron.
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16. These numbers are assigned the values n = 1, 2, 3, 4, and so forth.
Atomic Orbitals
The energy levels of electrons in the quantum mechanical model are labeled by principal quantum numbers (n).
These numbers are assigned the values n = 1, 2, 3, 4, and so forth.
For each principal energy level greater than 1, there are several orbitals with different shapes and at different energy levels.
These energy levels within a principal energy level constitute energy sublevels.
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17. Atomic Orbitals
Each energy sublevel corresponds to one or more orbitals of different shapes. The orbitals describe where an electron is likely to be found.
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18. Different atomic orbitals are denoted by letters.
The s orbitals are spherical.
The p orbitals are dumbbell-shaped.
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19. Atomic Orbitals
For a given principal energy level greater than 1, there is one s orbital…
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20. Atomic Orbitals
For a given principal energy level greater than 1, there is one s orbital, 3 p orbitals...
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21. Atomic Orbitals
For a given principal energy level greater than 1, there is one s orbital, 3 p orbitals, and 5 d orbitals.
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22. Atomic Orbitals
Four of the five d orbitals have the same shape but different orientations in space.
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23. Atomic Orbitals
The numbers and types of atomic orbitals depend on the principal energy level.
Summary of Principal Energy Levels and Sublevels
Principal energy level
Number of sublevels
Type of sublevel
Maximum number of electrons
n = 1 1
1s (1 orbital) 2
n = 2
2s (1 orbital), 2p (3 orbitals) 8
n = 3 3
3s (1 orbital), 3p (3 orbitals),
3d (5 orbitals) 18
n = 4 4
4s (1 orbital), 4p (3 orbitals),
4d (5 orbitals), 4f (7 orbitals) 32
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24. The number of orbitals in a principal energy level is equal to n2.
Atomic Orbitals
The principal quantum number, n, always equals the number of sublevels within that principal energy level.
The number of orbitals in a principal energy level is equal to n2.
A maximum of two electrons can occupy an orbital.
Therefore, the maximum number of electrons that can occupy a principal energy level is given by the formula 2n2.
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25. Calculate the maximum number of electrons in the 5th principal energy level (n = 5).
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26. Calculate the maximum number of electrons in the 5th principal energy level (n = 5).
The maximum number of electrons that can occupy a principal energy level is given by the formula 2n2. If n = 5, 2n2 = 50.
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27. CHEMISTRY & YOU
Why do scientists no longer use physical models to describe the motion of electrons?
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28. CHEMISTRY & YOU
Why do scientists no longer use physical models to describe the motion of electrons?
Previous models of the atom were physical models based on the motion of large objects.
Theoretical calculations and experimental results showed that these models did not always correctly describe electron motion.
Schrödinger devised a mathematical equation describing the behavior of the electron in a hydrogen atom. The quantum mechanical model came from the solutions to the Schrödinger equation.
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29. Electron Arrangement in Atoms Revising the Atomic Model
Atomic Emission Spectra and
the Quantum Mechanical Model
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30. Electron Configurations
The ways in which electrons are arranged in various orbitals around the nuclei of atoms are called electron configurations.
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31. Electron Configurations
Three rules—the aufbau principle, the Pauli exclusion principle, and Hund’s rule—tell you how to find the electron configurations of atoms.
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32. Electron Configurations
Aufbau Principle
According to the aufbau principle, electrons occupy the orbitals of lowest energy first. In the aufbau diagram, each box represents an atomic orbital.
Increasing energy 6s 5s 4s 3s 2s 1s 6p 5p 5d 4p 4d 4f 3p 3d 2p
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33. Electron Configurations
Aufbau Principle
Increasing energy 6s 5s 4s 3s 2s 1s 6p 5p 5d 4p 4d 4f 3p 3d 2p
The aufbau diagram shows the relative energy levels of the various atomic orbitals. Orbitals of greater energy are higher on the diagram.
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34. Electron Configurations
Aufbau Principle
Increasing energy 6s 5s 4s 3s 2s 1s 6p 5p 5d 4p 4d 4f 3p 3d 2p
The range of energy levels within a principal energy level can overlap the energy levels of another principal level.
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35. Electron Configurations
Pauli Exclusion Principle
According to the Pauli exclusion principle, an atomic orbital may describe at most two electrons.
To occupy the same orbital, two electrons must have opposite spins; that is, the electron spins must be paired.
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36. Electron Configurations
Pauli Exclusion Principle
Spin is a quantum mechanical property of electrons and may be thought of as clockwise or counterclockwise.
A vertical arrow indicates an electron and its direction of spin ( or ).
An orbital containing paired electrons is written as .
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37. Electron Configurations
Hund’s Rule
According to Hund’s rule, electrons occupy orbitals of the same energy in a way that makes the number of electrons with the same spin direction as large as possible.
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38. Electron Configurations
Hund’s Rule
Three electrons would occupy three orbitals of equal energy as follows.
Electrons then occupy each orbital so that their spins are paired with the first electron in the orbital.
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39. Electron Configurations
Look at the orbital filling diagram of the oxygen atom.
An oxygen atom contains eight electrons.
Electron Configurations of Selected Elements
Element 1s 2s
2px 2py 2pz 3s
Electron configuration H
1s1 He
1s2 Li
1s22s1 C
1s22s22p2 N
1s22s22p3 O
1s22s22p4 F
1s22s22p5 Ne
1s22s22p6 Na
1s22s22p63s1
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40. Electron Configurations
Look at the orbital filling diagram of the oxygen atom.
Electron Configurations of Selected Elements
Element 1s 2s
2px 2py 2pz 3s
Electron configuration H
1s1 He
1s2 Li
1s22s1 C
1s22s22p2 N
1s22s22p3 O
1s22s22p4 F
1s22s22p5 Ne
1s22s22p6 Na
1s22s22p63s1
The 1s orbital has two electrons of opposite spin.
The 2s orbital also has two electrons of opposite spin.
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41. Electron Configurations
Look at the orbital filling diagram of the oxygen atom.
Electron Configurations of Selected Elements
Element 1s 2s
2px 2py 2pz 3s
Electron configuration H
1s1 He
1s2 Li
1s22s1 C
1s22s22p2 N
1s22s22p3 O
1s22s22p4 F
1s22s22p5 Ne
1s22s22p6 Na
1s22s22p63s1
Each of the three 2p orbitals has one electron. The remaining electron now pairs with an electron occupying one of the 2p orbitals.
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42. Electron Configurations
A convenient shorthand method for showing the electron configuration of an atom involves writing the energy level and the symbol for every sublevel occupied by an electron.
You indicate the number of electrons occupying that sublevel with a superscript.
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43. Electron Configurations
For hydrogen, with one electron in a 1s orbital, the electron configuration is written 1s1.
For oxygen, with two electrons in a 1s orbital, two electrons in a 2s orbital, and four electrons in 2p orbitals, the electron configuration is 1s22s22p4.
Note that the sum of the superscripts equals the number of electrons in the atom.
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44. CHEMISTRY & YOU
Explain why the correct electron configuration of oxygen is 1s22s22p4 and not 1s22s22p33s1.
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45. CHEMISTRY & YOU
Explain why the correct electron configuration of oxygen is 1s22s22p4 and not 1s22s22p33s1.
The 2p orbitals are lower in energy than the 3s orbital, so they will be completely filled before any electrons will be found in the 3s orbital.
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46. Writing Electron Configurations
Sample Problem 5.1
Writing Electron Configurations
The atomic number of phosphorus is 15. Write the electron configuration of a phosphorus atom.
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47. Apply the concepts to this problem.
Sample Problem 5.1
Apply the concepts to this problem.
Use the aufbau diagram to place electrons in the orbital with the lowest energy (1s) first.
Continue placing electrons in each orbital with the next higher energy level. 1s 2s 2p 3p 3s 4s
The electron configuration of phosphorus is 1s22s22p63s23p3.
The superscripts add up to the number of electrons.
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48. Solve Apply the concepts to this problem.
Sample Problem 5.1
Solve Apply the concepts to this problem. 2
Write the electron configuration.
The electron configuration of phosphorus is 1s22s22p63s23p3.
The superscripts add up to the number of electrons.
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49. Electron Configurations
Exceptional Electron Configurations
You can obtain correct electron configurations for the elements up to vanadium (atomic number 23) by following the aufbau diagram for orbital filling.
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50. Electron Configurations
Exceptional Electron Configurations
You can obtain correct electron configurations for the elements up to vanadium (atomic number 23) by following the aufbau diagram for orbital filling.
If you were to continue in that fashion, however, you would assign chromium and copper the following incorrect configurations.
Cr 1s22s22p63s23p63d44s2
Cu 1s22s22p63s23p63d94s2
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51. Electron Configurations
Exceptional Electron Configurations
The correct electron configurations are as follows:
Cr 1s22s22p63s23p63d54s1
Cu 1s22s22p63s23p63d104s1
These arrangements give chromium a half-filled d sublevel and copper a filled d sublevel.
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52. Electron Configurations
Exceptional Electron Configurations
Some actual electron configurations differ from those assigned using the aufbau principle because although half-filled sublevels are not as stable as filled sublevels, they are more stable than other configurations.
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53. What is the correct electron configuration of a sulfur atom?
A. 1s22s22p43s23p6
B. 1s22s22p63s23p3
C. 1s22s22p63s23p4
D. 1s22s22p63s63p2
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54. What is the correct electron configuration of a sulfur atom?
A. 1s22s22p43s23p6
B. 1s22s22p63s23p3
C. 1s22s22p63s23p4
D. 1s22s22p63s63p2
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55. Atomic Emission Spectra and the Quantum Mechanical Model
Revising the Atomic Model
Electron Arrangement in Atoms
Atomic Emission Spectra
and the Quantum
Mechanical Model
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56. What gives gas-filled lights their colors?
CHEMISTRY & YOU
What gives gas-filled lights their colors?
An electric current passing through the gas in each glass tube makes the gas glow with its own characteristic color.
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57. Light and Atomic Emission Spectra
The Nature of Light
By the year 1900, there was enough experimental evidence to convince scientists that light consisted of waves.
The amplitude of a wave is the wave’s height from zero to the crest.
The wavelength, represented by  (the Greek letter lambda), is the distance between the crests.
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58. Light and Atomic Emission Spectra
The Nature of Light
The frequency, represented by  (the Greek letter nu), is the number of wave cycles to pass a given point per unit of time.
The SI unit of cycles per second is called the hertz (Hz).
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59. Light and Atomic Emission Spectra
The Nature of Light
The product of frequency and wavelength equals a constant (c), the speed of light.
c = ln
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60. Light and Atomic Emission Spectra
The frequency () and wavelength () of light are inversely proportional to each other. As the wavelength increases, the frequency decreases.
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61. Light and Atomic Emission Spectra
The Nature of Light
According to the wave model, light consists of electromagnetic waves.
Electromagnetic radiation includes radio waves, microwaves, infrared waves, visible light, ultraviolet waves, X-rays, and gamma rays.
All electromagnetic waves travel in a vacuum at a speed of  108 m/s.
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62. Light and Atomic Emission Spectra
The Nature of Light
The sun and incandescent light bulbs emit white light, which consists of light with a continuous range of wavelengths and frequencies.
When sunlight passes through a prism, the different wavelengths separate into a spectrum of colors.
In the visible spectrum, red light has the longest wavelength and the lowest frequency.
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63. Light and Atomic Emission Spectra
The electromagnetic spectrum consists of radiation over a broad range of wavelengths.
Low energy
( = 700 nm)
High energy
( = 380 nm)
Frequency  (s-1)
3 x 106
3 x 1012
3 x 1022
102
10-8
10-14
Wavelength  (m)
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64. Light and Atomic Emission Spectra
When atoms absorb energy, their electrons move to higher energy levels. These electrons lose energy by emitting light when they return to lower energy levels.
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65. Light and Atomic Emission Spectra
A prism separates light into the colors it contains. White light produces a rainbow of colors.
Screen
Slit
Prism
Light
bulb
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66. Light and Atomic Emission Spectra
Light from a helium lamp produces discrete lines.
Screen
Slit
Prism
Helium
lamp
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67. Light and Atomic Emission Spectra
The energy absorbed by an electron for it to move from its current energy level to a higher energy level is identical to the energy of the light emitted by the electron as it drops back to its original energy level.
The wavelengths of the spectral lines are characteristic of the element, and they make up the atomic emission spectrum of the element.
No two elements have the same emission spectrum.
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68. Calculating the Wavelength of Light
Sample Problem 5.2
Calculating the Wavelength of Light
Calculate the wavelength of the yellow light emitted by a sodium lamp if the frequency of the radiation is 5.09 × 1014 Hz (5.09 × 1014/s).
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69. Analyze List the knowns and the unknown.
Sample Problem 5.2 1
Analyze List the knowns and the unknown.
Use the equation c = ln to solve for the unknown wavelength.
KNOWNS
frequency (n) = 5.09 × 1014 /s
c = × 108 m/s
UNKNOWN
wavelength (l) = ? m
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70. Calculate Solve for the unknown.
Sample Problem 5.2 2
Calculate Solve for the unknown.
Write the expression that relates the frequency and wavelength of light.
c = 
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71. Calculate Solve for the unknown.
Sample Problem 5.2
Calculate Solve for the unknown. 2
Rearrange the equation to solve for l.
Solve for l by dividing both sides by n: = n c ln
c = ln
l = n c
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72. Calculate Solve for the unknown.
Sample Problem 5.2
Calculate Solve for the unknown. 2
Substitute the known values for n and c into the equation and solve.
 = = = 5.89  10–7 m
c  108 m/s
  1014 /s
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73. Evaluate Does the answer make sense?
Sample Problem 5.2 3
Evaluate Does the answer make sense?
The magnitude of the frequency is much larger than the numerical value of the speed of light, so the answer should be much less than 1. The answer should have 3 significant figures.
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74. What is the frequency of a red laser that has a wavelength of 676 nm?
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75. What is the frequency of a red laser that has a wavelength of 676 nm?
c = ln c 
 =
 = = = 4.43  1014 /s
c  108 m/s
  10–7 m
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76. The Quantum Concept and Photons
The Quantization of Energy
German physicist Max Planck (1858–1947) showed mathematically that the amount of radiant energy (E) of a single quantum absorbed or emitted by a body is proportional to the frequency of radiation (n).
E n or E = hn
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77. The Quantum Concept and Photons
The Quantization of Energy
The constant (h), which has a value of  10–34 J·s (J is the joule, the SI unit of energy), is called Planck’s constant.
E n or E = hn
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78. The Quantum Concept and Photons
The Photoelectric Effect
Albert Einstein used Planck’s quantum theory to explain the photoelectric effect.
In the photoelectric effect, electrons are ejected when light shines on a metal.
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79. The Quantum Concept and Photons
The Photoelectric Effect
Not just any frequency of light will cause the photoelectric effect.
Red light will not cause potassium to eject electrons, no matter how intense the light.
Yet a very weak yellow light shining on potassium begins the effect.
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80. The Quantum Concept and Photons
The Photoelectric Effect
The photoelectric effect could not be explained by classical physics.
Classical physics correctly described light as a form of energy.
But, it assumed that under weak light of any wavelength, an electron in a metal should eventually collect enough energy to be ejected.
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81. The Quantum Concept and Photons
The Photoelectric Effect
To explain the photoelectric effect, Einstein proposed that light could be described as quanta of energy that behave as if they were particles.
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82. The Quantum Concept and Photons
The Photoelectric Effect
These light quanta are called photons.
Einstein’s theory that light behaves as a stream of particles explains the photoelectric effect and many other observations.
Light behaves as waves in other situations; we must consider that light possesses both wavelike and particle-like properties.
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83. The Quantum Concept and Photons
The Photoelectric Effect
No electrons are ejected because the frequency of the light is below the threshold frequency.
If the light is at or above the threshold frequency, electrons are ejected.
If the frequency is increased, the ejected electrons will travel faster.
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84. Calculating the Energy of a Photon
Sample Problem 5.3
Calculating the Energy of a Photon
What is the energy of a photon of microwave radiation with a frequency of 3.20 × 1011/s?
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85. Analyze List the knowns and the unknown.
Sample Problem 5.3 1
Analyze List the knowns and the unknown.
Use the equation E = h × n to calculate the energy of the photon.
KNOWNS
frequency (n) = 3.20 × 1011/s
h = × 10–34 J·s
UNKNOWN
energy (E) = ? J
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86. Calculate Solve for the unknown.
Sample Problem 5.3 2
Calculate Solve for the unknown.
Write the expression that relates the energy of a photon of radiation and the frequency of the radiation.
E = h n
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87. Calculate Solve for the unknown.
Sample Problem 5.3 2
Calculate Solve for the unknown.
Substitute the known values for n and h into the equation and solve.
E = h  = (6.626  10–34 J·s)  (3.20  1011/s)
= 2.12  10–22 J
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88. Evaluate Does the result make sense?
Sample Problem 5.3 3
Evaluate Does the result make sense?
Individual photons have very small energies, so the answer seems reasonable.
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89. What is the frequency of a photon whose energy is 1.166  10–17 J?
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90. What is the frequency of a photon whose energy is 1.166  10–17 J?
E = h n
n = h E
 = = =  1016 Hz
E  10–17 J·s
h  10–34 J
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91. An Explanation of Atomic Spectra
When an electron has its lowest possible energy, the atom is in its ground state.
In the ground state, the principal quantum number (n) is 1.
Excitation of the electron by absorbing energy raises the atom to an excited state with n = 2, 3, 4, 5, or 6, and so forth.
A quantum of energy in the form of light is emitted when the electron drops back to a lower energy level.
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92. An Explanation of Atomic Spectra
The light emitted by an electron moving from a higher to a lower energy level has a frequency directly proportional to the energy change of the electron.
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93. An Explanation of Atomic Spectra
The three groups of lines in the hydrogen spectrum correspond to the transition of electrons from higher energy levels to lower energy levels.
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94. CHEMISTRY & YOU
The glass tubes in lighted signs contain helium, neon, argon, krypton, or xenon gas, or a mixture of these gases. Why do the colors of the light depend on the gases that are used?
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95. CHEMISTRY & YOU
The glass tubes in lighted signs contain helium, neon, argon, krypton, or xenon gas, or a mixture of these gases. Why do the colors of the light depend on the gases that are used?
Each different gas has its own characteristic emission spectrum, creating different colors of light when excited electrons return to the ground state.
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96. In the hydrogen spectrum, which of the following transitions produces a spectral line of the greatest energy?
A. n = 2 to n = 1
B. n = 3 to n = 2
C. n = 4 to n = 3
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97. In the hydrogen spectrum, which of the following transitions produces a spectral line of the greatest energy?
A. n = 2 to n = 1
B. n = 3 to n = 2
C. n = 4 to n = 3
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98. Quantum Mechanics
Given that light behaves as waves and particles, can particles of matter behave as waves?
Louis de Broglie referred to the wavelike behavior of particles as matter waves.
His reasoning led him to a mathematical expression for the wavelength of a moving particle.
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99. The Wavelike Nature of Matter
Quantum Mechanics
The Wavelike Nature of Matter
Today, the wavelike properties of beams of electrons are useful in viewing objects that cannot be viewed with an optical microscope.
The electrons in an electron microscope have much smaller wavelengths than visible light.
These smaller wavelengths allow a much clearer enlarged image of a very small object, such as this pollen grain, than is possible with an ordinary microscope.
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100. Quantum Mechanics
Classical mechanics adequately describes the motions of bodies much larger than atoms, while quantum mechanics describes the motions of subatomic particles and atoms as waves.
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101. The Heisenberg Uncertainty Principle
Quantum Mechanics
The Heisenberg Uncertainty Principle
The Heisenberg uncertainty principle states that it is impossible to know both the velocity and the position of a particle at the same time.
This limitation is critical when dealing with small particles such as electrons.
But it does not matter for ordinary-sized objects such as cars or airplanes.
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102. To locate an electron, you might strike it with a photon.
Quantum Mechanics
To locate an electron, you might strike it with a photon.
The electron has such a small mass that striking it with a photon affects its motion in a way that cannot be predicted accurately.
The very act of measuring the position of the electron changes its velocity, making its velocity uncertain.
After collision: The impact changes the electron’s velocity, making it uncertain.
Before collision: A photon strikes an electron during an attempt to observe the electron’s position.
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103. The Heisenberg uncertainty principle states that it is impossible to simultaneously know which two attributes of a particle?
velocity and position
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