Chapter 6. Electronic Structure of Atoms
Media Resources
Figures and Tables in Transparency Pack: Section:
Figure 6.3 Electromagnetic Waves 6.1 The Wave Nature of Light
Table 6.1 Common Wavelength Units for 6.1 The Wave Nature of Light
Electromagnetic Radiation
Figure 6.4 The Electromagnetic Spectrum 6.1 The Wave Nature of Light
ml through n = 4
Figure 6.17 Energy Levels in the Hydrogen Atom 6.5 Quantum Mechanics and Atomic Orbitals
Figure 6.18 Radial Probability Distributions for the 6.6 Representations of Orbitals
1s, 2s, and 3s Orbitals of Hydrogen
Figure 6.21 Probability Density [
(r)]2 in the 1s, 6.6 Representations of Orbitals
2s and 3s Orbitals of Hydrogen
Figure 6.22 The p Orbitals 6.6 Representations of Orbitals
Activities: Section:
Electromagnetic Spectrum 6.1 The Wave Nature of Light
Bohr Model 6.3 Line Spectra and the Bohr Model
Animations: Section:
Photoelectric Effect 6.2 Quantized Energy and Photons
Movies: Section:
Flame Tests for Metals 6.3 Line Spectra and the Bohr Model
Electronic Structure of Atoms
73
Other Resources
Further Readings: Section:
Scientific American, September 2004 6.2 Quantized Energy and Photons
Put Body to Them! 6.2 Quantized Energy and Photons
Presenting the Bohr Atom 6.3 Line Spectra and the Bohr Model
Getting the Numbers Right–The Lonely Struggle 6.3 Line Spectra and the Bohr Model
of Rydberg
Quantum Reality
A Student’s Travels, Close Dancing, Bathtubs, 6.5 Quantum Mechanics and Atomic Orbitals
and the Shopping Mall: More Analogies in
Teaching Introductory Chemistry
The Mole, the Periodic Table, and Quantum 6.5 Quantum Mechanics and Atomic Orbitals
Numbers: An Introductory Trio
Electron Densities: Pictorial Analogies for 6.6 Representations of Orbitals
Apparent Ambiguities in Probability
Calculations
Mind over Matter 6.7 Many-Electron Atoms
Aufbau Principle
Housing Electrons: Relating Quantum Numbers, 6.8 Electron Configurations
Energy Levels, and Electron Configurations
Pictorial Analogies VII: Quantum Numbers and 6.8 Electron Configurations
Orbitals
The Quantum Shoe Store and Electron Structure 6.8 Electron Configurations
Chapter 6
74
The Noble Gas Configuration—Not the Driving 6.8 Electron Configurations
Live Demonstrations: Section:
Simple and Inexpensive Classroom Demonstration 6.8 Electron Configurations
of Nuclear Magnetic Resonance and Magnetic
Resonance Imaging
Electronic Structure of Atoms
75
Chapter 6. Electronic Structure of Atoms
Common Student Misconceptions
• Some students have difficulty converting between angstroms, nanometers, etc. and meters.
• Students often have difficulty switching from the language of certainties to the language of
probabilities.
Teaching Tips
• This is often students’ first glimpse at the realm of quantum theory. They need to understand that the
model has been built up to rationalize experimental data. They also need to know that elements of
one theory are maintained in the subsequent theory.
cannot tell where each one currently is. You can know position or path, but not both.
Lecture Outline
6.1 The Wave Nature of Light
1
,
2
,
3
,
4
• The electronic structure of an atom refers to the arrangement of electrons.
• Visible light is a form of electromagnetic radiation or radiant energy.
• Radiation carries energy through space.
• Electromagnetic radiation is characterized by its wave nature.
• All waves have a characteristic wavelength,
(lambda), and amplitude, A.
• The frequency,
(nu), of a wave is the number of cycles that pass a point in one second.
• The units of
are hertz (1 Hz = 1 s–1).
Chapter 6
76
• The speed of a wave is given by its frequency multiplied by its wavelength.
• For light, speed, c =
,
• Electromagnetic radiation moves through a vacuum with a speed of 3.00 108 m/s.
FORWARD REFERENCES
• X-Ray diffraction will be discussed in Chapter 12.
• Light emitting diodes will be described in Chapter 11 (section 11.7).
6.2 Quantized Energy and Photons
• Some phenomena can’t be explained using a wave model of light:
• Blackbody radiation is the emission of light from hot objects.
• The photoelectric effect is the emission of electrons from metal surfaces on which light shines.
• Emission spectra are the emissions of light from electronically excited gas atoms.
Hot Objects and the Quantization of Energy
• Heated solids emit radiation (black body radiation)
• The wavelength distribution depends on the temperature (i.e., fired hot” objects are cooler than
fiwhite hot” objects).
• Planck investigated black body radiation.
The Photoelectric Effect and Photons
5
,
6
,
7
,
8
• The photoelectric effect provides evidence for the particle nature of light.
• It also provides evidence for quantization.
• Einstein assumed that light traveled in energy packets called photons.
• The energy of one photon is E = h
.
• Light shining on the surface of a metal can cause electrons to be ejected from the metal.
• The electrons will only be ejected if the photons have sufficient energy (work function):
• Below the threshold frequency no electrons are ejected.
Electronic Structure of Atoms
77
• Above the threshold frequency, the excess energy appears as the kinetic energy of the ejected
electrons.
• Light has wave-like AND particle-like properties.
FORWARD REFERENCES
• Photoconductivity in solar energy conversions and emission of photons by semiconductor
6.3 Line Spectra and the Bohr Model
Line Spectra
9
,
10
,
11
• Radiation composed of only one wavelength is called monochromatic.
• Radiation that spans a whole array of different wavelengths is called continuous.
• When radiation from a light source, such as a lightbulb, is separated into its different wavelength
components, a spectrum is produced.
Bohr’s Model
12
,
13
• Rutherford assumed that electrons orbited the nucleus analogous to planets orbiting the sun.
• However, a charged particle moving in a circular path should lose energy.
• This means that the atom should be unstable according to Rutherford’s theory.
9
Figure 6.9 from Transparency Pack
10
fiFlame Tests for Metals” Movie from Instructor’s Resource CD/DVD
Chapter 6
78
The Energy States of the Hydrogen Atom
14
,
15
,
16
• Colors from excited gases arise because electrons move between energy states in the atom.
• Since the energy states are quantized, the light emitted from excited atoms must be quantized and
appear as line spectra.
• The first orbit in the Bohr model has n = 1 and is closest to the nucleus.
• The furthest orbit in the Bohr model has n = and corresponds to E = 0.
• Electrons in the Bohr model can only move between orbits by absorbing and emitting energy in
quanta (E = h
).
• The ground state is the lowest energy state.
Limitations of the Bohr Model
17
,
18
• The Bohr Model has several limitations:
• It cannot explain the spectra of atoms other than hydrogen.
• Electrons do not move about the nucleus in circular orbits.
• However, the model introduces two important ideas:
• The energy of an electron is quantized: electrons exist only in certain energy levels described by
quantum numbers.
• Energy gain or loss is involved in moving an electron from one energy level to another.
FORWARD REFERENCES
• Absorption of sufficient amount of energy to ionize an atom will be further discussed in
Chapter 7 (section 7.4).
14
fiGetting the Numbers Right–The Lonely Struggle of Rydberg” from Further Readings
15
Figure 6.12 from Transparency Pack
Electronic Structure of Atoms
79
6.4 The Wave Behavior of Matter
19
• Knowing that light has a particle nature, it seems reasonable to ask whether matter has a wave nature.
• This question was answered by Louis deBroglie.
• Using Einstein’s and Planck’s equations, deBroglie derived:
The Uncertainty Principle
20
,
21
• Heisenberg’s uncertainty principle: we cannot determine the exact position, direction of motion,
and speed of subatomic particles simultaneously.
• For electrons: we cannot determine their momentum and position simultaneously.
6.5 Quantum Mechanics and Atomic Orbitals
22
,
23
• Schrödinger proposed an equation containing both wave and particle terms.
• Solving the equation leads to wave functions,
.
• The wave function describes the electron’s matter wave.
Orbitals and Quantum Numbers
24
,
25
,
26
,
27
• If we solve the Schrödinger equation we get wave functions and energies for the wave
functions.
• We call
orbitals.
• Schrödinger’s equation requires three quantum numbers:
• Principal quantum number, n. This is the same as Bohr’s n.
• As n becomes larger, the atom becomes larger and the electron is further from the nucleus.
• Angular momentum quantum number, l. This quantum number depends on the value of n.
19
fiOn a Relation between the Heisenberg and deBroglie Principles” from Further Readings
20
fiIntroducing the Uncertainty Principle Using Diffraction of Light Waves” from Further Readings
Chapter 6
80
• The values of l begin at 0 and increase to n – 1.
• We usually use letters for l (s, p, d and f for l = 0, 1, 2, and 3). Usually we refer to the s, p, d and f
orbitals.
• This quantum number defines the shape of the orbital.
6.6 Representations of Orbitals
28
,
29
The s Orbitals
30
,
31
,
32
• All s orbitals are spherical.
• As n increases, the s orbitals get larger.
• As n increases, the number of nodes increases.
• A node is a region in space where the probability of finding an electron is zero.
•
= 0 at a node.
• For an s orbital the number of nodes is given by n – 1.
28
fiThe Origin of the s, p, d, f Orbital Labels” from Further Readings
29
fiElectron Densities: Pictorial Analogies for Apparent Ambiguities in Probability Calculations” from
Further Readings
30
fiRadial Electron Distribution” Animation from Instructor’s Resource CD/DVD
Electronic Structure of Atoms
81
The d and f Orbitals
34
• There are five d and seven f orbitals.
• Three of the d orbitals lie in a plane bisecting the x-, y-, and z-axes.
FORWARD REFERENCES
• An overlap of atomic orbitals will be introduced in Chapter 9 (section 9.4).
• Hybridization of atomic orbitals will be discussed in Chapter 9 (section 9.5).
6.7 Many-Electron Atoms
Orbitals and Their Energies
35
,
36
,
37
• In a many-electron atom, for a given value of n,
• The energy of an orbital increases with increasing value of l.
• Orbitals of the same energy are said to be degenerate.
Electron Spin and the Pauli Exclusion Principle
38
• Line spectra of many electron atoms show each line as a closely spaced pair of lines.
• Stern and Gerlach designed an experiment to determine why.
• A beam of atoms was passed through a slit and into a magnetic field and the atoms were then
detected.
34
Figure 6.23 from Transparency Pack
35
Figure 6.24 from Transparency Pack
Chapter 6
82
6.8 Electron Configurations
39
,
40
,
41
,
42
,
43
• Electron configurations tell us how the electrons are distributed among the various orbitals of an
atom.
• The most stable configuration, or ground state, is that in which the electrons are in the lowest possible
energy state.
Hund’s Rule
44
,
45
,
46
,
47
,
48
,
49
,
50
,
51
,
52
,
53
• Hund’s rule: for degenerate orbitals, the lowest energy is attained when the number of electrons with
the same spin is maximized.
• Thus, electrons fill each orbital singly with their spins parallel before any orbital gets a second
electron.
• By placing electrons in different orbitals, electron-electron repulsions are minimized.
Condensed Electron Configurations
54
• Electron configurations may be written using a shorthand notation (condensed electron
configuration):
47
fiHousing Electrons: Relating Quantum Numbers, Energy Levels, and Electron Configurations” from
Further Readings
48
fiPictorial Analogies VII: Quantum Numbers and Orbitals” from Further Readings
49
fiThe Quantum Shoe Store and Electron Structure” from Further Readings
50
Table 6.3 from Transparency Pack
51
fiElectron Configuration” Activity from Instructor’s Resource CD/DVD
52
fiSome Analogies for Teaching Atomic Structure at the High School Level” from Further Readings
Electronic Structure of Atoms
83
Transition Metals
• After Ar the d orbitals begin to fill.
• After the 3d orbitals are full the 4p orbitals begin to fill.
• The ten elements between Ti and Zn are called the transition metals or transition elements.
The Lanthanides and Actinides
• The 4f orbitals begin to fill with Ce.
• Note: The electron configuration of La is [Xe]6s25d1.
• The actinide elements are radioactive and most are not found in nature.
FORWARD REFERENCES
• Periodic properties associated with electron configurations, such as atomic radii, ionization
energies and electron affinities, will be discussed throughout Chapter 7.
• Valence electrons and the Octet Rule will be discussed in Chapter 8.
• Valence electrons of atoms within molecules and ions will be added and distributed according
6.9 Electron Configurations and the Periodic Table
55
,
56
,
57
,
58
,
59
• The periodic table can be used as a guide for electron configurations.
• The period number is the value of n.
• Groups 1A and 2A have their s orbitals being filled.
• Groups 3A–8A have their p orbitals being filled.
• The s-block and p–block of the periodic table contain the representative, or main-group, elements.
• Groups 3B–2B have their d orbitals being filled.
• The lanthanides and actinides have their f orbitals being filled.
Chapter 6
84
Anomalous Electron Configurations
• There are many elements that appear to violate the electron configuration guidelines.
• Examples:
• Chromium is [Ar]3d54s1 instead of [Ar]3d44s2.
• Copper is [Ar]3d104s1 instead of [Ar]3d94s2.
• Half-full (d5) and full (d10) d subshells are particularly stable.
FORWARD REFERENCES
Electronic Structure of Atoms
85
Further Readings:
1. Robert R. Perkins, fiPut Body to Them!” J. Chem. Educ., Vol. 72, 1995, 151–152. This reference
includes analogies for quantized states.
6. Max Tegmark and John Archibald Wheeler, fi100 Years of Quantum Mysteries,” Scientific American,
February 2001, 68–75.
7. Dennis R. Sievers, fiNiels Bohr,” J. Chem. Educ., Vol. 59, 1982, 303–304. A short biography of Niels
Bohr.
8. Pedro L. Muiño, fiIntroducing the Uncertainty Principle Using Diffraction of Light Waves,” J. Chem.
Educ., Vol. 77, 2000, 1025–1027.
12. Mali Yin and Raymond S. Ochs, fiThe Mole, the Periodic Table, and Quantum Numbers: An
Introductory Trio,” J. Chem. Educ., Vol. 78, 2001, 1345–1347.
13. Ronald J. Gillespie, James N. Spencer and Richard S. Moog, fiDemystifying Introductory Chemistry;
Part 1. Electron Configurations from Experiment,” J. Chem. Educ., Vol. 73, 1996, 617–622. The use of
experimental data to investigate electron configurations is presented in this reference.
14. Ngai Ling Ma, fiQuantum Analogies on Campus,” J. Chem. Educ., Vol. 73, 1996, 1016–1017.
Chapter 6
86
21. M. Bonneau, fiThe Quantum Shoe Store and Electron Structure,” J. Chem. Educ., Vol. 68, 1991, 837.
22. Robert D. Freeman, fi‘New’ Schemes for Applying the Aufbau Principle,” J. Chem. Educ., Vol. 67,
1990, 576.
26. Mark Fischetti, fiSeeing Inside,” Scientific American, August 2004, 92–93. A short article on medical
imaging devices.
27. Lyn Gladden, fiThe Magnetic Eye,” Chemistry in Britain, November 2000, 35–37. A short article
about the work of Wolfgang Pauli.
28. Roland Schmid, fiThe Noble Gas Configuration–Not the Driving Force but the Rule of the Game in
Chemistry,” J. Chem. Educ., Vol. 80, 2003, 931–937.
32. Suzanne T. Mabrouk, fiThe Periodic Table as a Mnemonic Device for Writing Electronic
Configurations,” J. Chem. Educ., Vol. 80, 2003, 894–898.
Live Demonstrations
1. Joel A. Olson, Karen J. Nordell, Marla A. Chesnik, Clark R. Landis, Arthur B. Ellis, M.S. Rzchowski,
S. Michael Condren, George C. Lisensky, and James W. Long, fiSimple and Inexpensive Classroom
Demonstration of Nuclear Magnetic Resonance and Magnetic Resonance Imaging,” J. Chem. Educ., Vol.
77, 2000, 882–889.