Rayner-Canham et al., Descriptive Inorganic Chemistry 5th Edition 2010
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Descriptive
Inorganic Chemistry
FIFTH EDITION
Geoff Rayner-Canham Sir Wilfred Grenfell College Memorial University Tina Overton University of Hull W. H. FREEMAN AND COMPANY NEW YORK
Publisher: Clancy Marshall
Acquisitions Editors: Jessica Fiorillo/Kathryn Treadway
Marketing Director: John Britch Media Editor: Dave Quinn Cover and Text Designer: Vicki Tomaselli Senior Project Editor: Mary Louise Byrd Illustrations: Network Graphics/Aptara Senior Illustration Coordinator: Bill Page Production Coordinator: Susan Wein Composition: Aptara Printing and Binding: World Color Versailles Library of Congress Control Number: 2009932448ISBN-13: 978-1-4292-2434-5
ISBN-10: 1-4292-1814-2
@2010, 2006, 2003, 2000 by W. H. Freeman and Company
All rights reserved Printed in the United States of America First printing W. H. Freeman and Company41 Madison Avenue New York, NY 10010 Houndmills, Basingstoke RG21 6XS, England
Overview
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Contents
Contents
Contents
CHAPTER 24 ON THE WEB www.whfreeman.com/descriptive5e The Rare Earth and Actinoid Elements 651w
24.1 The Group 3 Elements 653w
24.2 The Lanthanoids 653w
Superconductivity 655w
23.3 The Actinoids 656w
24.4 Uranium 659w
A Natural Fission Reactor 661w
24.5 The Postactinoid Elements 662w
ON THE
Appendix 9 Standard Half-Cell Electrode Potentials of Selected Elements A-25w
ON THE
Appendix 10 Electron Confi guration of the Elements A-35w
Contents
escriptive inorganic chemistry was traditionally concerned with the prop- erties of the elements and their compounds. Now, in the renaissance of
D
the subject, with the synthesis of new and novel materials, the properties are being linked with explanations for the formulas and structures of compounds together with an understanding of the chemical reactions they undergo. In addition, we are no longer looking at inorganic chemistry as an isolated subject but as a part of essential scientifi c knowledge with applications throughout science and our lives. Because of a need for greater contextualization, we have added more features and more applications.
In many colleges and universities, descriptive inorganic chemistry is offered as a sophomore or junior course. In this way, students come to know something of the fundamental properties of important and interesting elements and their compounds. Such knowledge is important for careers not only in pure or applied chemistry but also in pharmacy, medicine, geology, and environmental science. This course can then be followed by a junior or senior course that focuses on the theoretical principles and the use of spectroscopy to a greater depth than is covered in a descriptive text. In fact, the theoretical course builds nicely on the descriptive background. Without the descriptive grounding, however, the theory becomes sterile, uninteresting, and irrelevant.
Education has often been a case of the “swinging pendulum,” and this has been true of inorganic chemistry. Up until the 1960s, it was very much pure descriptive, requiring exclusively memorization. In the 1970s and 1980s, upper-level texts focused exclusively on the theoretical principles. Now it is ap- parent that descriptive is very important—not the traditional memorization of facts but the linking of facts, where possible, to underlying principles. Students need to have modern descriptive inorganic chemistry as part of their educa- tion. Thus, we must ensure that chemists are aware of the “new descriptive inorganic chemistry.”
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Inorganic chemistry goes beyond academic interest: it is an im- portant part of our lives.
norganic chemistry is interesting—more than that—it is exciting! So much of our twenty-fi rst-century science and technology rely on natural and syn-
I thetic materials, often inorganic compounds, many of which are new and novel.
Inorganic chemistry is ubiquitous in our daily lives: household products, some pharmaceuticals, our transportation—both the vehicles themselves and the synthesis of the fuels—battery technology, and medical treatments. There is the industrial aspect, the production of all the chemicals required to drive our economy, everything from steel to sulfuric acid to glass and cement. Environ- mental chemistry is largely a question of the inorganic chemistry of the atmo- sphere, water, and soil. Finally, there are the profound issues of the inorganic chemistry of our planet, the solar system, and the universe.
This textbook is designed to focus on the properties of selected interesting, important, and unusual elements and compounds. However, to understand inorganic chemistry, it is crucial to tie this knowledge to the underlying chemi- cal principles and hence provide explanations for the existence and behavior of compounds. For this reason, almost half the chapters survey the relevant concepts of atomic theory, bonding, intermolecular forces, thermodynamics, acid-base behavior, and reduction-oxidation properties as a prelude to, and preparation for, the descriptive material.
For this fi fth edition, the greatest change has been the expansion of coverage of the 4d and 5d transition metals to a whole chapter. The heavier transition metals have unique trends and patterns, and the new chapter highlights these. Having an additional chapter on transition met- als also better balances the coverage between the main group elements and the transition elements. Also, the fi fth edition has a second color. With the addition of a second color, fi gures are much easier to understand, and tables and text are easier to read. On a chapter-by-chapter basis, the signifi cant improvements are as follows:
Chapter 1: The Electronic Structure of the Atom: A Review Introduction and Section 1.3, The Polyelectronic Atom, have been revised. The Chapter 3: Covalent Bonding Network Covalent Substances, has a new subsection: Amorphous Section 3.11, Silicon. Chapter 4: Metallic Bonding Nanometal Particles, was added. Section 4.6, Magnetic Properties of Metals, was added.
Preface
Chapter 5: Ionic Bonding Section 5.3, Polarization and Covalency, has a new subsection: The Ionic- Covalent Boundary. Section 5.4, Ionic Crystal Structures, has a new subsection: Quantum Dots. Chapter 9: Periodic Trends Section 9.3, Isoelectronic Series in Covalent Compounds, has been revised and improved. Section 9.8, The “Knight’s Move” Relationship, has been revised and improved. Chapter 10: Hydrogen Section 10.4, Hydrides, has a revised and expanded subsection: Ionic Hydrides. Chapter 11: The Group 1 Elements Section 11.14, Ammonium Ion as a Pseudo–Alkali-Metal Ion, moved from Chapter 9. Chapter 13: The Group 13 Elements Section 13.10, Aluminides, was added. Chapter 14: The Group 14 Elements Section 14.2, Contrasts in the Chemistry of Carbon and Silicon, was added. Section 14.3, Carbon, has a new subsection: Graphene. Section 14.7, Carbon Dioxide, has a new subsection: Carbonia. Chapter 15: The Group 15 Elements Section 15.2, Contrasts in the Chemistry of Nitrogen and Phosphorus, was added. Section 15.18, The Pnictides, was added. Chapter 16: The Group 16 Elements Section 16.2, Contrasts in the Chemistry of Oxygen and Sulfur, was added. Section 16.14, Sulfi des, has a new subsection: Disulfi des. Chapter 17: The Group 17 Elements Section 17.2, Contrasts in the Chemistry of Fluorine and Chlorine, was added. Section 17.12, Cyanide Ion as a Pseudo-halide Ion, moved from Chapter 9. Chapter 18: The Group 18 Elements Section 18.7, Other Noble Gas Compounds, was added. Chapter 19: Transition Metal Complexes Section 19.10, Ligand Field Theory, was added. Chapter 20: Properties of the 3d Transition Metals Section 20.1, Overview of the 3d Transition Metals, was added.
Chapter 21: Properties of the 4d and 5d Transition Metals
EW HAPTERN C added (for details, see the previous page).
Chapter 24: The Rare Earth and Actinoid Elements This chapter has been signifi cantly revised with the new subsections Scandium,Preface ALSO Video Clips
Descriptive inorganic chemistry by defi nition is visual, so what better way to appreciate a chemical reaction than to make it visual? We now have a series of
at least 60 Web-based video clips to bring some of the reactions to life. The text has a margin icon to indicate where a reaction is illustrated.
Text Figures and Tables
All the illustrations and tables in the book are available as .jpg fi les for inclusion in PowerPoint presentations on the instructor side of the Web site at
Additional Resources CIENTIFIC MERICAN
A list of relevant S A articles is found on the text Web site at The text has a margin icon to indicate where a Scientifi c American article is available.
Supplements
The Student Solutions Manual, ISBN: 1-4292-2434-7 contains the worked solutions to all the odd-numbered end-of-chapter problems.
The Companion Web Site
Contains the following student-friendly materials: Chapter 24: The Rare Earth and Actinoid Elements, Appendices, Lab Experiments, Tables, and over 50 useful videos of elements and metals in reactions and oxidations.
Instructor’s Resource CD-ROM, ISBN: 1-4292-2428-2
Includes PowerPoint and videos as well as all text art and solutions to all prob- lems in the book. This textbook was written to pass on to another generation our fascination with descriptive inorganic chemistry. Thus, the comments of readers, both stu- dents and instructors, will be sincerely appreciated. Any suggestions for added or updated additional readings are also welcome. Our current e-mail addresses are grcanham@swgc.mun.ca and T.L.Overton@hull.ac.uk.
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any thanks must go to the team at W. H. Freeman and Company who have contributed their talents to the fi ve editions of this book. We offer our sincere
M
gratitude to the editors of the fi fth edition, Jessica Fiorillo, Kathryn Treadway, and Mary Louise Byrd; of the fourth edition, Jessica Fiorillo, Jenness Crawford, and Mary Louise Byrd; of the third edition, Jessica Fiorillo and Guy Copes; of the second edition, Michelle Julet and Mary Louise Byrd; and a special thanks to Deborah Allen, who bravely commissioned the fi rst edition of the text. Each one of our fabulous editors has been a source of encouragement, support, and helpfulness.
We wish to acknowledge the following reviewers of this edition, whose criticisms and comments were much appreciated: Theodore Betley at Harvard University; Dean Campbell at Bradley University; Maria Contel at Brooklyn College (CUNY); Gerry Davidson at St. Francis College; Maria Derosa at Carleton University; Stan Duraj at Cleveland State University; Dmitri Giarkios at Nova Southeastern University; Michael Jensen at Ohio University–Main Campus; David Marx at the University of Scranton; Joshua Moore at Tennessee State University–Nashville; Stacy O’Reilly at Butler University; William Pen- nington at Clemson University; Daniel Rabinovich at the University of North Carolina at Charlotte; Hal Rogers at California State University–Fullerton; Thomas Schmedake at the University of North Carolina at Charlotte; Bradley Smucker at Austin College; Sabrina Sobel at Hofstra University; Ronald Strange at Fairleigh Dickinson University–Madison; Mark Walters at New York University; Yixuan Wang at Albany State University; and Juchao Yan at Eastern New Mexico University; together with prereviewers: Londa Borer at California State University–Sacramento; Joe Fritsch at Pepperdine Univer- sity; Rebecca Roesner at Illinois Wesleyan University, and Carmen Works at Sonoma College.
We acknowledge with thanks the contributions of the reviewers of the fourth edition: Rachel Narehood Austin at Bates College; Leo A. Bares at the University of North Carolina—Asheville; Karen S. Brewer at Hamilton College; Robert M. Burns at Alma College; Do Chang at Averett University; Georges Dénès at Concordia University; Daniel R. Derringer at Hollins University; Carl P. Fictorie at Dordt College; Margaret Kastner at Bucknell University; Michael Laing at the University of Natal, Durban; Richard H. Langley at Stephen F. Austin State University; Mark R. McClure at the University of North Carolina at Pembroke; Louis Mercier at Laurentian University; G. Merga at Andrews University; Stacy O’Reilly at Butler University; Larry D. Pedersen at College Misercordia; Robert D. Pike at the College of William and Mary; William Quintana at New Mexico State University; David F. Rieck at Salisbury University; John Selegue at the University of Kentucky; Melissa M. Strait at Alma College; Daniel J. Williams at Kennesaw State University; Juchao Yan at Eastern New Mexico University; and Arden P. Zipp at the State University of New York at Cortland.
Acknowledgments
And the contributions of the reviewers of the third edition: François Caron at Laurentian University; Thomas D. Getman at Northern Michigan Univer- sity; Janet R. Morrow at the State University of New York at Buffalo; Robert
D. Pike at the College of William and Mary; Michael B. Wells at Cambell Uni- versity; and particularly Joe Takats of the University of Alberta for his compre- hensive critique of the second edition.
And the contributions of the reviewers of the second edition: F. C. Hentz at North Carolina State University; Michael D. Johnson at New Mexico State University; Richard B. Kaner at the University of California, Los Angeles; Richard H. Langley at Stephen F. Austin State University; James M. Mayer at the University of Washington; Jon Melton at Messiah College; Joseph S. Merola at Virginia Technical Institute; David Phillips at Wabash College; John R. Pladziewicz at the University of Wisconsin, Eau Claire; Daniel Rabinovich at the University of North Carolina at Charlotte; David F. Reich at Salisbury State University; Todd K. Trout at Mercyhurst College; Steve Watton at the Virginia Commonwealth University; and John S. Wood at the University of Massachusetts, Amherst.
Likewise, the reviewers of the fi rst edition: E. Joseph Billo at Boston Col- lege; David Finster at Wittenberg University; Stephen J. Hawkes at Oregon State University; Martin Hocking at the University of Victoria; Vake Marganian at Bridgewater State College; Edward Mottel at the Rose-Hulman Institute of Technology; and Alex Whitla at Mount Allison University.
As a personal acknowledgment, Geoff Rayner-Canham wishes to especial- ly thank three teachers and mentors who had a major infl uence on his career: Briant Bourne, Harvey Grammar School; Margaret Goodgame, Imperial Col- lege, London University; and Derek Sutton, Simon Fraser University. And he expresses his eternal gratitude to his spouse, Marelene, for her support and encouragement.
Tina Overton would like to thank her colleague Phil King for his invaluable suggestions for improvements and his assistance with the illustrations. Thanks must also go to her family, Dave, John, and Lucy, for their patience during the months when this project fi lled all her waking hours.
hemistry is a human endeavor. New discoveries are the result of the work of enthusiastic people and groups of people who want to explore the
C
molecular world. We hope that you, the reader, will come to share our own fascination with inorganic chemistry. We have chosen to dedicate this book to two scientists who, for very different reasons, never did receive the ultimate accolade of a Nobel Prize.
Henry Moseley (1887–1915)
Although Mendeleev is identifi ed as the discoverer of the peri- odic table, his version was based on an increase in atomic mass. In some cases, the order of elements had to be reversed to match properties with location. It was a British scientist, Henry Moseley, who put the periodic table on a much fi rmer footing by discov- ering that, on bombardment with electrons, each element emit- ted X-rays of characteristic wavelengths. The wavelengths fi tted a formula related by an integer number unique to each element. We know that number to be the number of protons. With the es- tablishment of the atomic number of an element, chemists at last knew the fundamental organization of the table. Sadly, Moseley was killed at the battle of Gallipoli in World War I. Thus, one of the brightest scientifi c talents of the twentieth century died at the age of 27. The famous American scientist Robert Milliken commented: “Had the European War had no other result than the snuffi ng out of this young life, that alone would make it one of the most hideous and most irreparable crimes in history.” Unfortunately, Nobel Prizes are only awarded to living scientists. In 1924, the discovery of element 43 was claimed, and it was named mose- leyum; however, the claim was disproved by the very method that Moseley had pioneered.
Dedication Lise Meitner (1878–1968)
In the 1930s, scientists were bombarding atoms of heavy elements such as uranium with subatomic particles to try to make new ele- ments and extend the periodic table. Austrian scientist Lise Meit- ner had shared leadership with Otto Hahn of the German research team working on the synthesis of new elements; the team thought they had discovered nine new elements. Shortly after the claimed discovery, Meitner was forced to fl ee Germany because of her Jewish ancestry, and she settled in Sweden. Hahn reported to her that one of the new elements behaved chemically just like barium. During a famous “walk in the snow” with her nephew, physicist Otto Frisch, Meitner realized that an atomic nucleus could break in two just like a drop of water. No wonder the element formed behaved like barium: it was barium! Thus was born the concept of nuclear fi ssion. She informed Hahn of her proposal. When Hahn wrote the research paper on the work, he barely mentioned the vital contribution of Meitner and Frisch. As a result, Hahn and his colleague
Fritz Strassmann received the Nobel Prize. Meitner’s fl ash of genius was ignored. Only recently has Meitner received the acclaim she deserved by the naming of an element after her, element 109, meitnerium.
Additional reading H. G. J. Moseley. University of California Press, Berkeley, 1974.
Heibron, J. L.
Women in Chemistry: Rayner-Canham, M. F., and G. W. Rayner-Canham. Their Changing Roles from Alchemical Times to the Mid-Twentieth Century. Chemical Heritage Foundation, Philadelphia, 1998.
Lise Meitner: A Life in Physics. University of California Press, Sime, R. L. Berkeley, 1996.
Discovery of the Elements, 7th ed. Journal Weeks, M. E., and H. M. Leicester. of Chemical Education, Easton, PA, 1968.
To understand the behavior of inorganic compounds, we need to study the nature of chemical bonding. Bonding, in turn, relates to the behavior of electrons in the constituent atoms. Our study of inorganic chemistry,
1.1 The Schrödinger Wave therefore, starts with a review of the models of the atom and a survey of
Equation and Its Signifi cance the probability model’s applications to the electron confi gurations of atoms
Atomic Absorption Spectroscopy and ions.
1.2 Shapes of the Atomic Orbitals
1.3 The Polyelectronic Atom saac Newton was the original model for the absentminded professor.
1.4 Ion Electron Confi gurations
Supposedly, he always timed the boiled egg he ate at breakfast; one
1.5 Magnetic Properties of Atoms
I
morning, his maid found him standing by the pot of boiling water, hold-
1.6 Medicinal Inorganic Chemistry:
ing an egg in his hand and gazing intently at the watch in the bottom
An Introduction
of the pot! Nevertheless, it was Newton who initiated the study of the electronic structure of the atom in about 1700, when he noticed that the passage of sunlight through a prism produced a continuous visible spectrum. Much later, in 1860, Robert Bunsen (of burner fame) inves- tigated the light emissions from fl ames and gases. Bunsen observed that the emission spectra, rather than being continuous, were series of colored lines (line spectra).
The proposal that electrons existed in concentric shells had its origin in the research of two overlooked pioneers: Johann Jakob Balmer, a Swiss mathematician, and Johannes Robert Rydberg, a Swedish physicist. After an undistinguished career in mathematics, in 1885, at the age of 60, Balmer studied the visible emission lines of the hydrogen atom and found that there was a mathematical relationship between the wave- lengths. Following from Balmer’s work, in 1888, Rydberg deduced a more general relationship:
1
1
1
5 R H
2
2
2 a b
l n n f i where l is the wavelength of the emission line, R is a constant, later H known as the Rydberg constant, and n and n are integers. For the f i visible lines seen by Balmer and Rydberg, n had a value of 2. The f Rydberg formula received further support in 1906, when Theodore
CHAPTER 1 • The Electronic Structure of the Atom: A Review
FIGURE 1.1 The Rutherford-
. The sensitivity of this method is extremely high, and concentrations of parts per million are easy to determine; some elements can be detected at the parts per billion level. Atomic absorption spectroscopy has now become a routine analytical tool in chemistry, metal- lurgy, geology, medicine, forensic science, and many other fi elds of science—and it simply requires the movement of electrons from one energy level to another.
In 1955, two groups of scientists, one in Australia and the other in Holland, fi nally realized that the absorption method could be used to detect the presence of elements at very low concentrations. Each element has a particu- lar absorption spectrum corresponding to the various separations of (differences between) the energy levels in its atoms. When light from an atomic emission source is passed through a vaporized sample of an element, the particular wavelengths corresponding to the various en- ergy separations will be absorbed. We fi nd that the higher the concentration of the atoms, the greater the proportion of the light that will be absorbed. This linear relationship between light absorption and concentration is known as Beer’s law
However, in the early nineteenth century, a German sci- entist, Josef von Fraunhofer, noticed that the visible spec- trum from the Sun actually contained a number of dark bands. Later investigators realized that the bands were the result of the absorption of particular wavelengths by cooler atoms in the “atmosphere” above the surface of the Sun. The electrons of these atoms were in the ground state, and they were absorbing radiation at wavelengths corresponding to the energies needed to excite them to higher energy states. A study of these “negative” spectra led to the discovery of helium. Such spectral studies are still of great importance in cosmochemistry—the study of the chemical composition of stars.
A glowing body, such as the Sun, is expected to emit a continuous spectrum of electromagnetic radiation.
Bohr electron-shell model of the atom, showing the n 5 1, 2, and 3 energy levels.
corresponding to the Rydberg formula with n f 5 1. Then in 1908, Friedrich Paschen discovered a series of far-infrared hydrogen lines, fi tting the equation with n f 5 3.
In 1913, Niels Bohr, a Danish physicist, became aware of Balmer’s and Rydberg’s experimental work and of the Rydberg formula. At that time, he was trying to combine Ernest Rutherford’s planetary model for electrons in an atom with Max Planck’s quantum theory of energy exchanges. Bohr contended that an electron orbiting an atomic nucleus could only do so at certain fi xed distances and that whenever the electron moved from a higher to a lower orbit, the atom emitted characteristic electromagnetic radiation.
1 !Ze
2 n #
3 n #
n #
However, the Rutherford-Bohr model had a number of fl aws. For example, the spectra of multi-electron atoms had far more lines than the simple Bohr model predicted. Nor could the model explain the splitting of the spectral lines in a magnetic fi eld (a phenomenon known as the Zeeman effect). Within a short time, a radically different model, the quantum mechanical model, was proposed to account for these observations.
Rydberg had deduced his equation from experimental observations of atomic hydrogen emission spectra. Bohr was able to derive the same equation from quantum theory, showing that his theoretical work meshed with reality. From this result, the Rutherford-Bohr model of the atom of concentric elec- tron “shells” was devised, mirroring the recurring patterns in the periodic table of the elements (Figure 1.1). Thus the whole concept of electron energy levels can be traced back to Rydberg. In recognition of Rydberg’s contribution, excited atoms with very high values of the principal quantum number, n, are called Rydberg atoms.
$E # hv
1.1 The Schrödinger Wave Equation and Its Signifi cance
The more sophisticated quantum mechanical model of atomic structure was derived from the work of Louis de Broglie. De Broglie showed that, just as elec- tromagnetic waves could be treated as streams of particles (photons), moving particles could exhibit wavelike properties. Thus, it was equally valid to picture electrons either as particles or as waves. Using this wave-particle duality, Erwin Schrödinger developed a partial differential equation to represent the behavior of an electron around an atomic nucleus. One form of this equation, given here for a one-electron atom, shows the relationship between the wave function of the electron, C, and E and V, the total and potential energies of the system, re- spectively. The second differential terms relate to the wave function along each of the Cartesian coordinates x, y, and z, while m is the mass of an electron, and
h is Planck’s constant.
2
2
2
2
° ° ° 8p m
1
1
1
1E 2 V2° 5 0
2
2
2
2
0x 0y 0z h The derivation of this equation and the method of solving it are in the realm of physics and physical chemistry, but the solution itself is of great importance to inorganic chemists. We should always keep in mind, however, that the wave equation is simply a mathematical formula. We attach meanings to the solution simply because most people need concrete images to think about subatomic phenomena. The conceptual models that we create in our macroscopic world cannot hope to reproduce the subatomic reality.
It was contended that the real meaning of the equation could be found
2
from the square of the wave function, C , which represents the probability of fi nding the electron at any point in the region surrounding the nucleus. There are a number of solutions to a wave equation. Each solution describes a different orbital and, hence, a different probability distribution for an elec- tron in that orbital. Each of these orbitals is uniquely defi ned by a set of three integers: n, l, and m . Like the integers in the Bohr model, these integers are l also called quantum numbers. In addition to the three quantum numbers derived from the original theory, a fourth quantum number had to be defi ned to explain the results of an experi- ment in 1922. In this experiment, Otto Stern and Walther Gerlach found that passing a beam of silver atoms through a magnetic fi eld caused about half the atoms to be defl ected in one direction and the other half in the opposite direc- tion. Other investigators proposed that the observation was the result of two different electronic spin orientations. The atoms possessing an electron with one spin were defl ected one way, and the atoms whose electron had the oppo- site spin were defl ected in the opposite direction. This spin quantum number was assigned the symbol m . s
The possible values of the quantum numbers are defi ned as follows:
n
, the principal quantum number, can have all positive integer values from CHAPTER 1 • The Electronic Structure of the Atom: A Review FIGURE 1.2 The possible sets n
1
2 of quantum numbers for n 5 1 and n 5 2. l
1 m %1 !1 l
1s 2s 2p l , the angular momentum quantum number, can have all integer values from n 2 1 to 0. m , the magnetic quantum number, can have all integer values from 1l l through 0 to 2l.
1
1 m , the spin quantum number, can have values of 1 and 2 . s
2
2 When the value of the principal quantum number is 1, there is only one
possible set of quantum numbers n, l, and m (1, 0, 0), whereas for a principal l quantum number of 2, there are four sets of quantum numbers (2, 0, 0; 2, 1, –1; 2, 1, 0; 2, 1, 11). This situation is shown diagrammatically in Figure 1.2. To identify the electron orbital that corresponds to each set of quantum numbers, we use the value of the principal quantum number n, followed by a letter for the angular momentum quantum number l. Thus, when n 5 1, there is only the 1s orbital.
When n 5 2, there is one 2s orbital and three 2p orbitals (corresponding to the m values of 11, 0, and –1). The letters s, p, d, and f are derived from l categories of the spectral lines: sharp, principal, diffuse, and fundamental. The correspondences are shown in Table 1.1.
When the principal quantum number n 5 3, there are nine sets of quantum numbers (Figure 1.3). These sets correspond to one 3s, three 3p, and fi ve 3d orbitals. A similar diagram for the principal quantum number n 5 4 would show 16 sets of quantum numbers, corresponding to one 4s, three 4p, fi ve 4d,
Correspondence between angular momentum TABLE 1.1 number l and orbital designation
Orbital designation l Value s
1 p
2 d
3 f
FIGURE 1.3 The possible sets n
3 of quantum numbers for n 5 3. l
1
2 m l !1
%1 %2 %1 !1 !2 3s 3p 3d
and seven 4f orbitals (Table 1.2). Theoretically, we can go on and on, but as we will see, the f orbitals represent the limit of orbital types among the elements of the periodic table for atoms in their electronic ground states.
Correspondence between angular momentum TABLE 1.2 number l and number of orbitals
Number of orbitals l Value
1
1
3
2
5
3
7
Representing the solutions to a wave equation on paper is not an easy task. In fact, we would need four-dimensional graph paper (if it existed) to display the complete solution for each orbital. As a realistic alternative, we break the wave equation into two parts: a radial part and an angular part.
Each of the three quantum numbers derived from the wave equation rep- resents a different aspect of the orbital: The principal quantum number n indicates the size of the orbital. The angular momentum quantum number l represents the shape of the orbital. The magnetic quantum number m represents the spatial direction of the l orbital. The spin quantum number m has little physical meaning; it merely allows s two electrons to occupy the same orbital. It is the value of the principal quantum number and, to a lesser extent the angular momentum quantum number, which determines the energy of the electron. Although the electron may not literally be spinning, it behaves as if it was, and it has the magnetic properties expected for a spinning particle.
An orbital diagram is used to indicate the probability of fi nding an electron
CHAPTER 1 • The Electronic Structure of the Atom: A Review
found as an area of high electron density. Conversely, locations with a low prob- ability are called areas of low electron density.
The s Orbitals
The s orbitals are spherically symmetric about the atomic nucleus. As the prin- cipal quantum number increases, the electron tends to be found farther from the nucleus. To express this idea in a different way, we say that, as the principal quantum number increases, the orbital becomes more diffuse. A unique fea- ture of electron behavior in an s orbital is that there is a fi nite probability of fi nding the electron close to, and even within, the nucleus. This penetration by
s
orbital electrons plays a role in atomic radii (see Chapter 2) and as a means of studying nuclear structure.
Same-scale representations of the shapes (angular functions) of the 1s and 2s orbitals of an atom are compared in Figure 1.4. The volume of a 2s orbital is about four times greater than that of a 1s orbital. In both cases, the tiny nucleus is located at the center of the spheres. These spheres represent the region in which there is a 99 percent probability of fi nding an electron. The total prob- ability cannot be represented, for the probability of fi nding an electron drops to zero only at an infi nite distance from the nucleus.
The probability of fi nding the electron within an orbital will always be posi- tive (since the probability is derived from the square of the wave function and squaring a negative makes a positive). However, when we discuss the bonding of atoms, we fi nd that the sign related to the original wave function has impor- tance. For this reason, it is conventional to superimpose the sign of the wave function on the representation of each atomic orbital. For an s orbital, the sign is positive.
In addition to the considerable difference in size between the 1s and the 2s orbitals, the 2s orbital has, at a certain distance from the nucleus, a spherical surface on which the electron density is zero. A surface on which the probabil- ity of fi nding an electron is zero is called a nodal surface. When the principal quantum number increases by 1, the number of nodal surfaces also increases by 1. We can visualize nodal surfaces more clearly by plotting a graph of the ra- dial density distribution function as a function of distance from the nucleus for any direction. Figure 1.5 shows plots for the 1s, 2s, and 3s orbitals. These plots show that the electron tends to be farther from the nucleus as the principal quantum number increases. The areas under all three curves are the same.
FIGURE 1.4 Representations ofthe shapes and comparative sizes of the 1s and 2s orbitals.
1.2 Shapes of the Atomic Orbitals 1s
Probability 2s 3s
Probability Probability 0.2 0.4 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1.0 1.2 Distance (nm)
Distance (nm) Distance (nm)
FIGURE 1.5 The variation of the radial density distribution function with distance from the nucleus for electrons in the 1s, 2s, and 3s orbitals of a hydrogen atom.Electrons in an s orbital are different from those in p, d, or f orbitals in two signifi cant ways. First, only the s orbital has an electron density that varies in the same way in every direction out from the atomic nucleus. Second, there is a fi nite probability that an electron in an s orbital is at the nucleus of the atom. Every other orbital has a node at the nucleus.
The p Orbitals
Unlike the s orbitals, the p orbitals consist of two separate volumes of space (lobes), with the nucleus located between the two lobes. Because there are three p orbitals, we assign each orbital a direction according to Cartesian co- ordinates: we have p , p , and p . Figure 1.6 shows representations of the three x y z 2p orbitals. At right angles to the axis of higher probability, there is a nodal plane through the nucleus. For example, the 2p orbital has a nodal surface in z the xy plane. In terms of wave function sign, one lobe is positive and the other negative.
FIGURE 1.6 Representations of the shapes of the 2p x , 2p y , and 2p z orbitals. CHAPTER 1 • The Electronic Structure of the Atom: A Review FIGURE 1.7 The variation of 2s 2p the radial density distribution function with distance from the nucleus for electrons in the 2s and
Probability Probability 2p orbitals of a hydrogen atom.
0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 Distance (nm) Distance (nm)