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Atomic Orbitals for Nitrogen: A Deep Dive into Electronic Structure
Nitrogen, a cornerstone element in the air we breathe and the molecules of life, boasts a fascinating electronic structure. Understanding its atomic orbitals is key to unlocking its reactivity, its role in biological systems, and its importance in countless industrial applications. This comprehensive guide delves into the intricacies of nitrogen's atomic orbitals, providing a detailed explanation accessible to both students and enthusiasts. We'll explore the fundamental principles, visualize the orbital shapes, and discuss the implications of nitrogen's electron configuration. Get ready to embark on a journey into the quantum world of this essential element!
Understanding Electron Configuration and Quantum Numbers
Before diving into the specifics of nitrogen's atomic orbitals, it's crucial to understand the basics of electron configuration and the quantum numbers that describe them. The electron configuration of an atom describes how electrons are distributed among its various energy levels and sublevels. These energy levels are further subdivided into sublevels, each characterized by a specific type of atomic orbital. The four quantum numbers—principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (ml), and spin quantum number (ms)—define the properties of each electron within an atom.
Principal Quantum Number (n): This number defines the energy level of an electron and its distance from the nucleus. Higher n values indicate higher energy levels and greater distance.
Azimuthal Quantum Number (l): This number describes the shape of the orbital. For a given n, l can range from 0 to n-1. l = 0 corresponds to an s orbital (spherical), l = 1 to a p orbital (dumbbell-shaped), l = 2 to a d orbital, and so on.
Magnetic Quantum Number (ml): This number specifies the orientation of the orbital in space. For a given l, ml can range from -l to +l, including 0. This means that p orbitals, for example (l=1), have three possible orientations (ml = -1, 0, +1).
Spin Quantum Number (ms): This number describes the intrinsic angular momentum of an electron, often referred to as its "spin." It can have a value of +1/2 or -1/2. The Pauli Exclusion Principle states that no two electrons in an atom can have the same set of four quantum numbers.
Nitrogen's Electron Configuration and Orbital Occupancy
Nitrogen (N) has an atomic number of 7, meaning it has seven protons and seven electrons in a neutral atom. Following the Aufbau principle (filling orbitals in order of increasing energy) and Hund's rule (maximizing unpaired electrons within a sublevel), nitrogen's electron configuration is 1s²2s²2p³.
This configuration tells us that:
Two electrons occupy the 1s orbital (n=1, l=0).
Two electrons occupy the 2s orbital (n=2, l=0).
Three electrons occupy the 2p orbitals (n=2, l=1). These three electrons occupy each of the three 2p orbitals individually, with parallel spins, due to Hund's rule.
Visualization of Nitrogen's Atomic Orbitals
The 1s and 2s orbitals are spherically symmetrical, with the 2s orbital being larger and at a higher energy level than the 1s orbital. The 2p orbitals, however, are dumbbell-shaped, each oriented along one of the three Cartesian axes (x, y, z). They are designated as 2px, 2py, and 2pz. Each 2p orbital can hold a maximum of two electrons with opposite spins. In nitrogen, each of these 2p orbitals contains one electron.
Significance of Nitrogen's Atomic Orbitals in Chemical Bonding
The partially filled 2p orbitals are responsible for nitrogen's ability to form covalent bonds. These unpaired electrons can participate in sharing electron pairs with other atoms, leading to the formation of stable molecules. Nitrogen's tendency to form three covalent bonds (as in ammonia, NH₃) is a direct consequence of its three unpaired 2p electrons. Its ability to form multiple bonds (as in nitrogen gas, N₂) is due to the overlap of p orbitals to create pi bonds in addition to sigma bonds.
Applications and Importance
Understanding nitrogen's atomic orbitals is essential in numerous fields. In chemistry, it helps explain nitrogen's reactivity and its role in various chemical reactions. In biology, it's crucial to understanding the structure and function of amino acids, proteins, and nucleic acids, all of which contain nitrogen atoms. In industry, nitrogen's unique properties, derived from its electronic structure, make it indispensable in fertilizer production, ammonia synthesis (Haber-Bosch process), and various other applications.
Ebook Outline: Atomic Orbitals of Nitrogen
Ebook Title: Unveiling the Secrets of Nitrogen: A Comprehensive Guide to its Atomic Orbitals
Outline:
Introduction: Hooking the reader, overview of the ebook's content.
Chapter 1: Fundamentals of Atomic Structure: Electron configuration, quantum numbers, orbital shapes.
Chapter 2: Nitrogen's Electronic Structure: Detailed explanation of nitrogen's electron configuration (1s²2s²2p³).
Chapter 3: Visualization of Nitrogen's Orbitals: 3D representations and explanations of 1s, 2s, and 2p orbitals.
Chapter 4: Chemical Bonding and Nitrogen: Explanation of nitrogen's bonding behavior (single, double, triple bonds).
Chapter 5: Applications and Significance: Role of nitrogen in various fields (chemistry, biology, industry).
Conclusion: Summary of key concepts and future directions.
Frequently Asked Questions (FAQs)
1. What is the difference between s and p orbitals? s orbitals are spherically symmetrical, while p orbitals are dumbbell-shaped.
2. How many electrons can a 2p orbital hold? A single 2p orbital can hold a maximum of two electrons.
3. Why does nitrogen form three bonds? Nitrogen has three unpaired electrons in its 2p orbitals, each capable of forming a covalent bond.
4. What is Hund's rule? Hund's rule states that electrons will individually occupy each orbital within a subshell before doubling up in any one orbital.
5. What is the significance of the Aufbau principle? The Aufbau principle dictates the order in which electrons fill atomic orbitals, starting with the lowest energy level.
6. How are nitrogen's atomic orbitals involved in the formation of ammonia (NH₃)? Nitrogen's three unpaired 2p electrons form covalent bonds with the three hydrogen atoms.
7. How does nitrogen's electronic structure relate to its reactivity? The presence of three unpaired electrons makes nitrogen relatively reactive, leading to the formation of diverse compounds.
8. What is the role of nitrogen in biological systems? Nitrogen is a crucial component of amino acids, proteins, and nucleic acids, essential for life.
9. What are some industrial applications of nitrogen? Nitrogen is used in fertilizers, ammonia synthesis, and as an inert atmosphere in various industrial processes.
Related Articles:
1. Understanding Electron Configuration: A basic introduction to electron configurations and their significance.
2. Quantum Numbers and Atomic Orbitals: A detailed explanation of quantum numbers and their relationship to orbital properties.
3. Covalent Bonding and Molecular Geometry: A guide to covalent bonding and how it influences molecular shapes.
4. The Haber-Bosch Process: An in-depth look at the industrial process of ammonia synthesis.
5. Nitrogen in Biological Systems: The importance of nitrogen in the structure and function of biological molecules.
6. Hybridization of Atomic Orbitals: Explanation of orbital hybridization and its role in molecular bonding.
7. Molecular Orbital Theory: An introduction to the theory that describes bonding in molecules using molecular orbitals.
8. Valence Bond Theory: A contrasting theory to molecular orbital theory, focusing on atomic orbitals.
9. Periodic Trends and Electron Configuration: How electron configuration relates to periodic trends in the periodic table.
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atomic orbital for nitrogen: Student Solutions Manual to Accompany Atkins' Physical Chemistry 11th Edition Peter Bolgar, Vladimiras Oleinikovas, Aimee North, Haydn Lloyd, James Keeler, Stephanie Smith, 2018 The Student Solutions Manual to accompany Atkins' Physical Chemistry 11th Edition provides full worked solutions to the 'a' exercises, and the odd-numbered discussion questions and problems presented in the parent book. The manual is intended for students and provides helpful comments and friendly advice to aid understanding. |
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atomic orbital for nitrogen: Electron Flow in Organic Chemistry Paul H. Scudder, 2023-10-06 Electron Flow in Organic Chemistry Teaches students to solve problems in Organic Chemistry using methods of analysis that are valuable and portable to other fields Electron Flow in Organic Chemistry provides a unique decision-based approach that develops a chemical intuition based on a crosschecked analysis process. Assuming only a general background in chemistry, this acclaimed textbook teaches students how to write reasonable reaction mechanisms and use analytical tools to solve both simple and complex problems in organic chemistry. As in previous editions, the author breaks down challenging organic mechanisms into a limited number of core elemental mechanistic processes, the electron flow pathways, to explain all organic reactions—using flow charts as decision maps, energy surfaces as problem space maps, and correlation matrices to display all possible interactions. The third edition features entirely new chapters on crosschecking chemical reactions through good mechanistic thinking and solving spectral analysis problems using organic structure elucidation strategies. This edition also includes more biochemical reaction mechanism examples, additional exercises with answers, expanded discussion of how general chemistry concepts can show that structure determines reactivity, and new appendix covering transition metal organometallics. Emphasizing critical thinking rather than memorization to solve mechanistic problems, this popular textbook: Features new and expanded material throughout, including more flowcharts, correlation matrices, energy surfaces, and algorithms that illustrate key decision-making processes Provides examples from the field of biochemistry of relevance to students in chemistry, biology, and medicine Incorporates principles from computer science and artificial intelligence to teach decision-making processes Contains a general bibliography, quick-reference charts and tables, pathway summaries, a major decisions guide, and other helpful tools Offers material for instructors including a solutions manual, supplemental exercises with detailed answers for each chapter usable as an exam file, and additional online resources Electron Flow in Organic Chemistry: A Decision-Based Guide to Organic Mechanisms, Third Edition, is the perfect primary textbook for advanced undergraduate or beginning graduate courses in organic reaction mechanisms, and an excellent supplement for graduate courses in physical organic chemistry, enzymatic reaction mechanisms, and biochemistry. |
atomic orbital for nitrogen: Structure in Protein Chemistry Jack Kyte, 2006-11-01 The second edition of Structure in Protein Chemistry showcases the latest developments and innovations in the field of protein structure analysis and prediction. The book begins by explaining how proteins are purified and describes methods for elucidating their sequences of amino acids and defining their posttranslational modifications. Comprehensive explanations of crystallography and of noncovalent forces-ionic interactions, hydrogen bonding, and the hydrophobic effect-act as a prelude to an exhaustive description of the atomic details of the structures of proteins. The resulting understanding of protein molecular structure forms the basis for discussions of the evolution of proteins, the symmetry of the oligomeric associations that produce them, and the chemical, mathematical, and physical basis of the techniques used to study their structures. The latter include image reconstruction, nuclear magnetic resonance spectroscopy, proton exchange, optical spectroscopy, electrophoresis, covalent cross-linking, chemical modification, immunochemistry, hydrodynamics, and the scattering of light, X-radiation, and neutrons. These procedures are applied to study the folding of polypeptides and the assembly of oligomers. Biological membranes and their proteins are also discussed. Structure in Protein Chemistry, Second Edition, bridges the gap between introductory biophysical chemistry courses and research literature. It serves as a comprehensive textbook for advanced undergraduates and graduate students in biochemistry, biophysics, and structural and molecular biology. Professionals engaged in chemical, biochemical, and molecular biological research will find it a useful reference. |
atomic orbital for nitrogen: EPR Spectroscopy Daniella Goldfarb, Stefan Stoll, 2018-03-06 This unique, self-contained resource is the first volume on electron paramagnetic resonance (EPR) spectroscopy in the eMagRes Handbook series. The 27 chapters cover the theoretical principles, the common experimental techniques, and many important application areas of modern EPR spectroscopy. EPR Spectroscopy: Fundamentals and Methods is presented in four major parts: A: Fundamental Theory, B: Basic Techniques and Instrumentation, C: High-Resolution Pulse Techniques, and D: Special Techniques. The first part of the book gives the reader an introduction to basic continuous-wave (CW) EPR and an overview of the different magnetic interactions that can be determined by EPR spectroscopy, their associated theoretical description, and their information content. The second provides the basics of the various EPR techniques, including pulse EPR, and EPR imaging, along with the associated instrumentation. Parts C and D builds on parts A and B and offer introductory accounts of a wide range of modern advanced EPR techniques, with examples of applications. The last two parts presents most of the new advances that do not appear in most of the classical EPR textbooks that focus on CW EPR. EPR Spectroscopy: Fundamentals and Methods contains, in concise form, all the material needed to understand state-of-the-art EPR spectroscopy at the graduate school/research level, whilst the editors have ensured that it presents the topic at a level accessible to newcomers to the field and others who want to know its range of application and how to apply it. |
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atomic orbital for nitrogen: Transition Metals in Biochemistry A. S. Brill, 2012-12-06 Transition metal ions in biological systems are of interest in biology, biochemistry, chemistry, medicine, and physics. Scien tists with rather different viewpoints, employing many methods, have contributed to this area. A concise review of the current state of the field will, to some extent, reflect the special knowledge of the person writing it - in this case application of physical methods to the investigation of metal coordination. x ray diffraction is one of the most important of these methods, but a useful treatment of X-ray structure analysis would be com parable in size with and beyond the scope of the monograph. Many results of X-ray diffraction studies are, of course, presented. Electron paramagnetic resonance spectroscopy has played a major part in the rapid advance in knowledge of the electronic struc tures of transition metal ions in biological systems. More gener ally, measurements involving light, microwaves, and magnetic fields are capable of producing much new information, and the required instrumentation is available at most research institu tions. Therefore light absorption and paramagnetic resonance are treated in depth. The principles described in the latter discus sions are broadly applicable, for example to the promising tech niques of X-ray spectroscopy (utilizing synchrotron radiation) and lanthanide-perturbed, very high-resolution nuclear magnetic resonance spectroscopy. |
atomic orbital for nitrogen: Structure and Bonding Jack Barrett, 2001 Structure and Bonding covers introductory atomic and molecular theory as given in first and second year undergraduate courses at university level. This book explains in non-mathematical terms where possible, the factors that govern covalent bond formation, the lengths and strengths of bonds and molecular shapes. Throughout the book, theoretical concepts and experimental evidence are integrated. An introductory chapter summarizes the principles on which the Periodic Table is established, and describes the periodicity of various atomic properties which are relevant to chemical bonding. Symmetry and group theory are introduced to serve as the basis of all molecular orbital treatments of molecules. This basis is then applied to a variety of covalent molecules with discussions of bond lengths and angles and hence molecular shapes. Extensive comparisons of valence bond theory and VSEPR theory with molecular orbital theory are included. Metallic bonding is related to electrical conduction and semi-conduction. The energetics of ionic bond formation and the transition from ionic to covalent bonding is also covered. Ideal for the needs of undergraduate chemistry students, Tutorial Chemistry Texts is a major series consisting of short, single topic or modular texts concentrating on the fundamental areas of chemistry taught in undergraduate science courses. Each book provides a concise account of the basic principles underlying a given subject, embodying an independent-learning philosophy and including worked examples. |
atomic orbital for nitrogen: Inorganic Chemistry for Geochemistry and Environmental Sciences George W. Luther, III, 2016-08-01 Inorganic Chemistry for Geochemistry and Environmental Sciences: Fundamentals and Applications discusses the structure, bonding and reactivity of molecules and solids of environmental interest, bringing the reactivity of non-metals and metals to inorganic chemists, geochemists and environmental chemists from diverse fields. Understanding the principles of inorganic chemistry including chemical bonding, frontier molecular orbital theory, electron transfer processes, formation of (nano) particles, transition metal-ligand complexes, metal catalysis and more are essential to describe earth processes over time scales ranging from 1 nanosec to 1 Gigayr. Throughout the book, fundamental chemical principles are illustrated with relevant examples from geochemistry, environmental and marine chemistry, allowing students to better understand environmental and geochemical processes at the molecular level. Topics covered include: • Thermodynamics and kinetics of redox reactions • Atomic structure • Symmetry • Covalent bonding, and bonding in solids and nanoparticles • Frontier Molecular Orbital Theory • Acids and bases • Basics of transition metal chemistry including • Chemical reactivity of materials of geochemical and environmental interest Supplementary material is provided online, including PowerPoint slides, problem sets and solutions. Inorganic Chemistry for Geochemistry and Environmental Sciences is a rapid assimilation textbook for those studying and working in areas of geochemistry, inorganic chemistry and environmental chemistry, wishing to enhance their understanding of environmental processes from the molecular level to the global level. |
atomic orbital for nitrogen: Organic Chemistry David R. Klein, 2020-12-22 In Organic Chemistry, 4th Edition, Dr. David Klein builds on the phenomenal success of the first three editions, with his skills-based approach to learning organic chemistry. The Klein program covers all the concepts typically covered in an organic chemistry course while placing a special emphasis on the skills development needed to support these concepts. Students in organic chemistry need to be able to bridge the gap between theory (concepts) and practice (problem-solving skills). Klein's SkillBuilder examples and activities offer extensive opportunities for students to develop proficiency in the key skills necessary to succeed in organic chemistry. |
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atomic orbital for nitrogen: From Quarks to the Universe Eleftherios N. Economou, 2015-12-15 This book takes the reader for a short journey over the structures of matter showing that their main properties can be obtained even at a quantitative level with a minimum background knowledge including, besides first year calculus and physics, the extensive use of dimensional analysis and the three cornerstones of science, namely the atomic idea, the wave-particle duality and the minimization of energy as the condition for equilibrium. Dimensional analysis employing the universal physical constants and combined with “a little imagination and thinking”, to quote Feynman, allow an amazing short-cut derivation of several quantitative results concerning the structures of matter. In the current 2nd edition, new material and more explanations with more detailed derivations were added to make the book more student-friendly. Many multiple-choice questions with the correct answers at the end of the book, solved and unsolved problems make the book also suitable as a textbook. This book is of interest to students of physics, engineering and other science and to researchers in physics, material science, chemistry and engineering who may find stimulating the alternative derivation of several real world results which sometimes seem to pop out the magician’s hat. |
atomic orbital for nitrogen: The Porphyrin Handbook Karl Kadish, Kevin M. Smith, Roger Guilard, 2000 The Porphyrin Handbook, Volume 17: Phthalocyanines: Properties and Materials provides information pertinent to every aspect of the chemistry, synthesis, spectroscopy, and structure of phthalocyanines. This book examines the biology and medical implications of porphyrin systems. Organized into five chapters, this volume begins with an overview of the effects of pressure, temperature, electromagnetic radiation, and particle impact on phthalocyanines. This text then examines. Other chapters consider the research on phthalocyanine thin films, with emphasis on studies that are concerned primarily with film structures. This book discusses as well the nature of the phthalocyanine aggregation process, how an aggregate is defined, and the issues of its bonding and structure. The final chapter deals with the advances in the design of composites of phthalocyanines or porphyrins and inorganic hosts and some of the most significant finding in the catalysis with these systems. This book is a valuable resource for research scientists, engineers, and clinicians. |
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atomic orbital for nitrogen: Solutions Manual to Accompany Inorganic Chemistry 7th Edition Alen Hadzovic, 2018 This solutions manual accompanies the 7th edition of Inorganic chemistry by Mark Weller, Tina Overton, Jonathan Rourke and Fraser Armstrong. As you master each chapter in Inorganic Chemistry, having detailed solutions handy allows you to confirm your answers and develop your ability to think through the problem-solving process. |
atomic orbital for nitrogen: Organic Chemistry Marye Anne Fox, James K. Whitesell, 2004 Accompanying CD-ROM ... has been enhanced with updated animated illustrations to accompany the presentations [and] Chem3D files for helpful structure visualization.--Page 4 of cover. |
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atomic orbital for nitrogen: Physical Chemistry for the Biosciences Raymond Chang, 2005-02-11 This book is ideal for use in a one-semester introductory course in physical chemistry for students of life sciences. The author's aim is to emphasize the understanding of physical concepts rather than focus on precise mathematical development or on actual experimental details. Subsequently, only basic skills of differential and integral calculus are required for understanding the equations. The end-of-chapter problems have both physiochemical and biological applications. |
atomic orbital for nitrogen: Pericyclic Chemistry Dipak Kumar Mandal, 2018-03-26 Pericyclic Chemistry: Orbital Mechanisms and Stereochemistry is a complete guide to the topic that is ideal for graduate students, advanced undergraduate students and researchers in organic chemistry. An introduction to molecular orbital theory and relevant stereochemical concepts is provided as background, with all four classes of pericyclic reactions discussed and illustrated with orbital picture representations. Also included are chapters on cycloadditions, the most versatile class, and electrocyclic reactions, sigmatropic rearrangements and group transfer reactions. A separate chapter on the construction of correlation diagrams is also included, emphasizing a practical, hands on approach. Author Dipak Kumar Mandal brings over 30 years of teaching experience to the topic and illuminates pericyclic chemistry with a clear and fresh perspective. - Comprehensive guide featuring unifying mechanistic approaches, stereochemical details and novel rules and mnemonics to delineate product stereochemistry - Includes two background chapters on molecular orbitals and stereochemical concepts - Emphasizes a theoretical understanding using perturbation theory (Salem-Klopman equation) and physical insights from orbital and state correlation analyses |
atomic orbital for nitrogen: The Chemical Physics of Surfaces S. Morrison, 2012-12-06 * At the present stage of development of surface science, there has seemed to be a need for a book-length review spanning the disciplines of surface physics and surface chemistry-a review to summarize and show the con nection between the observations from each discipline. The various results and theories, derived on the one hand from studies of the physical, electronic, and optical properties of surfaces and on the other hand from studies of the chemical activity of surfaces, supplement each other in the search for a realistic model of the surface. The improved understanding possible with such an interdisciplinary approach has been confirmed by recent develop ments which cannot be classified as either surface chemistry or surface physics. Specifically, recent new experimental techniques and quantum mechanical models have provided a much more accurate picture of the nature of the electronic energy levels (bonding orbitals) present at a solid surface. With this more accurate picture we are now able to reconcile the various chemical and physical models that appeared in the early literature on surfaces. The objective of this work has therefore been to describe the results and current models of surface science spanning a broad gray area between surface physics and surface chemistry with some overlap into each of these disciplines. Relevant aspects of surface chemistry are discussed; we cover chemical interactions where bonding and electronic properties dominate, but stop short of specialized topics such as surfactants or liquid/liquid interfaces. |
atomic orbital for nitrogen: Quantum Computational Chemistry Taku Onishi, 2017-09-22 This book is for both theoretical and experimental chemists to begin quantum molecular orbital calculations for functional materials. First, the theoretical background including the molecular orbital calculation method and modelling are explained. This is followed by an explanation of how to do modelling and calculation and to interpret calculated molecular orbitals, with many research examples in the field of batteries, catalysts, organic molecules and biomolecules. Finally, future trends in computational chemistry are introduced. |
atomic orbital for nitrogen: Mathematical Methods in Chemistry and Physics M.E. Starzak, 1989-03-31 Imposingly thick text derived from a one-semester course intended to acquaint advanced undergraduate (and beginning graduate) students with the concepts and methods of linear mathematics. Though physics is referred to in the title, the book is in almost every organizational and notational respect |
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atomic orbital for nitrogen: Bonding in Electron-Rich Molecules Richard D. Harcourt, 2015-10-30 This second edition was updated to include some of the recent developments, such as “increased-valence” structures for 3-electron-3-centre bonding, benzene, electron conduction and reaction mechanisms, spiral chain O4 polymers and recoupled-pair bonding. The author provides qualitative molecular orbital and valence-bond descriptions of the electronic structures for primarily electron-rich molecules, with strong emphasis given to the valence-bond approach that uses “increased-valence” structures. He describes how “long-bond” Lewis structures as well as standard Lewis structures are incorporated into “increased-valence” structures for electron-rich molecules. “Increased-valence” structures involve more electrons in bonding than do their component Lewis structures, and are used to provide interpretations for molecular electronic structure, bond properties and reactivities. Attention is also given to Pauling “3-electron bonds”, which are usually diatomic components of “increased-valence” structures for electron-rich molecules. |
atomic orbital for nitrogen: BIOS Instant Notes in Chemistry for Biologists Julie Fisher, John Arnold, 2003-09-25 Instant Notes in Chemistry for Biologists is a concise book for undergraduates who have a limited background in chemistry. This book covers the main concepts in chemistry, provides simple explanations of chemical terminology, and illustrates underlying principles and phenomena in the life sciences with clear biological examples. Building on the success of the first edition, the second edition has been fully revised and updated and comprises new sections on water as a biological solvent, inorganic molecules and biological macromolecules. |
atomic orbital for nitrogen: Modeling Marvels Errol G. Lewars, 2008-12-05 The aim of this highly original book is to survey a number of chemical compounds that some chemists, theoretical and experimental, find fascinating. This is the first book to feature compounds/classes of compounds of theoretical interest that have been studied theoretically but have defied synthesis. It is hoped that this collection of idiosyncratic molecules will appeal to chemists who find the study of chemical oddities interesting and, on occasion, even rewarding. |
atomic orbital for nitrogen: Text Book of Coordination Chemistry R. K. Sharma, 2007 This book Power Series has been written for the students of B.A./B.Sc., of all Indian universities. Each chapter of this book contains complete theory and a fairly large number of solved examples. Sufficient problems have also been selected from various universities examination paper and included in the end of each chapter. Contents: Power Series and Double Series, Uniform Convergence, Fourier Series and Riemann Integral. |
atomic orbital for nitrogen: SiC, Natural and Synthetic Diamond and Related Materials A.A. Gippius, R. Helbig, J.P.F. Sellschop, 1992-04-24 This volume addresses the burgeoning field of wide band gap materials. The 64 contributed and invited papers will do much to stimulate the well-justified ongoing work, both theoretical and experimental, in this area. The high standard of the papers attests to the significant progress that has been made in this field, as well as reporting on the challenging problems that still remain to be solved. |
atomic orbital for nitrogen: Symmetry and Structure Sidney F. A. Kettle, 1995-06-15 This revised and updated edition emphasizes the physical concepts and applications of group theory rather than complex mathematics. User-friendly, it offers a simple approach to space groups, answering many frequently asked questions in detail. Features a new chapter on solid state, scores of diagrams and problems and more questions and answers. Mathematical proofs are included in the appendices. |
atomic orbital for nitrogen: Maths for Chemistry Paul Monk, Lindsey J. Munro, 2021-08-11 Mathematical skills and concepts lie at the heart of chemistry, yet they are the aspect of the subject that many students fear the most. Maths for Chemistry recognizes the challenges faced by many students in equipping themselves with the maths skills necessary to gain a full understanding of chemistry. Working from foundational principles, the book builds the student's confidence by leading them through the subject in a steady, progressive way from basic algebra to quantum mathematics. Opening with the core mathematics of algebra, logarithms and trigonometry, the book goes on to cover calculus, matrices, vectors, complex numbers, and laboratory mathematics to cover everything that a chemistry student needs. With its modular structure, the book presents material in short, manageable sections to keep the content as accessible and readily digestible as possible. Maths for Chemistry is the perfect introduction to the essential mathematical concepts which all chemistry students should master. |
atomic orbital for nitrogen: Quantum Mechanics for Chemists David O. Hayward, 2002 This book is designed to provide chemistry undergraduates with a basic understanding of the principles of quantum mechanics. |
atomic orbital for nitrogen: BIOS Instant Notes in Organic Chemistry Graham Patrick, 2003-11-27 Instant Notes in Organic Chemistry Second Edition condenses the essentials of organic chemistry into a manageable text. It concentrates solely on the basics without going into exhaustive detail or repetitive examples, with the key notes at the start of each topic focusing the mind on the essentials. The first six sections cover structure, bonding, functional groups, stereochemistry, and basic reaction and mechanism theory. The rest of the book looks at the reactions and mechanisms of the common functional groups important in chemistry and biochemistry, with an additional section on spectroscopy and analysis. |
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