Inorganic Chemistry A

Transcription

1 Inorganic Chemistry A CHEMA 3320 نموذج لخطة مساق الك م اء الغ ر عضو ة أ الجاهعة اإلسالهية غزة كلية: العلوم قسن: الكيوياء الفصل الدراس : االول العام الدراس : 2014/2013 مدرس المساق: د. سع د محمود الكردي أوال : وصف المساق المفاه م األساس ة ف الك م اء غ ر العضو ة و الذرة والرموز الخاصة بالتوز ع اإللكترون ثم الروابط والترك ب البنائ ف الجز ئات ثنائ ة ومتعددة الذرات والتماثل والمجموعات النقط ة. وترك ب المركبات األ ون ة وك م اء بعض األ ونات وك م اء المذ بات والمحال ل والحوامض والقواعد الجدول الدوري وك م اء العناصر النموذج ة. 1

2 ثان ا : األهداف العامة للمساق هدف هذا المساق بصورة عامة إلى تعر ف الطالب بأساس ات الك م اء غ ر العضو ة و الت حتاجها الطالب خالل دراسته التخصص ة و الت تمثل ارض ة تأسس ة لفروع الك م اء المختلفة المتصلة بدراستهم مما ؤدي إلى تنم ة القدرة على التفك ر العلم المبن على قواعد علم ة ثابتة تنم لد هم اتجاهات تطب ق ة. ثالثا : محتوى المساق: ( مفردات المساق و توز عها على الفصل الدراس ) المحتوى Basic concepts: atoms Basic concepts: molecules امتحان نصف Nuclear properties الفصل األول %20. An introduction to molecular symmetry Bonding in polyatomic molecules Structures and energetics of metallic and ionic solids امتحان نصف الفصل الثان %20. Acids, bases and ions in aqueous solution Reduction and oxidation االمتحان النهائ Non-aqueous media %50 األول والثان األسبوع الثالث والرابع الخامس السادس السابع الثامن والتاسع العاشر - الثان عشر الثالث عشر الرابع عشر والخامس عشر 2

3 رابعا : مخرجات المساق : معرفة وفهم المبادئ األساس ة ف الك م اء الغ ر عضو ة واستخدامها لحل المسائل المتعلقة بموضوعات المنهاج باإلضافة إلى تحق ق أهداف المساق. خامسا : أسلوب تدر س المساق : تم شرح الموضوعات العلم ة السابقة بأسلوب المحاضرة والنقاش واستخدام المجسمات ح ن لزومها تعقد مناقشة للمسائل ف نها ة كل وحدة. و تم تكل ف الطلبة بواجبات ب ت ه و امتحانات سر عة على كل وحدة. سادسا : مراجع المساق: المرجع الرئ س )الكتاب المقرر(: Inorganic Chemistry/ Catherine E. Housecroft & Alan G. Sharpe / 3 rd edition (2008) المراجع اإلضاف ة Inorganic Chemistry /Miessler and Tarr (1991) Advanced Inorganic Chemistry / Cotton, Wilkinson / 5 th Ed. (1988( Dr. Said M. El-Kurdi 6 3

4 سابعا : الساعات المكتب ة : السبت واالثن ن 9-10 األحد والثالثاء مبنى اإلدارة الطابق الثالث - كل ة العلوم لالتصال: skurdi@iugaza.edu.ps ثامنا : متطلبات دراسة المساق : الحضور الواجبات الب ت ة االختبارات القص رة تاسعا : التق م: أ- أعمال الفصل )...% ) و تشمل : 1. امتحان النصف األول % امتحان النصف الثان % الواجبات الب ت ة %10 4. اختبارات قص رة %5. ب- اختبار نها ة الفصل )%50 (. Dr. Said M. El-Kurdi 7 Chapter 1 Basic concepts: atoms Dr. Said M. El-Kurdi 8 4

5 1.1 Introduction Inorganic chemistry: it is not an isolated branch of chemistry Inorganic chemistry is the chemistry of all elements except carbon. Inorganic chemistry is not simply the study of elements and compounds; it is also the study of physical principles. Dr. Said M. El-Kurdi 9 To understand why some compounds are soluble in a given solvent and others are not, we apply laws of thermodynamics. If our aim is to propose details of a reaction mechanism, then a knowledge of reaction kinetics is needed. Study of molecular structure. In the solid state, X-ray diffraction methods are routinely used to obtain pictures of the spatial arrangements of atoms in a molecule or molecular ion. Dr. Said M. El-Kurdi 10 5

6 To interpret the behaviour of molecules in solution, we use physical techniques such as nuclear magnetic resonance (NMR) spectroscopy. In Chapters 1 and 2, we will outline some concepts fundamental to an understanding of inorganic chemistry. Dr. Said M. El-Kurdi Fundamental particles of an atom An atom is the smallest unit quantity of an element that is capable of existence, either alone or in chemical combination with other atoms of the same or another element. The fundamental particles of which atoms are composed are the proton, electron and neutron. Dr. Said M. El-Kurdi 12 6

7 Table 1.1 Properties of the proton, electron and neutron. Dr. Said M. El-Kurdi Atomic number, mass number and isotopes Nuclides, atomic number and mass number Dr. Said M. El-Kurdi 14 7

8 Relative atomic mass Since the electrons are of minute mass, the mass of an atom essentially depends upon the number of protons and neutrons in the nucleus. We define the atomic mass unit as 1/12th of the mass of a 12 6C atom so that it has the value kg. atomic masses (A r ) are thus all stated relative to 12 6 C = The masses of the proton and neutron can be considered to be 1u where u is the atomic mass unit (1 u kg). Dr. Said M. El-Kurdi 15 Isotopes Nuclides of the same element possess the same number of protons and electrons but may have different mass numbers Nuclides of a particular element that differ in the number of neutrons and, therefore, their mass number, are called isotopes Isotopes of some elements occur naturally while others may be produced artificially. Dr. Said M. El-Kurdi 16 8

9 Elements that occur naturally with only one nuclide are 31 monotopic and include phosphorus, and fluorine, 19 P F 15 9 Elements that exist as mixtures of isotopes include 12 6 C and 13 6 C 16 8 O, 17 8 O and 18 8 O Dr. Said M. El-Kurdi 17 Relative atomic mass, Dr. Said M. El-Kurdi 18 9

10 Do not confuse isotope and allotrope! Allotropes of an element are different structural modifications of that element. S 8 Dr. Said M. El-Kurdi 19 Mass number of isotope (% abundance) Ruthenium Ru 96(5.52) 98(1.88) 99(12.7) 100(12.6) 101(17.0) 102(31.6) 104(18.7) Fig. 1.1 Mass spectrometric traces for atomic Ru Dr. Said M. El-Kurdi 20 10

11 1.4 Successes in early quantum theory Atomic Structure The structures of hydrogenic atoms Initially, we consider hydrogen-like or hydrogenic atoms, which have only one electron and so are free of the complicating effects of electron electron repulsions. Then we use the concepts these atoms introduce to build up an approximate description of the structures of manyelectron atoms (or polyelectron atoms), which are atoms with more than one electron. We saw that electrons in an atom occupy a region of space around the nucleus. The importance of electrons in determining the properties of atoms, ions and molecules, including the bonding between or within them, means that we must have an understanding of the electronic structures of each species. It is not possible to discus the electronic structure without reference to quantum theory and wave mechanics. 11

12 In brief, classical mechanics 1) predicts a precise trajectory for particles, with precisely specified locations and momenta at each instant. 2) allows the translational, rotational, and vibrational modes of motion to be excited to any energy simply by controlling the forces that are applied. Careful experiments show that classical mechanics fails when applied to the transfers of very small energies and to objects of very small mass. Waves Waves are disturbances that travel through space with a finite velocity Waves can be characterized by a wave equation, a differential equation that describes the motion of the wave in space and time. Harmonic waves are waves with displacements that can be expressed as sine or cosine functions. A harmonic wave at a particular instant in time. A is the amplitude and λ is the wavelength. 12

13 Electromagnetic Radiation In 1873 James Clerk Maxwell proposed that visible light consists of electromagnetic waves. In particular, his model accurately describes how energy in the form of radiation can be propagated through space as vibrating electric and magnetic fields. The electromagnetic field In classical physics, electromagnetic radiation is understood in terms of the electromagnetic field Electromagnetic field, an oscillating electric and magnetic disturbance that spreads as a harmonic wave through empty space, the vacuum. The wave travels at a constant speed called the speed of light, c, which is about m s 1. An electromagnetic field has two components 1. an electric field that acts on charged particles (whether stationary of moving) 2. a magnetic field that acts only on moving charged particles. These two components have the same wavelength and frequency, and hence the same speed, but they travel in mutually perpendicular planes Electromagnetic radiation is the emission and transmission of energy in the form of electromagnetic waves. 13

14 The electromagnetic field is characterized by 1. wavelength, (lambda), the distance between the neighboring peaks of the wave 2. Frequency, v (nu), the number of times per second at which its displacement at a fixed point returns to its original value, the frequency is measured in hertz, where 1Hz = 1s 1 The wavelength and frequency of an electromagnetic wave are related by =c Therefore, the shorter the wavelength, the higher the frequency. ~ 1 c Types of electromagnetic radiation 14

15 Light As An Electromagnetic Wave Electromagnetic waves would be reflected by metal mirrors would be refracted by dielectrics like glass would exhibit polarization and interference and would travel outward from the wire through a vacuum with a speed of m/s. The failures of classical physics 1. Black-body radiation When solids are heated, they emit electromagnetic radiation over a wide range of wavelengths. Examples of radiation from heated solids. The dull red glow of an electric heater The bright white light of a tungsten light bulb 15

16 The Planck distribution The German physicist Max Planck studied black-body radiation from the viewpoint of thermodynamics. E=nhv n = 0, 1, 2, 3, 4,.. where h is called Planck s constant v is the frequency of radiation Planck said that atoms and molecules could emit (or absorb) energy only in discrete quantities Planck gave the name quantum to the smallest quantity of energy that can be emitted (or absorbed) in the form of electromagnetic radiation. The energy E of a single quantum of energy is given by E=hv The limitation of energies to discrete values is called the quantization of energy. Photoelectric effect A phenomenon in which electrons are ejected from the surface of certain metals exposed to light of at least a certain minimum frequency, called the threshold frequency (v 0 ). The kinetic energy (m/2)v 2 of the photoelectrons is dependent solely on the wavelength λ of the incident light, not on its intensity! The number of ejected photoelectrons is proportional to the light intensity. Below the threshold frequency no electrons were ejected no matter how intense the light. Fig. Photoelectric effect apparatus. 16

17 The photoelectric effect could not be explained by the wave theory of light. Using Planck s quantum theory of radiation as a starting point, Einstein, however, made an extraordinary assumption. The energy of light is not distributed evenly over the classical wavefront, but is concentrated in discrete regions (or in bundles ), called quanta, each containing energy, hv. Photon with energy hv Fig. (a) A classical view of a traveling light wave. (b) Einstein s photon picture of a traveling light wave. These particles of light are now called photons. each photon must possess energy E, given by the equation E h This situation is summarized by the equation K h max Where is the work function The work function is the minimum energy required to detach an electron from a given substance With any theory, one looks not only for explanations of previously observed results but also for new predictions. 17

18 This observation can be understood if the energy of the atoms or molecules is also confined to discrete values, for then energy can be discarded or absorbed only in discrete amounts Then, if the energy of an atom decreases by DE, the energy is carried away as radiation of frequency v, and an emission 'line', a sharply defined peak, appears in the spectrum. DE=hv Wave-particle duality The energies of the electromagnetic field and of oscillating atoms are quantized. That electromagnetic radiation-which classical physics treats as wave-likeactually also displays the characteristics of particles. Emission Spectrum of The Hydrogen Atom 18

19 where R is the Rydberg constant, an empirical constant with the value m 1. The n are integers, with n 1 =1, 2,... and n 2 = n 1 +1, n 1 +2,.... The series with n 1 =1 is called the Lyman series and lies in the ultraviolet. The series with n 1 =2 lies in the visible region and is called the Balmer series. The infrared series include the Paschen series (n 1 =3) and the Brackett series (n 1 = 4). 19

20 Bohr s theory of the atomic spectrum of hydrogen In 1913, Niels Bohr combined elements of quantum theory and classical physics in a treatment of the hydrogen atom. Stationary states exist in which the energy of the electron is constant; such states are characterized by circular orbits about the nucleus in which the electron has an angular momentum mvr given by Energy is absorbed or emitted only when an electron moves from one stationary state to another and the energy change is given by substitution of n = 1 gives a radius for the first orbit of the H atom of m, or pm. This value is called the Bohr radius of the H atom and is given the symbol a 0. 20

21 An increase in the principal quantum number from n = 1 to n= infinity has a special significance; it corresponds to the ionization of the atom and the ionization energy, IE, can be determined FIG. The emission process in an excited hydrogen atom, according to Bohr s theory. 21

22 A characteristic property of waves is that they interfere with one another, giving a greater displacement where peaks or troughs coincide, leading to constructive interference, and a smaller displacement where peaks coincide with troughs, leading to destructive interference (see the illustration: (a) constructive, (b) destructive). The wave character of particles French physicist Louis de Broglie, in 1924, suggested that any particle, not only photons, travelling with a linear momentum p should have (in some sense) a wavelength given by the de Broglie relation: h p De Broglie proposed that all material particles are associated with waves, which he called matter waves, but that the existence of these waves is likely to be observable only in the behaviors of extremely light particles. A particle with a high linear momentum has a short wavelength (Fig.). Macroscopic bodies have such high momenta (because their mass is so great), even when they are moving slowly, that their wavelengths are undetectably small, and the wave-like properties cannot be observed. 22

23 Why the energies of the hydrogen electron are quantized. In a more concrete way, Why is the electron in a Bohr atom restricted to orbiting the nucleus at certain fixed distances? According to de Broglie An electron bound to the nucleus behaves like a standing wave. Standing waves can be generated by plucking, say, a guitar string (Fig.). The waves are described as standing, or stationary, because they do not travel along the string. Some points on the string, called nodes, do not move at all; that is, the amplitude of the wave at these points is zero. There is a node at each end, and there may be nodes between the ends. Dr. Said M. El-Kurdi The greater the frequency of vibration, the shorter the wavelength of the standing wave and the greater the number of nodes. As the Figure shows, there can be only certain wavelengths in any of the allowed motions of the string. de Broglie argued that if an electron does behave like a standing wave in the hydrogen atom, the length of the wave must fit the circumference of the orbit exactly (Figure a). Otherwise the wave would partially cancel itself on each successive orbit. Eventually the amplitude of the wave would be reduced to zero, and the wave would not exist. (Figure b). Dr. Said M. El-Kurdi 23

24 Notes: When examined on an atomic scale, the classical concepts of particle and wave melt together, particles taking on the characteristics of waves, and waves the characteristics of particles. Not only has electromagnetic radiation the character classically ascribed to particles, but electrons (and all other particles) have the characteristics classically ascribed to waves. This joint particle and wave character of matter and radiation is called waveparticle duality. Duality strikes at the heart of classical physics, where particles and waves are treated as entirely distinct entities. We have also seen that the energies of electromagnetic radiation and of matter cannot be varied continuously, and that for small objects the discreteness of energy is highly significant. In classical mechanics, in contrast, energies could be varied continuously. Such total failure of classical physics for small objects implied that its basic concepts were false A new mechanics had to be devised to take its place. 24

25 Heisenberg uncertainty principle The Heisenberg uncertainty principle: it is impossible to know simultaneously both the momentum p and the position of a particle with certainty. Stated mathematically, h DxDp 4 where Dx and Dp are the uncertainties in measuring the position and momentum, respectively. Applying the Heisenberg uncertainty principle to the hydrogen atom, we see that in reality the electron does not orbit the nucleus in a well-defined path, as Bohr thought. The Schrodinger equation Is our fundamental equation of quantum mechanics. (fundamental postulate) like Newton s law, F=ma The solutions to the Schrödinger equation are called wave functions ( ). The wave function ( ) gives a complete description of any system 25

26 A wavefunction is a mathematical function that contains detailed information about the behaviour of an electron. An atomic wavefunction consists of a radial component, R(r), and an angular component, A(, ). The region of space defined by a wavefunction is called an atomic orbital. The probability of finding an electron at a given point in space is determined from the function 2 where is the wavefunction. 26

27 The Born interpretation of the wavefunction The wavefunction contains all the dynamical information about the system it describes. Here we concentrate on the information it carries about the location of the particle. Max Born made use of an analogy with the wave theory of light, in which the square of the amplitude of an electromagnetic wave in a region is interpreted as its intensity and therefore (in quantum terms) as a measure of the probability of finding a photon present in the region. 2 It states that the value at a point is proportional to the probability of finding the particle in a region around that point. Specifically, for a onedimensional system. 27

28 There is no direct significance in the negative (or complex) value of a wavefunction: only the square modulus, a positive quantity, is directly physically significant, and both negative and positive regions of a wavefunction may correspond to a high probability of finding a particle in a region According to this interpretation, there is a high probability of finding the electron where 2 is large, and the electron will not be found where 2 is zero. The quantity 2 is called the probability density of the electron. Normalization A mathematical feature of the Schrodinger equation is that, if is a solution, then so is N, where N is any constant. This freedom to vary the wavefunction by a constant factor means that it is always possible to find a normalization constant, N, such that the proportionality of the Born interpretation becomes an equality. For a normalized wavefunction N, the probability that a particle is in the region dx is equal to (N *)(N )dx (we are taking N to be real). Furthermore, the sum over all space of these individual probabilities must be 1 (the probability of the particle being somewhere is 1). N 2 * dx 1 28

29 Wavefunctions in general have regions of positive and negative amplitude, or sign. when two wavefunctions spread into the same region of space and interact. Positive region of one wavefunction may add to a positive region of the other wavefunction to give a region of enhanced amplitude. Constructive interference A positive region of one wavefunction may be cancelled by a negative region of the second wavefunction. Destructive interference The interference of wavefunctions is of great importance in the explanation of chemical bonding. 29

30 Atomic orbitals The wavefunction of an electron in an atom is called an atomic orbital. (a) Hydrogenic energy levels Each of the wavefunctions obtained by solving the Schrodinger equation for a hydrogenic atom is uniquely labelled by a set of three integers called quantum numbers. Each quantum number specifies a physical property of the electron Principal quantum number, n n specifies the energy The value of n also indicates the size of the orbital Orbital angular momentum quantum number, l l labels the magnitude of the orbital angular momentum The value of l also indicates the angular shape of the orbital, with the number of lobes increasing as l increases Magnetic quantum number, m l m l labels the orientation of that angular momentum m l also indicates the orientation of the lobes. For a hydrogenic atom of atomic number Z, the allowed energies are specified by the principal quantum number, n 30

31 Positive values of the energy correspond to unbound states of the electron in which it may travel with any velocity and hence possess any energy. The energies given by eqn. are all negative, signifying that the energy of the electron in a bound state is lower than a widely separated stationary electron and nucleus. the energy levels converge as the energy increases (becomes less negative) The value of l specifies the magnitude of the orbital angular momentum through {l(l + 1)} 1/2 h, with l = 0, 1, 2,.... We can think of l as indicating the rate at which the electron circulates around the nucleus. 31

32 (b) Shells, subshells, and orbitals In a hydrogenic atom, all orbitals with the same value of n have the same energy and are said to be degenerate. n defines a series of shells of the atom, or sets of orbitals with the same value of n and hence with the same energy and approximately the same radial extent. Shells with n = 1, 2, 3... are commonly referred to as K, L, M,... shells. The orbitals belonging to each shell are classified into subshells distinguished by a quantum number l. For a given value of n, the quantum number l can have the values l = 0, 1,..., n 1, giving n different values in all. A subshell with quantum number l consists of 2l + 1 individual orbitals. These orbitals are distinguished by the magnetic quantum number, m l m l can have the 2l + 1 integer values from +l down to l. m l specifies the component of orbital angular momentum around an arbitrary axis (commonly designated z) passing through the nucleus. 32

33 (c) Electron spin An electron can be regarded as having an angular momentum arising from a spinning motion Spin is described by two quantum numbers, s and m s. s is the analogue of l for orbital motion but it is restricted to the single, unchangeable value s = 1/2. The magnitude of the spin angular momentum is given by the expression {s(s + 1)} 1/2 h The second quantum number, the spin magnetic quantum number, m s, may take only two values, +1/2 (anticlockwise spin, imagined from above) and 1/2 (clockwise spin). The two states are often represented by the two arrows ( spin-up, m s +1/2) and ( spin-down, m s 1/2 ) or by the Greek letters and β, respectively. The state of an electron in a hydrogenic atom is characterized by four quantum numbers, namely n, l, m l, and m s Solutions of the Schrödinger equation for the hydrogen atom which define the 1s, 2s and 2p atomic orbitals. For these forms of the solutions, the distance r from the nucleus is measured in atomic units. 33

34 (d) Nodes Inorganic chemists generally find it adequate to use visual representations of atomic orbitals rather than mathematical expressions. Because the potential energy of an electron in the field of a nucleus is spherically symmetric, the orbitals are best expressed in terms of the spherical polar coordinates Nodes The positions where either component of the wavefunction passes through zero. Radial nodes occur where the radial component of the wavefunction passes through zero. Angular nodes occur where the angular component of the wavefunction passes through zero. The numbers of both types of node increase with increasing energy and are related to the quantum numbers n and l. 34

35 (e) The radial variation of atomic orbitals 1s orbital, the wavefunction with n =1, l= 0, and m l =0, decays exponentially with distance from the nucleus and never passes through zero. All orbitals decay exponentially at sufficiently great distances from the nucleus and this distance increases as n increases. As the principal quantum number of an electron increases, it is found further away from the nucleus and its energy increases. in general radial nodes = n l 1. However, a 2p orbital, like all orbitals other than s orbitals, is zero at the nucleus. 35

36 (f) The radial distribution function A radial distribution function gives the probability that an electron will be found at a given distance from the nucleus, regardless of the direction. How tightly the electron is bound? The total probability of finding the electron in a spherical shell of radius r and thickness dr is the integral of 2 d over all angles. In general, a radial distribution function for an orbital in a shell of principal quantum number n has n 1 peaks, the outermost peak being the highest. (f) The radial distribution function The radial distribution function of a hydrogenic 1s, 2s, and 3s orbital. 36

37 Radial distribution functions, 4 r 2 R(r) 2, for the 3s, 3p and 3d atomic orbitals of the hydrogen atom. The most probable distance decreases as the nuclear charge increases (because the electron is attracted more strongly to the nucleus), and specifically The most probable distance increases as n increases because the higher the energy, the more likely it is that the electron will be found far from the nucleus. 37

38 (g) The angular variation of atomic orbitals The boundary surface of an orbital indicates the region of space within which the electron is most likely to be found; orbitals with the quantum number l have l nodal planes. The angular wavefunction expresses the variation of angle around the nucleus and this describes the orbital s angular shape. s orbital is spherically symmetrical The orbital is normally represented by a spherical surface (boundary surface) with the nucleus at its center. Boundary surface defines the region of space within which there is a high (typically percent) probability of finding the electron. Angular nodes or nodal planes The planes on which the angular wavefunction passes through zero An electron will not be found anywhere on a nodal plane. A nodal plane cuts through the nucleus and separates the regions of positive and negative sign of the wavefunction. 38

39 39

40 Orbital energies in a hydrogen-like species Size of orbitals For a given atom, a series of orbitals with different values of n but the same values of l and m l (e.g. 1s, 2s, 3s, 4s,...) differ in their relative size (spatial extent). The larger the value of n, the larger the orbital, although this relationship is not linear. An increase in size also corresponds to an orbital being more diffuse. 40

41 The ground state of the hydrogen atom The most energetically favorable (stable) state of the H atom is its ground state in which the single electron occupies the 1s (lowest energy) atomic orbital. The electron can be promoted to higher energy orbitals to give excited states. 1.7 Many-electron atoms The helium atom: two electrons attraction between electron (1) and the nucleus; attraction between electron (2) and the nucleus; repulsion between electrons (1) and (2). The net interaction determines the energy of the system. 41

42 In terms of obtaining wavefunctions and energies for the atomic orbitals of He, it has not been possible to solve the Schrödinger equation exactly and only approximate solutions are available. For atoms containing more than two electrons, it is even more difficult to obtain accurate solutions to the wave equation. In a multi-electron atom, orbitals with the same value of n but different values of l are not degenerate. Ground state electronic configurations: experimental data Now consider the ground state electronic configurations of isolated atoms of all the elements (Table 1.3). These are experimental data, and are nearly always obtained by analyzing atomic spectra. Most atomic spectra are too complex for discussion here and we take their interpretation on trust. The following sequence is approximately true for the relative energies (lowest energy first) of orbitals in neutral atoms: 42

43 1.6 Penetration and shielding Ground-state electron configuration Pauli exclusion principle: No more than two electrons may occupy a single orbital and, if two do occupy a single orbital, then their spins must be paired. This negative charge reduces the actual charge of the nucleus, Ze, to Z effe, where Z eff (more precisely, Z eff e) is called the effective nuclear charge. empirical shielding constant, This effective nuclear charge depends on the values of n and l of the electron of interest The reduction of the true nuclear charge to the effective nuclear charge by the other electrons is called shielding. Penetration The presence of an electron inside shells of other electrons. The penetration of a 2s electron through the inner core is greater than that of a 2p electron because the latter vanishes at the nucleus. Therefore, the 2s electrons are less shielded than the 2p electrons. We can conclude that a 2s electron has a lower energy (is bound more tightly) than a 2p electron, and therefore that the 2s orbital will be occupied before the 2p orbitals 43

44 Box 1.6 Effective nuclear charge and Slater s rules Slater s rules Effective nuclear charges, Z eff, experienced by electrons in different atomic orbitals may be estimated using Slater s rules. These rules are based on experimental data for electron promotion and ionization energies, and Z eff is determined from the equation: 44

45 where Z = nuclear charge, Zeff = effective nuclear charge, S = screening (or shielding) constant. Values of S may be estimated as follows: 1. Write out the electronic configuration of the element in the following order and groupings: (1s), (2s, 2p), (3s, 3p), (3d ), (4s, 4p), (4d ), (4f ), (5s, 5p) etc. 2. Electrons in any group higher in this sequence than the electron under consideration contribute nothing to S. 3. Consider a particular electron in an ns or np orbital: (i) Each of the other electrons in the (ns, np) group contributes S = (ii) Each of the electrons in the (n 1) shell contributes S = (iii) Each of the electrons in the (n 2) or lower shells contributes S = Consider a particular electron in an nd or nf orbital: (i) Each of the other electrons in the (nd, nf ) group contributes S = (ii) Each of the electrons in a lower group than the one being considered contributes S =

46 An s electron in the outermost shell of the atom is generally less shielded than a p electron of that shell. As a result of penetration and shielding, the order of energies in many-electron atoms is typically ns < np < nd < nf because, in a given shell, s orbitals are the most penetrating and f orbitals are the least penetrating. 1.7 The building-up principle The ground-state electron configurations of many-electron atoms are determined experimentally by spectroscopy The building-up principle Aufbau principle is a procedure that leads to plausible ground-state configurations. 46

47 Orbitals are filled in order of energy, the lowest energy orbitals being filled first. Hund s rule: in a set of degenerate orbitals, electrons may not be spin-paired in an orbital until each orbital in the set contains one electron; electrons singly occupying orbitals in a degenerate set have parallel spins, i.e. they have the same values of m s. Pauli exclusion principle: no two electrons in the same atom may have the same set of n, l, m l and m s quantum numbers; it follows that each orbital can accommodate a maximum of two electrons with different m s values (different spins=spin-paired). 1.8 The periodic table Dmitri Mendele ev and Lothar Meyer stated that the properties of the elements can be represented as periodic functions of their atomic weights, and set out their ideas in the form of a periodic table. 47

48 1.8 The periodic table 48

49 Valence and core electrons The configuration of the outer or valence electrons is of particular significance. These electrons determine the chemical properties of an element. Electrons that occupy lower energy quantum levels are called core electrons. Diagrammatic representations of electronic configurations 49

50 1.10 Ionization energies and electron affinities The first ionization energy, IE 1, of an atom is the internal energy change at 0 K, U(0 K), associated with the removal of the first valence electron 50

51 the high values of IE 1 associated with the noble gases. the very low values of IE 1 associated with the group 1 elements. the general increase in values of IE 1 as a given period is crossed. Electron affinities The first electron affinity (EA1) is minus the internal energy change (equation ) for the gain of an electron by a gaseous atom The attachment of an electron to an atom is usually exothermic. 51

52 52