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AtomicStructureReading

AtomicStructureReading - Some basic concepts l Fundamental...

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Unformatted text preview: Some basic concepts l Fundamental particles I Atomic number, mass number and isotopes I An overview of quantum theory I Orbitals of the hydrogen atom and quantum numbers I The multi-electron atom, the aufbau principle and electronic configurations l The periodic table Ionization energies and electron affinities I Lewis structures 1.1 Introduction Inorganic chemistry: it is not an isolated branch of chemistry If organic chemistry is considered to be the ‘chemistry of carbon’. then inorganic chemistry is the chemistry of all elements except carbon. In its broadest sense. this is true. but of course there are overlaps between branches of chemistry. A topical example is the chemistry of the fill/cr- enes (see Section 13.4) including C60 (see Figure 13.5) and C70; this was the subject of the award of the 1996 Nobel Prize in Chemistry to Professors Sir Harry Kroto. Richard Smalley and Robert Curl. An understanding of such molecules and related species called nanom/ms involves studies by organic. inorganic and physical chemists as well as by physicists and materials scientists. Inorganic chemistry is not simply the study of elements and compounds; it is also the study of physical principles. For example. in order 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. Overlap between physical and inorganic chemistry is also significant in the 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 Valence bond theory Fundamentals of molecular orbital theory The octet rule Electronegativity Dipole moments MO theory: heteronuclear diatomic molecules Isoelectronic molecules Molecular shape and the VSEPR model Geometrical isomerism molecule or molecular ion. To interpret the behaviour of molecules in solution, we use physical techniques such as nuclear magnetic resonance (NMR) spectroscopy; the equivalence or not of particular nuclei on a spectroscopic timescale may indicate whether a molecule is static or under- going a dynamic process (see .S'm'ri'on ,7./'/), In this text, we describe the results of such experiments but we will not. in general. discuss underlying theories; several texts which cover experimental details of such techniques are listed at the end of Chapter I. The aims of Chapter 7] In this chapter. we outline some concepts fundamental to an understanding of inorganic chemistry. We have assumed that readers are to some extent familiar with most of these concepts and our aim is to give a point of reference for review purposes. 1.2 Fundamental particles of an atom An mom is the smallest unit quantity of an element that is capable ofexistence, 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. elem-on and neutron. 2 Chapter 1 0 Some basic concepts Table 1.1 Properties of the proton. electron and neutron. Proton Electron Neutron Charge/C +1.602 x 10*[9 —1 .602 x 10"9 0 Charge number (relative charge) 1 —1 0 7 Rest mass/kg 1.673 >< 10—27 9.109 x 10‘31 1.675 X 10“7 Relative mass 1837 1 1839 A neutron and a proton have approximately the same mass and, relative to these, an electron has negligible mass (Table 1.1). The charge on a proton is positive and of equal mag- nitude, but opposite sign, to that on a negatively charged electron; a neutron has no charge. In an atom of any element, there are equal numbers of protons and electrons and so an atom is neutral. The nucleus of an atom consists of protons and (with the exception of protium; see Syriion 9.3) neutrons, and is positively charged; the nucleus of pro- tium consists of a single proton The electrons occupy a region of space around the nucleus. Nearly all the mass of an atom is concentrated in the nucleus, but the volume of the nucleus is only a tiny fraction of that of the atom; the radius of the nucleus is about 10715m while the atom itself is about 105 times larger than this. It follows that the density of the nucleus is enormous, more than 1012 times than of the metal Pb. Although chemists tend to consider the electron, proton and neutron as the fundamental (or elementary) particles of an atom, particle physicists would disagree, since their research shows the presence of yet smaller particles. if , isotopes-g, ‘ Nuclides, atomic number and mass number A nuclide is a particular type of atom and possesses a charac— teristic atomic number, Z , which is equal to the number of pro- tons in the nucleus; because the atom is electrically neutral, Z also equals the number of electrons. The mass number, A. of a nuclide is the number of protons and neutrons in the nucleus. A shorthand method of showing the atomic number and mass number ofa nuclide along with its symbol, E, is: Mass number——> A e‘g‘ zoNe E 5- Element symbol 10 Atomic number ——> Z Atomic number = Z : number of protons in the nucleus = number of electrons Mass number = A = number of protons + number of neutrons Number of neutrons : A — Z Relative atomic mass Since the electrons are of minute mass, the mass of an atom essentially depends upon the number of protons and neu- trons in the nucleus. As Table 1.1 shows, the mass of a single atom is a very small, non-integral number, and for convenience we adopt a system of relative atomic masses. We define the atomic mass unit as l / 12th of the mass of a lgC atom so that it has the value 1.660 X 10 ’27 kg. Relative atomic masses (A) are thus all stated relative to lEC:12.0000. The masses of the proton and neutron can be considered to be ~1u where u is the atomic mass unit (1 u x 1.660 x 10‘27 kg). Isotopes Nuclides of the same element possess the same number of protons and electrons but may have different mass numbers; the number of protons and electrons defines the element but the number of neutrons may vary. Nuclides of a particular element that differ in the number of neutrons and, therefore, their mass number, are called isotopes (see Appemlix 5). Isotopes of some elements occur naturally while others may be produced artificially. Elements that occur naturally with only one nuclide are monotopic and include phosphorus, ‘gP, and fluorine, “3F. Elements that exist as mixtures of isotopes include C (léC and QC) and o (‘30, 'go and 130). Since the atomic number is constant for a given element. isotopes are often distinguished only by stating the atomic masses, eg. 12C and 13C. Worked example 1.1 Relative atomic mass Calculate the value of AIr for naturally occurring chlorine if the distribution of isotopes is 75.77% $0 and 24.23% flCl. Accurate masses for 35C] and 37Cl are 34.97 and 36.97. The relative atomic mass of chlorine is the weighted mean of the mass numbers of the two isotopes: Relative atomic mass, 75.77 24.23 Ar ~ ( 100 X 34.97) +( '00 x 36.97) - 35.45 CHEMICAL AND THEORETICAL BACKGROUND Chapter 1 0 Successes in early quantum theory 3 Box 1.1 Isotopes and allotropes Do not confuse isotope and allotropel Sulfur exhibits both iso- topes and allotropes. Isotopes of sulfur (with percentage naturally occurring abundances) are ?%S (95.02%), (0.75%). 123 (4.21%), fgs 10.02%). Allotropes of an element are different structural modifications Self—study exercises 1. 1f.~1r for CI is 35.45. what is the ratio 01'35C1:37C| present in a sample of C1 atoms containing naturally occurring C1? IAm‘. 3.17:1] 2. Calculate the Value of Ar for naturally occurring Cu if the distribution of isotopes is 69.2".) “Cu and 30.8"» “Cu; accurate masses are 62.93 and 64.93. Mm. 63.5] 3. Why in question 2 is it adequate to write “Cu rather than 63C ., 29 u. 4. Calculate Ar for naturally occurring Mg if the isotope distribu- tion is 78.99% “Mg. 10.00% 25Mg and 11.01% 2“Mg; accurate masses are 23.99. 24.99 and 25.98. IAm‘. 24.31] Isotopes can be separated by mass .8’])((‘ll'0l71€ll“1‘ and Figure 1.1a shows the isotopic distribution in naturally occurring Ru. Compare this plot (in which the most abundant 100 ” 75" 50‘ 25‘l Relative abundance Relative abundance 96 98 100 102 104 Mass number of that element. Allotropes of sulfur include cyclic structures, e.g. S6 (see below) and 83 (Figure He), and Sx-chains of various lengths (polycatenasulfur). Further examples of isotopes and allotropes appear throughout the book. 1% Part of the helical chain of SW isotope is set to 100) with the values listed in Appendix 5. Figure l.lb shows a mass spectrometric trace for molecular St. the structure of which is shown in Figure l.lc; five peaks are observed due to combinations of the isotopes of sulfur. (See problem 1.3 at the end of this chapter.) Isotopes of an element have the same atomic number. Z. but different atomic masses. 1.4 Successes in early quantum theory We saw in Section 1.2 that electrons in an atom occupy a region 01‘ 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 256 258 260 Mass number (1)) (C) (a) m Fig. 1.1 Mass spectrometric traces for (a) atomic Ru and (b) molecular 53; the mass:charge ratio is m]; and in these traces : : l. (c) The molecular structure of S8. 4 Chapter 1 ' Some basic concepts electronic structures ofeach species. No adequate discussion of electronic structure is possible without reference to quantum theory and ware III(’('/ltlllft‘.\‘. In this and the next few sections. we review some of the crucial concepts. The treatment is mainly qualitative. and for greater detail and more rigorous derivations of mathematical relationships. the references at the end ofChapter I should be consulted. The development of quantum theory took place in two stages. In the older theories (I900 I925). the electron was treated as a particle. and the achievements ofgreatest signif— icance to inorganic chemistry were the interpretation of atomic spectra and assignment of electronic conligurations. In more recent models. the electron is treated as a wave (hence the name wary I)I(’(‘/I(Illf(‘.\') and the main successes in chemistry are the elucidation of the basis ofstereochemistry and methods for calculating the properties of molecules (exact ()II/_t‘ for species involving light atoms). Since all the results obtained by using the older quantum theory may also be obtained from wave mechanics. it may seem unnecessary to refer to the former: indeed. sophisticated treatments of theoretical chemistry seldom do. However. most chemists often find it easier and more convenient to con- sider the electron as a particle rather than a wave. Some important successes of classical quantum theory Historical discussions of the developments of quantum theory are dealt with adequately elsewhere. and so we focus only on some key points of (‘/ll.\'.\'f('tl/ quantum theory (in which the electron is considered to be a particle). At low temperatures. the radiation emitted by a hot body is mainly of low energy and occurs in the infrared. but as the temperature increases. the radiation becomes successively dull red. bright red and white. Attempts to account for this observation failed until. in 1901. Planck suggested that energy could be absorbed or emitted only in quanta of mag- nitude .315 related to the frequency of the radiation. 1/. by equation 1.]. The proportionality constant is It. the Planck constant (It : (3.626 x It) “l .I s). Ali : ln/ Units: 15 in .I: l/ in s l or Hz (1.1) (' 4- /\1/ Units: /\ in m: 1/ in s l or Hz (1.2) The hertz. Hz. is the SI Ltnit of freqtiency. I‘IJIIIICI seltcs Since the frequency of radiation is related to the wave- length. /\. by equation 1.2. in which (‘ is the speed of light in a vacuum (t' : 2.998 X 10“. ms 1). we can rewrite equation 1.1 in the form of equation 1.3 and relate the energy of radiation to its wavelength. Alf : ’1‘! (1.3) ,\ On the basis of this relationship. Planck derived a relative intensity wavelength temperature relationship which was in good agreement with experimental data. This derivation is not straightforward and we shall not reproduce it here. One of the most important applications of early quantum theory was the interpretation of the atomic spectrum of hydrogen on the basis of the RutherfordiBohr model of the atom. When an electric discharge is passed through a sample of dihydrogen. the H3 molecules dissociate into atoms. and the electron in a particular excited H atom may be [)I'OIHUIt’l/ to one of many high energy levels. These states are transient and the electron falls back to a lower energy state. emitting energy as it does so. The consequence is the observation of spectral lines in the emission spectrum of hydrogen: the spectrum (a small part of which is shown in Figure 1.2) consists of groups of discrete lines corresponding to electronic transitions. each of (If.\'('l'(’lt’ energy. As long ago as 1885. Balmer pointed out that the wavelengths of the spectral lines observed in the visible region of the atomic spectrum of hydrogen obeyed equation 1.4. in which R is the Rydberg constant for hydrogen. 17 is the wavenumbcr in cm I. and n is an integer 3. 4. This series of spectral lines is known as the Bu/ntvr .vt'rim. Wavenumber : reciprocal of wavelength; convenient (non- SI) units are ‘reciprocal centimetres‘. cm I 1 l /:—:R —7——1 ' A (2— n—) l l R : Rydberg constant for hydrogen : 1.097 X itfm ‘ : 1.097 X 105cm Other series of spectral lines occur in the ultraviolet (Lyman series) and infrared (Paschen. Brackett and Pfund series). All VISIBLE ULTRAVIOLET ~> Increasing energy Fig. 1.2 Part of the emission spectrum of atomic hydrogen. Groups of lines have particular names. e.g. Balmer and Lyman series. Fig. 1.3 : lines in 1 equation the Balm Pfund se some of series in of the VI rules, to Bohr's hydrog In 1913, and clas: He state: 0 Statit is con abou‘ mom the p. mvr = when radiu be w1 \ 11 O N 11 ,..i l,_\i‘.1.msct:c:t / l; *8” n=1 '— Chapter 1 - Successes in early quantum theory 5 N 11 N n : oo : the continuum Fig. 1.3 Some of the transitions that make up the Lyman and Balmer series in the emission spectrum of atomic hydrogen. lines in all the series obey the general expression given in equation 1.5 where n’ > n. For the Lyman series, n : 1. for the Balmer series, 11 : 2. and for the Paschen. Brackett and Pfund series. 17 : 3, 4 and 5 respectively. Figure 1.3 shows some of the allowed transitions of the Lyman and Balmer series in the emission spectrum of atomic H. Note the use of the word allowed; the transitions must obey selection rules. to which we return in Section 20.6. , 1 1 1 V:X:R<H_Z_ITZ> (1.5) 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. He stated two postulates for an electron in an atom: o Stationary stares 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 mor given by equation 1.6. The integer. n. is the principal quantum number. l1 nun 711<TF> (1.6) where "1 : mass of electron; 11 : velocity of electron; r : radius of the orbit; lz : the Planck constant; li/27r may be written as l7. 0 Energy is absorbed or emitted only when an electron moves from one stationary state to another and the energy change is given by equation 1.7 where 111 and n2 are the principal quantum numbers referring to the energy levels E,“ and En: respectively. AE : E”: i E,“ : lzu (1.7) If we apply the Bohr model to the H atom, the radius of each allowed circular orbit can be determined from equation 1.8. The origin of this expression lies in the centrifugal force acting on the electron as it moves in its circular orbit; for the orbit to be maintained. the centrifugal force must equal the force of attraction between the negatively charged electron and the positively charged nucleus. 7 EUIZZI/F rn : (1.8) 7 Trim 6” permittivity of a vacuum 1| where 50 : 8.854 x1042 Fm'l l7 : Planck constant : 6.626 X 10’34 Js n : 1,27 3 . . . describing a given orbit my 2 electron rest mass : 9.109 X 10’31 kg 6 : charge on an electron (elementary charge) : 1.602 X 104°C From equation 1.8. substitution of n :1 gives a radius for the first orbit of the H atom of 5.293 X IO’Hm. or 6 Chapter 1 0 Some basic concepts 53.03 pm, This \alue is called the Bohr rat/I'm ol‘ the H atom and is giyen the symbol a”, .\n increase in the principal quantum number l‘rom II c l to H \ has a special signilicance: it corresponds to the ioni/ation ol‘ the atom (equation 1.9) and the ionization energy. 11-). can be determined by combining equations l5 and I.7. as shown in equation |.l(l. Values ol‘ Ilis are quoted per NIH/U u/ ulmm: ()ne mole ol‘ a substance contains the Ay'ogadro number. 1.. ol‘ particles: 1. ~ 6.032 *» ltlzl mol llth >l'l (gt ~ e (|.*)l (1.1m \ 5 t‘ / l ‘l: E k A l tal— l /l_ ml V 3.179 l() I\i \' 1m s in " (m2: -- Wilma 1.311 |()(‘.l mol 7 1312 kl mol Although the SI unit ol‘ energy is the joulc. ioni/ation energies are ol‘ten expressed in electron \olts (e\") (le\" : 90.4%} t 96.5 k.l mol I). linprcssiye as the success ol‘ the Bohr model was \\ hen applied to the H atom. extensiye modilications “etc required to cope \\ith species containing more than one electron; \\e shall not pursue this t'urther here. 1.5 An introduction to wave mechanics The wave—nature of electrons The quantum theory ol‘ radiation introduced by M ax Planck and Albert liinstcin implies a particle theory ol‘ light. in addition to the nave theory ol‘ light required by the phenomena ol‘ interference and dill‘raction. in l924. Louis de Broglie argued that it" light were composed ol‘ particles and yet shoyyed \\aye—like properties. the same should be true ot‘ electrons and other particles. This phenomenon is rel‘erred to as n'urt' pul'lie/t' t/im/t'lr. The de Broglie relation— ship (equation l.ll) combines the concepts ol‘ classical mechanics with the idea ol‘ \yaye-like properties by show- ing that a particle \\ith momentum Mr (I): : mass and 1' ' \eloeity ol‘ the particle) possesses an associated \\‘ay'e ol‘yyayelength /\. II . ,\ 7. I)”. \\ here It is the Planck constant (1.] 1) An important physical obscry'ation \\hich is a consequence ol‘ the de Broglie relationship is that electrons accelerated to a \‘elocity ot‘ (1 - It)“ in s l (by a potential ol‘ l()()\7) haye an associated \\ayelength ot‘ alltlpm and such electrons are dill‘racted as they pass through a crystal. This phenom- enon is the basis ol‘ electron dill‘raetion techniques used to determine structures ol‘ehemical compounds (sec l. The uncertainty principle 11‘ an electron has \\ay‘e—like properties. there is an important and dillicult consequence: it becomes impossible to knoyy exactly both the momentum and position ol‘ the electron a! l/It‘ yume [Initial in Iilllt‘. This is a statement ot‘ l leisenberg‘s mut'rmimy principle. In order to get around this problem. rather than trying to deline its e\act position and momen- tum. \\e use the pru/w/a/irr ti/ Hut/mg I/lt’ electron in a giy'cn yolume ol‘ space, The probability ol‘ linding an electron at a giy en point in space is determined l‘rom the t‘unction 1': \\‘here 1' is a mathematical l‘unction \\hich describes the behayiour oli an electron—\\ay'e: t,‘ is the n'ui'e/i/nt'rimr The probability ol‘ linding an electron at a giyen point in space is determined from the l'unction (" \\‘here 1.‘ is the u'urc/um‘liu/l. The Schrédinger wave equation Information about the \\ayet‘unction is obtained l‘rom the Schrodinger \\aye equation. \\hich can be set up and solved either exactly or approximately: the Schrodinger equation can be soly'ed t’.\'(l('l[l'(1/l[l [or a species conta...
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