16 ATOMIC ORBITAL THEORY 1.36 d ORBITALS Orbitals having an angular momentum /equal to 2 and,therefore,magnetic quantum numbers,(m of +2.+1,0.-1,-2.These five magnetic quantum numbers describe the five degenerate d orbitals.In the Cartesian coordinate system,these orbitals are desig ated as de d and d:the last four of the d orbitals are characterized by two nodal planes. hil thehas surfaces of revolution. Example.The five d orbitals are depicted in Fig.1.36.The d orbital that by con- vention is the sum of d and d and,hence,really d is strongly directed along the z-axis with a negative"doughnut"in the xy-plane.The dorbital has lobes pointed along thex-and y-axes,while the ddanddorbitals have lobes that are pointed half-way between the axes and in the planes designated by the subscripts 02 d Figure 1.36.The five d orbitals.The shaded and unshaded areas represent lobes of different signs. 1.37 fORBITALS Orbitals having an angular momentum equal to 3 and,therefore,magnetic quantum numbers,m of +3,+2,+1,0,-1,-2,-3.These seven magnetic quantum numbers
1.36 d ORBITALS Orbitals having an angular momentum l equal to 2 and, therefore, magnetic quantum numbers, (ml ) of 2, 1, 0, 1, 2. These five magnetic quantum numbers describe the five degenerate d orbitals. In the Cartesian coordinate system, these orbitals are designated as dz2, dx2 y2, dxy, dxz, and dyz; the last four of these d orbitals are characterized by two nodal planes, while the dz2 has surfaces of revolution. Example. The five d orbitals are depicted in Fig. 1.36. The dz2 orbital that by convention is the sum of dz2 x2 and dz2 y2 and, hence, really d2 z2 x2 y2 is strongly directed along the z-axis with a negative “doughnut” in the xy-plane. The dx2 y 2 orbital has lobes pointed along the x- and y-axes, while the dxy, dxz, and dyz orbitals have lobes that are pointed half-way between the axes and in the planes designated by the subscripts. 1.37 f ORBITALS Orbitals having an angular momentum l equal to 3 and, therefore, magnetic quantum numbers, ml of 3, 2, 1, 0, 1, 2, 3. These seven magnetic quantum numbers 16 ATOMIC ORBITAL THEORY y z x dz2 dx2−y2 dxy dxz dyz Figure 1.36. The five d orbitals. The shaded and unshaded areas represent lobes of different signs. c01.qxd 5/17/2005 5:12 PM Page 16
AUFBAU (G.BUILDING UP)PRINCIPLE 17 escribe the seven degenerate forbitals.The forbitals are characterized by thre nodal planes.They the chemistry metals (Sect1.4). 1.38 ATOMIC ORBITALS FOR MANY-ELECTRON ATOMS Modified hydrogenlike orbitals that are used to describe the electron distribution in many-electron atoms.The names of the orbitals.s.p.and so on,are taken from the rresponding hydro ce of n hanoneelectonin atom can br ebiasTepwOobia ak the degenerac with t 2p orbitals are higher in energy than he same n value.Thus,the when electrons are present in them.For a given n,the orbital energies increase in the order s<p<d<f<.... 1.39 PAULI EXCLUSION PRINCIPLE According to this principle,as formulated by Wolfgang Pauli (1900-1958),a maxi an orbital,and then,only if the spins of the elec. paired).th her m ust have Stated alternatively,no two electrons in the same atom can have the same values of n.l,m and m. 1.40 HUND'S RULE According to this rule.as formulated by Friedrich Hund(1896-1997).a single elec- enerate orbitals)bef of the degenerae set.Furthemore.cach of theec equal energy( the degenerate orbitals has the same (unpaired)spin.This arrangement means that these electrons repel each other as little as possible because any particular electron is prohibited from entering the orbital space of any other electron in the degenerate set. 1.41 AUFBAU (GER.BUILDING UP)PRINCIPLE s in the Periodic Table.Orbitals n orde of increa sing energy and the ons of the atom in question are placed in the unfilled orbital of lowest energy,filling this orbital before proceeding to place electrons in the next higher-energy orbital.The sequential placement of elec- trons must also be consistent with the Pauli exclusion principle and Hund's rule. Erample.The placement of electrons in the orbitals of the nitrogen atom (atomic number of 7)is shown in Fig.1.41.Note that the 2p orbitals are higher in energy chp orital in the degenerate 2p set hasa single ee
describe the seven degenerate f orbitals. The f orbitals are characterized by three nodal planes. They become important in the chemistry of inner transition metals (Sect. 1.44). 1.38 ATOMIC ORBITALS FOR MANY-ELECTRON ATOMS Modified hydrogenlike orbitals that are used to describe the electron distribution in many-electron atoms. The names of the orbitals, s, p, and so on, are taken from the corresponding hydrogen orbitals. The presence of more than one electron in a manyelectron atom can break the degeneracy of orbitals with the same n value. Thus, the 2p orbitals are higher in energy than the 2s orbitals when electrons are present in them. For a given n, the orbital energies increase in the order s p d f .... 1.39 PAULI EXCLUSION PRINCIPLE According to this principle, as formulated by Wolfgang Pauli (1900–1958), a maximum of two electrons can occupy an orbital, and then, only if the spins of the electrons are opposite (paired), that is, if one electron has ms 1/2, the other must have ms 1/2. Stated alternatively, no two electrons in the same atom can have the same values of n, l, ml , and ms. 1.40 HUND’S RULE According to this rule, as formulated by Friedrich Hund (1896–1997), a single electron is placed in all orbitals of equal energy (degenerate orbitals) before a second electron is placed in any one of the degenerate set. Furthermore, each of these electrons in the degenerate orbitals has the same (unpaired) spin. This arrangement means that these electrons repel each other as little as possible because any particular electron is prohibited from entering the orbital space of any other electron in the degenerate set. 1.41 AUFBAU (GER. BUILDING UP) PRINCIPLE The building up of the electronic structure of the atoms in the Periodic Table. Orbitals are indicated in order of increasing energy and the electrons of the atom in question are placed in the unfilled orbital of lowest energy, filling this orbital before proceeding to place electrons in the next higher-energy orbital. The sequential placement of electrons must also be consistent with the Pauli exclusion principle and Hund’s rule. Example. The placement of electrons in the orbitals of the nitrogen atom (atomic number of 7) is shown in Fig. 1.41. Note that the 2p orbitals are higher in energy than the 2s orbital and that each p orbital in the degenerate 2p set has a single electron of the same spin as the others in this set. AUFBAU (G. BUILDING UP) PRINCIPLE 17 c01.qxd 5/17/2005 5:12 PM Page 17
18 ATOMIC ORBITAL THEORY 29 Figure 1.41.The placement of electrons in the orbitals of the nitrogen atom 1.42 ELECTRONIC CONFIGURATION The orbital occupation of the electrons of an atom written in a notation that consists of listing the principal quantum number,followed by the azimuthal quantum num- ber designation (s.p,d,f).followed in each case by a superscript indicating the number of electrons in the particular orbitals.The listing is given in the order of increasing energy of the orbitals. Erample.The total numbe er of electrons to be placed in orbitals is equal to the atomi numbe of the atom,which is also equal to the number of protons in the nucleus of th atom.The electronic configuration of the nitrogen atom,atomic number 7(Fig.1.41). is 1s2 2s2 2p;for Ne,atomic number 10,it is 1s22s22p;for Ar,atomic number 18,it is 1s2222p53s23p;and for Sc.atomic number 21,it is [Ar)4523d,where [Ar]repre- sents the rare gas,18-electron electronic configuration of Ar in which all s and p 1.43 SHELL DESIGNATION The letters K,L,M,N.and O are used to designate the principal quantum number n. Eromple.The 1s orbital which has the lowest principal quantum number.n=1.is designated the K shell;the shell when n=2 is the L shell, ade up of the 2s.2 and 2p.orbitals;and the shell whe =3 is the M shell co of the 3s.the thr and the fi itals.Althoug h the for she deienation is not clearly domentd h en s e origin of he letters K. that these letters were abstracted from the name of physicist Charles Barkla(1877- 1944,who received the Nobel Prize,in 1917).He along with collaborators had noted that two rays were characteristically emitted from the inner shells of an element after
1.42 ELECTRONIC CONFIGURATION The orbital occupation of the electrons of an atom written in a notation that consists of listing the principal quantum number, followed by the azimuthal quantum number designation (s, p, d, f ), followed in each case by a superscript indicating the number of electrons in the particular orbitals. The listing is given in the order of increasing energy of the orbitals. Example. The total number of electrons to be placed in orbitals is equal to the atomic number of the atom, which is also equal to the number of protons in the nucleus of the atom. The electronic configuration of the nitrogen atom, atomic number 7 (Fig. 1.41), is 1s2 2s2 2p3 ; for Ne, atomic number 10, it is 1s2 2s2 2p6 ; for Ar, atomic number 18, it is 1s2 2s2 2p6 3s2 3p6 ; and for Sc, atomic number 21, it is [Ar]4s2 3d1 ,where [Ar] represents the rare gas, 18-electron electronic configuration of Ar in which all s and p orbitals with n 1 to 3, are filled with electrons. The energies of orbitals are approximately as follows: 1s 2s 2p 3s 3p 4s ≈3d 4p 5s ≈ 4d. 1.43 SHELL DESIGNATION The letters K, L, M, N, and O are used to designate the principal quantum number n. Example. The 1s orbital which has the lowest principal quantum number, n 1, is designated the K shell; the shell when n 2 is the L shell, made up of the 2s, 2px, 2py, and 2pz orbitals; and the shell when n 3 is the M shell consisting of the 3s, the three 3p orbitals, and the five 3d orbitals. Although the origin of the use of the letters K, L, M, and so on, for shell designation is not clearly documented, it has been suggested that these letters were abstracted from the name of physicist Charles Barkla (1877– 1944, who received the Nobel Prize, in 1917). He along with collaborators had noted that two rays were characteristically emitted from the inner shells of an element after 18 ATOMIC ORBITAL THEORY 1s 2s 2p Figure 1.41. The placement of electrons in the orbitals of the nitrogen atom. c01.qxd 5/17/2005 5:12 PM Page 18
THE PERIODIC TABLE 19 X-ray bombardment and these were designated K and L.He chose these mid-alphabe letters from his ame because he anticipated the discovery of other rays.and wished to leave alphabetical space on either side for future labeling of these rays. 1.44 THE PERIODIC TABLE An arrangement in tabular form of all the known elements in rows and columns in sequen of their mbers.The P iodic Table is ar expression oft tha ates many of the properties of the ization energies.,ele tron affinities,electronegativities,etc.)are a periodic f of their atomic numbers.By some estimates there may be as many as 700 different versions of the Periodic Table.A common display of this table.Fig.1.44a.consists of boxes placed in rows and columns.Each box shown in the table contains the sym- bol of the element,its atomic number,and a number at the bottom that is the aver- age atomic weight of the element determined from the natural abundance of its various isotopes s.There are seven rows of the elements corresp nding to the increas ing values of the principa m I to7.Ea rows bea with an element having one electron in the ns orbit tal and termi having the number of electrons corresponding to the completely filled K.M. and O shell containing 2,8,18,32,and 32 electrons,respectively.Row I consists of the elements H and He only;row 2 runs from Li to Ne;row 3 from Na to Ar,and so on.It is in the numbering of the columns,often called groups or families,where there is substantial disagreement among interested chemists and historians. The table shown in Fig.144g is a pular version (sometimes denoted as the American ABA scheme)of the Peri Table.In the ABA ve rsion the ele ents in d as belo ing ith Rom The elements are furthe erals r an A group or a B group.The A group elements are called representative or main group ele ments.The last column is sometimes designated as Group 0 or Group VIIIA.These are the rare gases;they are characterized by having completely filled outer shells: they occur in monoatomic form;and they are relatively chemically inert.The B group elements are the transition metal elements;these are the elements with ele rons in partially filled (n-1)d or(n-2)f orbitals.The 4th and 5th row transition metals alle tals nd the ele ments sho own in the 6th and 7th oat the om of Fig.1.44a are the sition me ough there is n of metd they are classified as such if they possess the following group characteristics:high electrical conductivity that decreases with increasing temperature;high thermal conductivity:high ductiliry (easily stretched,not brittle);and malleability (can be hammered and formed with- out breaking).Those elements in Fig.1.44a that are considered metals are shaded either lightly(A group)or more darkly (B group):those that are not shaded are non- metals:those having pr perties intermediate between metals and nonmetals are cross-hatc ed.Th of this last group are s called metalloids o these include .Thelements in the A sou have one to eisht ecro in hir oueosD boron,sil con,germar arsenic ony.and tel
X-ray bombardment and these were designated K and L. He chose these mid-alphabet letters from his name because he anticipated the discovery of other rays, and wished to leave alphabetical space on either side for future labeling of these rays. 1.44 THE PERIODIC TABLE An arrangement in tabular form of all the known elements in rows and columns in sequentially increasing order of their atomic numbers. The Periodic Table is an expression of the periodic law that states many of the properties of the elements (ionization energies, electron affinities, electronegativities, etc.) are a periodic function of their atomic numbers. By some estimates there may be as many as 700 different versions of the Periodic Table. A common display of this table, Fig. 1.44a, consists of boxes placed in rows and columns. Each box shown in the table contains the symbol of the element, its atomic number, and a number at the bottom that is the average atomic weight of the element determined from the natural abundance of its various isotopes. There are seven rows of the elements corresponding to the increasing values of the principal quantum number n, from 1 to 7. Each of these rows begins with an element having one electron in the ns orbital and terminates with an element having the number of electrons corresponding to the completely filled K, L, M, N, and O shell containing 2, 8, 18, 32, and 32 electrons, respectively. Row 1 consists of the elements H and He only; row 2 runs from Li to Ne; row 3 from Na to Ar, and so on. It is in the numbering of the columns, often called groups or families, where there is substantial disagreement among interested chemists and historians. The table shown in Fig. 1.44a is a popular version (sometimes denoted as the American ABA scheme) of the Periodic Table. In the ABA version the elements in a column are classified as belonging to a group, numbered with Roman numerals I through VIII. The elements are further classified as belonging to either an A group or a B group. The A group elements are called representative or main group elements. The last column is sometimes designated as Group 0 or Group VIIIA. These are the rare gases; they are characterized by having completely filled outer shells; they occur in monoatomic form; and they are relatively chemically inert. The B group elements are the transition metal elements; these are the elements with electrons in partially filled (n 1)d or (n 2)f orbitals. The 4th and 5th row transition metals are called outer transition metals, and the elements shown in the 6th and 7th row at the bottom of Fig. 1.44a are the inner transition metals. Although there is no precise chemical definition of metals, they are classified as such if they possess the following group characteristics: high electrical conductivity that decreases with increasing temperature; high thermal conductivity; high ductility (easily stretched, not brittle); and malleability (can be hammered and formed without breaking). Those elements in Fig. 1.44a that are considered metals are shaded either lightly (A group) or more darkly (B group); those that are not shaded are nonmetals; those having properties intermediate between metals and nonmetals are cross-hatched. The members of this last group are sometimes called metalloids or semimetals; these include boron, silicon, germanium, arsenic antimony, and tellurium. The elements in the A group have one to eight electrons in their outermost THE PERIODIC TABLE 19 c01.qxd 5/17/2005 5:12 PM Page 19
屋嘎暖得号国 隆…理理经清越 任滑隆道 54路 子…避 任刘进明 6 看唱 86 8 88 858 R (A 8 6E9 8 F'I!d 罗 8> 88 6止图
Figure 1.44. (a) A Periodic Table of the elements. ∗Lanthanides Actinides 1 H 1.0080 3 Li 6.941 4 Be 9.01218 11 Na 22.9898 12 Mg 24.305 56 Ba 137.34 55 Cs 132.9055 88 Ra 226.0254 87 Fr (223) 38 Sr 87.62 37 Rb 85.4678 19 K 39.102 20 Ca 40.08 27 Co 58.9332 45 Rh 102.9055 44 Ru 101.07 43 Tc 98.9062 42 Mo 95.94 77 Ir 192.22 76 Os 190.2 75 Re 186.2 74 W 183.85 73 Ta 180.9479 72 Hf 178.49 ∗ 106 105 Ha 104 Rf (260) 89 Ac (227) 90 Th 232.0381 91 Pa 231.0359 92 U 238.029 93 Np 237.0482 94 Pu (242) 95 Am (243) 96 Cm (247) 97 Bk (247) 98 Cf (251) 99 Es (254) 100 Fm (257) 101 Md (256) 102 No (256) 103 Lr (257) 57 La 138.9055 58 Ce 140.12 59 Pr 140.9077 60 Nd 144.24 61 Pm (145) 62 Sm 150.4 63 Eu 151.96 64 Gd 157.25 65 Tb 158.9254 66 Dy 162.50 67 Ho 164.9303 68 Er 167.26 69 Tm 168.9342 70 Yb 173.04 71 Lu 174.97 41 Nb 92.9064 40 Zr 91.22 39 Y 88.9059 21 Sc 44.9559 22 Ti 47.90 23 V 50.9414 24 Cr 51.996 25 Mn 54.9380 26 Fe 55.847 I A II A III B IV B V B VI B VII B Transition elements Representative elements Representative elements I B II B III A IV A V A VI A VII A 0 (VIII A) VIII (VII B) Period 1 2 3 4 5 6 7 18 Ar 39.948 51 Sb 121.75 52 Te 127.60 53 I 126.9045 54 Xe 131.30 50 Sn 118.69 49 In 114.82 48 Cd 112.40 47 Ag 107.868 46 Pd 106.4 78 Pt 195.09 79 Au 196.9665 80 Hg 200.59 81 Tl 204.37 82 Pb 207.2 83 Bi 208.9806 84 Po (210) 85 At (210) 86 Rn (222) 28 Ni 58.71 29 Cu 63.546 30 Zn 65.37 31 Ga 69.72 32 Ge 72.59 33 As 74.9216 34 Se 78.96 35 Br 79.904 36 Kr 83.80 13 Al 26.9815 14 Si 28.086 15 P 30.9738 16 S 32.06 17 Cl 35.453 10 Ne 20.179 9 F 18.9984 8 O 15.9994 7 N 14.0067 6 C 12.0111 5 B 10.81 2 He 4.00260 1 H 1.0080 Inner transition elements 20 c01.qxd 5/17/2005 5:12 PM Page 20