TOPICS
1.8 The periodic table
In 1869 and 1870 respectively, 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. As new elements have been discovered, the original form of
†The IUPAC recommends the names lanthanoid and actinoid in preference to lanthanide and actinide; the ending ‘-ide’ usually implies a negatively charged ion.
Chapter 1 . Many-electron atoms 17
Table 1.3 Ground state electronic configurations of the elements up to Z¼ 103.
Atomic Element Ground state Atomic Element Ground state
number electronic configuration number electronic configuration
1 H 1s1
2 He 1s2¼ [He]
3 Li [He]2s1
4 Be [He]2s2
5 B [He]2s22p1
6 C [He]2s22p2
7 N [He]2s22p3
8 O [He]2s22p4
9 F [He]2s22p5
10 Ne [He]2s22p6¼ [Ne]
11 Na [Ne]3s1
12 Mg [Ne]3s2
13 Al [Ne]3s23p1
14 Si [Ne]3s23p2
15 P [Ne]3s23p3
16 S [Ne]3s23p4
17 Cl [Ne]3s23p5
18 Ar [Ne]3s23p6¼ [Ar]
19 K [Ar]4s1
20 Ca [Ar]4s2
21 Sc [Ar]4s23d1
22 Ti [Ar]4s23d2
23 V [Ar]4s23d3
24 Cr [Ar]4s13d5
25 Mn [Ar]4s23d5
26 Fe [Ar]4s23d6
27 Co [Ar]4s23d7
28 Ni [Ar]4s23d8
29 Cu [Ar]4s13d10
30 Zn [Ar]4s23d10
31 Ga [Ar]4s23d104p1 32 Ge [Ar]4s23d104p2 33 As [Ar]4s23d104p3 34 Se [Ar]4s23d104p4 35 Br [Ar]4s23d104p5 36 Kr [Ar]4s23d104p6= [Kr]
37 Rb [Kr]5s1
38 Sr [Kr]5s2
39 Y [Kr]5s24d1
40 Zr [Kr]5s24d2
41 Nb [Kr]5s14d4
42 Mo [Kr]5s14d5
43 Tc [Kr]5s24d5
44 Ru [Kr]5s14d7
45 Rh [Kr]5s14d8
46 Pd [Kr]5s04d10
47 Ag [Kr]5s14d10
48 Cd [Kr]5s24d10
49 In [Kr]5s24d105p1 50 Sn [Kr]5s24d105p2 51 Sb [Kr]5s24d105p3 52 Te [Kr]5s24d105p4
53 I [Kr]5s24d105p5
54 Xe [Kr]5s24d105p6¼ [Xe]
55 Cs [Xe]6s1
56 Ba [Xe]6s2
57 La [Xe]6s25d1
58 Ce [Xe]4f16s25d1
59 Pr [Xe]4f36s2
60 Nd [Xe]4f46s2
61 Pm [Xe]4f56s2
62 Sm [Xe]4f66s2
63 Eu [Xe]4f76s2
64 Gd [Xe]4f76s25d1
65 Tb [Xe]4f96s2
66 Dy [Xe]4f106s2
67 Ho [Xe]4f116s2
68 Er [Xe]4f126s2
69 Tm [Xe]4f136s2
70 Yb [Xe]4f146s2
71 Lu [Xe]4f146s25d1
72 Hf [Xe]4f146s25d2
73 Ta [Xe]4f146s25d3
74 W [Xe]4f146s25d4
75 Re [Xe]4f146s25d5
76 Os [Xe]4f146s25d6
77 Ir [Xe]4f146s25d7
78 Pt [Xe]4f146s15d9
79 Au [Xe]4f146s15d10
80 Hg [Xe]4f146s25d10
81 Tl [Xe]4f146s25d106p1
82 Pb [Xe]4f146s25d106p2
83 Bi [Xe]4f146s25d106p3
84 Po [Xe]4f146s25d106p4
85 At [Xe]4f146s25d106p5
86 Rn [Xe]4f146s25d106p6= [Rn]
87 Fr [Rn]7s1
88 Ra [Rn]7s2
89 Ac [Rn]6d17s2
90 Th [Rn]6d27s2
91 Pa [Rn]5f27s26d1
92 U [Rn]5f37s26d1
93 Np [Rn]5f47s26d1
94 Pu [Rn]5f67s2
95 Am [Rn]5f77s2
96 Cm [Rn]5f77s26d1
97 Bk [Rn]5f97s2
98 Cf [Rn]5f107s2
99 Es [Rn]5f117s2
100 Fm [Rn]5f127s2
101 Md [Rn]5f137s2
102 No [Rn]5f147s2
103 Lr [Rn]5f147s26d1
Fig. 1.12 Radial distribution functions, 4r2RðrÞ2, for the 1s, 2s and 2p atomic orbitals of the hydrogen atom.
CHEMICAL AND THEORETICAL BACKGROUND Box 1.6 Effective nuclear charge and Slater’s rules
Slater’s rules
Effective nuclear charges, Zeff, 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 Zeff is determined from the equation:
Zeff¼ Z S
where Z¼ nuclear charge, Zeff¼ effective nuclear charge, S¼ 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 = 0.35.
(ii) Each of the electrons in the ðn 1Þ shell contri-butes S¼ 0:85.
(iii) Each of the electrons in theðn 2Þ or lower shells contributes S¼ 1:00.
4. Consider a particular electron in an nd or nf orbital:
(i) Each of the other electrons in the (nd, nf ) group contributes S¼ 0:35.
(ii) Each of the electrons in a lower group than the one being considered contributes S¼ 1:00.
An example of how to apply Slater’s rules
Question: Confirm that the experimentally observed electro-nic configuration of K, 1s22s22p63s23p64s1, is energetically more stable than the configuration 1s22s22p63s23p63d1.
For K, Z¼ 19:
Applying Slater’s rules, the effective nuclear charge experienced by the 4s electron for the configuration 1s22s22p63s23p64s1is:
Zeff¼ Z S
¼ 19 ½ð8 0:85Þ þ ð10 1:00Þ
¼ 2:20
The effective nuclear charge experienced by the 3d electron for the configuration 1s22s22p63s23p63d1is:
Zeff¼ Z S
¼ 19 ð18 1:00Þ
¼ 1:00
Thus, an electron in the 4s (rather than the 3d) atomic orbital is under the influence of a greater effective nuclear charge and in the ground state of potassium, it is the 4s atomic orbital that is occupied.
Slater versus Clementi and Raimondi values of Zeff Slater’s rules have been used to estimate ionization energies, ionic radii and electronegativities. More accurate effective nuclear charges have been calculated by Clementi and Raimondi by using self-consistent field (SCF) methods, and indicate much higher Zeff values for the d electrons.
However, the simplicity of Slater’s approach makes this an attractive method for ‘back-of-the-envelope’ estimations
of Zeff. "
Chapter 1 . Many-electron atoms 19
the periodic table has been extensively modified, and it is now recognized that periodicity is a consequence of the variation in ground state electronic configurations. A modern periodic table (Figure 1.13) emphasizes the blocks of 2, 6, 10 and 14 elements which result from the filling of the s, p, d and f atomic orbitals respectively. An exception is He, which, for reasons of its chemistry, is placed in a groupwith Ne, Ar, Kr, Xe and Rn. A more detailed periodic table is given inside the front cover of the book.
The IUPAC (International Union of Pure and Applied Chemistry) has produced guidelines† for naming blocks and groups of elements in the periodic table. In summary, . blocks of elements may be designated by use of the letters
s, p, d or f (Figure 1.13);
Self-study exercises
1. Show that Slater’s rules give a value of Zeff¼ 1:95 for a 2s electron in a Be atom.
2. Show that Slater’s rules give a value of Zeff¼ 5:20 for a 2p electron of F.
3. Use Slater’s rules to estimate values of Zeff for (a) a 4s and (b) a 3d electron in a V atom.
[Ans. (a) 3.30; (b) 4.30]
4. Using your answer to question 3, explain why the valence configuration of the ground state of a Vþion is likely to be 3d34s1rather than 3d24s2.
Further reading
G. Wulfsberg (2000) Inorganic Chemistry, University Science Books, Sausalito, CA – Contains a fuller treatment of Slater’s rules and illustrates their application, particularly to the assessment of electronegativity.
Fig. 1.13 The modern periodic table in which the elements are arranged in numerical order according to the number of protons (and electrons) they possess. The division into groups places elements with the same number of valence electrons into vertical columns within the table. Under IUPAC recommendations, the groups are labelled from 1 to 18 (Arabic numbers). The vertical groups of three d-block elements are called triads. Rows in the periodic table are called periods. The first period contains H and He, but the row from Li to Ne is sometimes referred to as the first period. Strictly, the lanthanoids include the 14 elements Ce–Lu, and the actinoids include Th–Lr; however, common usage places La with the lanthanoids, and Ac with the actinoids (see Chapter 24).
†IUPAC: Nomenclature of Inorganic Chemistry (Recommendations 1990), ed. G.J. Leigh, Blackwell Scientific Publications, Oxford.
. elements (except H) in groups 1, 2 and 13–18 are called main group elements;
. with the exception of group 18, the first two elements of each main group are called typical elements;
. elements in groups 3–11 (i.e. those with partially filled d orbitals) are called transition elements.
Note the distinction between a transition and d-block element.
Elements in groups 3–12 inclusive are collectively called d-block elements, but by the IUPAC rulings, a transition metal is an element, an atom of which possesses an incomplete d-shell or which gives rise to a cation with an incomplete d-shell. Thus, elements in group 12 are not classed as transition elements. Collective names for some of the groups of elements in the periodic table are given in Table 1.4.