(G S Manku, email: manku.gs@gmail.com)

(4.2).1 Types of Elements

Based on the electronic configuration of the incompletely filled shells of electrons, the elements are classified as (1) Main period representative or R elements, (2) Transition or T elements, and (3) Inner-transition or IT elements.

(4.2).1.1 REPRESENTATIVE ELEMENTS

In representative elements or the R families, only the outermost shell has incompletely filled orbitals. Thus, only the outermost n-th shell is the valence shell of R elements.  These elements are further classified   as: 

1. s-Block Elements, having configuration of outermost shell of the atom as n¹ or ns². These elements belong to group I A and II A of  Mendeleev’s or classical periodic table and groups 1 and 2 of the long periodic table.
2. p-Block Elements, having electronic configuration of the outermost valence shell  of atom as ns²np^x, where x = 1, 2, 3, 4, 5 or 6. In the long periodic table, these are groups 13 to 18 elements (group number = 10 + y, (where y = 2 + x) is the total number of electrons in the outermost shell). These are also called R-3 to R-7 and R-0 families.

Table (4.2).1 The R Elements

——————————————————————————————
 Configuration    Group number    Family (Common) name
——————————————————————————————-
ns¹                           Group 1           R-1         Alkali metals ns²np¹ 
ns²                        Group 2           R-2         Alkaline earth metals
ns²np¹                   Group 13         R-3         Boron family
ns²np²                   Group 14         R-4         Carbon family
ns²np³                   Group 15         R-5         Nitrogen family
ns²np⁴                   Group 16         R-6         Oxygen family
ns²np⁵                   Group 17         R-7         The halogens
ns²np⁶                   Group 18         R-0         Group 0, noble elements
————————————————————————————

Strictly speaking, in the atoms of copper and zinc families, ytterbium and nobelium also, only the outermost shell is incomplete, all other underlying subshells are completely filled up with electrons and should also be considered as representative elements:

————————————————————————————

Copper        Z =29      [Ar] 3s²3p⁶3d¹⁰ 4s¹             Group 11   
                                                                          Transition element

Silver           Z =47      [Kr] 4s²4p⁶4d¹⁰ 5s¹             Group 11          
                                                                             Transition element

Gold             Z =79      [Xe] 4f¹⁴ 5s²5p⁶5d¹⁰ 6s¹      Group 11    
                                                                             Transition element

Zinc             Z =30      [Ar] 3s²3p⁶3d¹⁰ 4s²           Group 12 
                                                                              Transition element

Cadmium   Z =48      [Kr] 4s²4p⁶4d¹⁰ 5s²           Group 12
                                                                            Transition element

Mercury     Z =80      [Xe] 4f¹⁴ 5s²5p⁶5d¹⁰ 6s²     Group 12
                                                                              Transition element

Ytterbium   Z = 70     [Xe] 4f¹⁴ 6s¹                               4f block
                                                                       Inner transition element

Lutetium     Z = 71     [Xe] 4f¹⁴ 6s²                                5f block 
                                                                       Inner transition element

      —————————————————————————-

However, as the copper and zinc families have a close resemblance to the transition elements, they are considered as transition elements. Ytterbium and nobelium are similar to other inner transition elements, and are considered  inner transition elements.

On the basis of their chemical reactivity, the s²p⁶ elements are called group zero or noble elements (formerly called ‘the inert elements’) because of their extremely low reactivity. The remaining elements however, are called the R-1 to R-7 families as before.

(4.2).1.2 TRANSITION ELEMENTS

The transition elements have incompletely filled d orbitals in their ground state or in chemically combined state. The configuration of the incompletely filled electronic subshells of these atoms is:

(n – 1)s²(n – 1)p⁶ (n – 1)d^xns²                        (x = 1-10)

Thus, atoms of transition elements have two outermost incompletely filled shells, with principal quantum numbers = n and n – 1. Therefore, their valence shells consist of electrons present in two outermost electron shells and these elements can use the (n – 1)d, ns and np electrons for bonding in chemical compounds.

Four series of transition elements are known. These correspond to the filling up of the energy levels corresponding to 3d, 4d, 5d, and 6d orbitals respectively:

———————————————————————————————-
Series    Electronic configuration                Elements (Atomic number Z)
——————————————————————————————

3d                 [Ar] 3d^{1-10}4s^1,2                           Sc (21) – Zn (30)
4d                 [Kr] 4d^{1-10}5s^1,2                            Y (39) – Cd (48) 
5d                [Xe] 4f¹⁴ 5d^{1-10}6s^1,2                 La (57), Hf (72) – Hg (80)
6d                [Rn] 5f¹⁴ 6d^{1-10}7s^1,2                Ac (89), Rf (104) – Og (118)

——————————————————————————————-

Strictly speaking, the atoms of lutetium (Z = 71) and nobelium (Z = 103) have completely filled f¹⁴ subshell and have electronic configuration similar to those of the transition elements:

Lutetium   Z = 71   [Xe] 4f¹⁴ 5d¹ 6s²    Completely filled 4f orbitals
Nobelium  Z = 103 [Rn] 5f¹⁴ 6d¹ 7s²    Completely filled 5f orbitals

Yet they are classified as inner transitions elements because of a close resemblance between the properties of these elements and the preceding inner transition elements.

All the transition elements have similar physico-chamical properties: high melting and boiling points, malleability and ductility, tensile strength, metallic character, formation of alloys, coordination compounds, high as well as low oxidation states, formation of paramagnetic and colored ions, polynuclear and metallic clustered compounds, etc. Detailed discussion is in Coordination Compound and Transition elements.

(4.2).1.3 INNER TRANSITION ELEMENTS

The inner transition elements correspond to the filling   of electrons in  the $f$ orbitals of the atoms.The electronic configuration of these elements can be represented as

(n – 2)s² (n – 2)p⁶(n – 2)d¹⁰ (n – 2)f^(1-14) (n – 1)s²
(n – 1)p⁶(n – 1)d¹ ns²

The atoms  of  these elements have three outermost incompletely filled  shells, with principal quantum numbers =  n, n – 1 and  n – 2.Their valence shells, therefore, consist of electrons in these three outermost shells.

 Only two series of inner transition elements are known. These correspond to the filling up of the 4f and 5f orbitals, and contain fourteen elements each:

Series           Common Name                    (Z)
———————————————————————————
4f            Lanthanides or lanthanons           Ce (58) to Lu (71)
5f           Actinides or actinons                      Th (90) to Lr (103)
———————————————————————————

As the successive electrons in the lanthanide series are filled up in the low energy inner 4f subshell, they   generally, do not participate in chemical combinations. As a result, the lanthanides have almost similar properties and show a regular gradation throughout the series.

In the 5f or the actinide series, however, due to larger atomic sizes and considerably lower energy differences between the 5f, 6d and 7s orbitals, the actinide elements up to Z = 96 can use their 5f as well as 6d electrons for chemical bonding. Actually speaking, thorium (90), protactinium (91) and uranium (92) resemble transition elements titanium, vanadium and chromium respectively. As Z increases,  the energy of the lower shell 5f electrons decreases more as compared to that of higher shell 6d electrons, and the  relative stability of 5f electrons increases. As a result, the latter 5f elements resemble the lanthanide elements of 4f series.

All the inner transition elements show a uniform valence state of III by losing outermost shell ns and next inner shell electrons. However, due to the additional stability of completely vacant f⁰, half-filled f⁷ and completely filled f¹⁴ configurations of the f subshell, the elements having one electron less or one electron more show additional states of II and IV respectively also.

(4.2).1.4 Prediction of New Elements and Compounds

(4.2).1.4.1 Historical Developments

Newlands (1864) was first to predict the existence of a missing element between silicon and tin with atomic mass of 73. (Presently, accepted value for atomic mass of germanium, discovered by Winkler in 1886, is 72.59.) Mendeleev’s predictions, made in 1869–1871, were more exhaustive and indicate the depth of his understanding. Of the 26 undiscovered elements of his time between hydrogen and uranium,

Eleven were lanthanides, which are very similar to one another, and were established in 1871 to 1907.

Five are noble gases (helium, neon, argon, krypton, and xenon) present in small amounts in air and isolated around 1894–1898 .

 The four radioactive elements were discovered: polonium (Marie Curie, 1898), radium (M Curie and P Curie, 1898), actinium (A Debierne, 1899) and radon (Dorn, 1900).

(4.2).1.4.2  The super-heavy elements with atomic numbers > 103

A group of trans-uranium elements was synthesized by artificial nuclear reactions during 1940 onwards.  The 6d transition series starts with Z = 104 (rutherfordium, Rf) and is complete at Z = 112 (copernicium Cn), Other members of the series are Z = 105 (dubnium, Db), Z = 106 (seaborgium, Sg), Z = 107 (Bohrium, Bh), Z = 108 (hassium, Hs), Z = 109 (meitnerium, Mt), Z = 110 (darmstadtium, Ds) and Z = 111 (roentgenium, Rg). These elements are increasing unstable with respect to α decay or spontaneous fission with half-life of the order of less than 1 sec. It is unlikely that much chemistry can be developed for these elements, though their physicochemical constants have all been predicted.

After this, there follow the six 7p elements for Z = 113 to 118. These are (with their atomic numbers): 113 (nohonium, Nh), 114 (flevonium, Fl), 115 (moscovium, Mc), 116 (livermanium, Lv), 117 (tenessium Ts) and 118 (oganesson, Og). On the basis of present theories of nuclear stability, the ²⁹⁸₁₁₄Fl may be stable due to island of nuclear stability (number of protons = 114, a magic number for nuclear stability) with a long half-life.

(4.2).5 EFFECTIVE NUCLEAR CHARGE

 (4.2).5.1 Shielding Effect or Screening Effect

Almost all the physical and chemical properties of an element depend upon the electronic configuration of its atom and the hold of nucleus on these electrons.

 As example, consider a sodium atom having the electronic configuration of 1s²2s²2p⁶3s¹. Its properties depend upon the behavior of the outermost valence shell 3s¹ electron.  There are 2 + 8 = 10 electrons between the valence shell electron and the nucleus.  According to electrostatics, the net effect of charge on these electrons will be that of a point charge carrying 10 units of negative charge placed at the centre. This should reduce the effect of positive charge   at the nucleus by 10 units, so that the valence shell electrons should be attracted by a net positive charge of 1 unit only.

The decrease in the nuclear charge due to the presence of electrons in the inner shells is called the shielding effect or screening effect of electrons present in the  inner  shells. However, due to quantum mechanical considerations of penetration of orbitals and their orientations, all the inner electrons may not be equally effective in shielding the outer electrons (at some instant, they may be not be in line with nucleus and  outer electron). For example, an electron in p_x orbital will not be much effective in shielding another electron in say p_y or p_z orbital as they are mutually perpendicular to each other.

In multi-electron systems, the effective positive charge Z* experienced by the electrons is always less than the nuclear charge Z, and is given by J C Slater(1930) as

Z* = Z – σ

where σ is called  Slater’s shielding constant or screening constant.

(4.2).5.2 Slater’s Rules

Based on the general behavior of electrons in polyelectronic systems, Slater (1930) gave the following empirical rules for calculating the screening constant (σ).

1. Group the electrons present in the orbitals in the order

(1s)(2s, 2p) (3s, 3p) (3d), (4s, 4p) (4d, 4f) (5s, 5p), (5d, 5f) (6s, 6p), …

2. The electrons present in a particular group are not effective in shielding the electron in a group lower or left to it in the above order. Thus, σ for 4s electrons in shielding a 3d or 3s electron = 0.
3. The shielding is more if there are more electrons in the lower groups.
4. For calculating value of the shielding constant for an electron in ns or np orbital, σ for the other electrons present in the (ns, np) group is 0.35 each. However, for 1s orbital, σ = 0.30.
5. All the electrons in the next lower group contribute 0.85 each to the screening constant.
6. All the electrons in the second lower and other lower groups shield the electron completely (σ = 1.00 for each electron).
7. For the d or f electrons, contribution of the electrons in the same group remains 0.35 each, but all the electrons in the lower groups shield the d or f electrons completely and have σ = 1.00 each.

Numerical Example 

For bromine, calculate the effective nuclear charge for (a) valence shell electrons, (b) 3d electrons, (c) 3p, and (d) 2p electrons.

Solution: The electrons in the orbitals of bromine are grouped as

(1s²) (2s², 2p⁶) (3s², 3p⁶), (3d¹⁰), (4s², 4p⁵)

(a) For the valence shell electron of the 4s or 4p orbitals,

σ = 0.35 (electrons remaining in 4s and 4p orbitals = 6)
 0.85 (electrons in 3d orbitals = 10) + 1.00 (electrons in
1s, 2s, 2p, 3s and 3p orbitals = 18)

= 0.35 × 6 + 0.85 × 10 + 1.00 × 18
   = 28.60

Hence, Z* = Z – σ = 35.00 – 28.6 6.40

(b) For the 3d electrons,

 σ = 0.35 (electrons remaining in 3d orbitals = 9) + 1.00 (electrons
in 1s, 2s, 2p, 3s and 3p orbitals = 18)
         = 21.15

Hence, Z* = Z – σ  = 35.00 – 21.15 = 13.85.

(c) For electron in the 3p orbitals,

σ = 0.35 (electrons remaining in 3s and 3p orbitals = 7)
+ 0.85 (electrons in 2s and 2p orbitals = 8) 
+ 1.00 (electrons in 1s orbital = 2)

= 11.25

Hence,  Z* = Z – σ = 35.00 – 11.25 = 23.75.

(d) For the 2p  electrons,

 σ =  0.35 (electrons remaining in 2s and 2p orbitals = 7)
+ 0.85 (electrons in 1s orbital = 2)
= 4.15

Hence, Z* = Z – σ = 35.00 – 4.15 = 30.85.

As seen from the above example, the effective nuclear charge increases as one goes nearer the nucleus.

(4.2).5.3 Variation of Effective Nuclear Charge in a Period

Because of the incomplete shielding of the increasing nuclear charge by the incoming electrons, the effective nuclear charge for the valence shell electrons increases with atomic number across the period and is in the order:

Li(1.30) < Be(1.95) < B(2.60) < C(3.25) < N(3.90)
< O(4.55) < F(5.20) < Ne(5.85)

Sc(1.85) < Ti(2.00) < V(2.15) < Mn(2.45) < Fe(2.60)
 < Co(2.75) < Ni(2.90) < Zn(3.20)

Note that the effective nuclear charge increases more rapidly for the representative elements (by 0.65 units) than for the transition elements (by 0.15 unit only) as the electrons in the latter are accommodated in the better shielding inner orbitals. Effective nuclear charge for chromium (1.75) and copper (2.50) is much lower than that expected in the series due to the exchange energy which transfers one outer 4s electron to inner 3d orbital.

 (4.2).5.4 Limitations of Slater’s Rules

 1. Electrons in s and p orbitals as well as in d and f orbitals of a shell are considered to be affected to the same extent by the nuclear charge.

2. All the electrons in the s, p, d and f orbitals of a shell are considered to be equally effective in shielding electrons in higher orbitals. This is against the widely different energies and spatial orientations of these orbitals.

3. Penetration effects of orbitals are completely ignored.

4. These rules are approximate and do not give the actual energies of the orbitals in the atoms.

5. These rules are not much useful for elements with Z > 30.

 Slater’s orbitals: Slater proposed that to obtain hydrogen-like orbitals for polyelectronic atoms,

(1) The nuclear charge should be replaced by Z*, calculated as above, and

(2) For n > 3, n is changed to n*, where n* = 3.7 for n = 4, 4.0 for n = 5, 4.32 for n = 6, and 4.5 for n =7.

The orbitals so calculated are called Slater’s orbitals, and were useful in calculating energies of different electrons in atoms.