INTRODUCTION

Arrangements which give increase to similarities and differences in the properties of elements whose valence electrons appear in similar group and those whose valence electrons are in different groups correspondingly. These differences in the properties take place due to differences in atomic properties. These size of the atoms as measured in terms of radii.

Measurement of atomic radii:

Atomic radii are the measure of the size of the atom. Atomic radii are significant since another atomic property like electron affinity, electro negativity and ionization energy is related to them. The wave mechanical picture of an atom depicts an atom as composed of a compact nucleus enclosed via an electron cloud. This electron cloud does not have a specific boundary surface similar to that of a ball. There is a definite but extremely small probability of finding an electron at an infinite distance from the nucleus of the atom. Though this does not mean that the atom is indefinitely huge, thus we have to find a way to define the dimension of an atom. Accordingly, the radius of an atom can be identified as the distance from the centre of the nucleus to the point wherever the electron density is virtually zero.

Nowadays that we have described the size of an atom, we have to deal with the problem of measuring that size. We are instantaneously confronted with the problem of defining or accurately measuring that size we mean therefore, if we are measuring the dimension of an atom when it is occupying a lattice site of the crystal, the value will be different from one whenever it is colliding with other atom in the gaseous state. Furthermore, the size of a neutral atom will be different from the one whenever it is present as a anion and cation. Therefore, we cannot have one set of atomic radii appropriate under all conditions. It consequently becomes needed to identify the bonding conditions under which the size is being measured. Pertaining to the four major kinds of bonding, the atomic radii to be measured are:

I           Covalent radius,

II         Crystal or Metallic radius

III        Van der Waals radius

IV         Ionic radius

Covalent radius:

Covalent radius can be illustrated as one half of the distance between the nuclei of two like atoms bonded mutually via a single covalent bond. If in a homonuclear diatomic molecule of  A₂  type (eg  F₂, Cl₂ , Br₂ , I₂ ) r_A-A   is bond length and inter nucleus distance and r_A   is the covalent radius of the atom A, then r_A = 1/2 r_A-_A. The inter nuclear distance r_c -_c between two carbon atoms in diamond is 154pm, thus the covalent radius of carbon, re is equal to 77pm. likewise, the r _cl - _cl for solid cl₂ is 198 pm. r_cl is therefore 99pm.

In the heteronuclear, diatomic molecule of AB type, but the bonding is purely covalent, then the bond length r_A-_B is equal to the sum of covalent radii of A and B that is r = r_A + r_B. Therefore   covalent radii are additive. It is possible to determine the radius of one of the atoms in a heteronuclear diatomic molecule of AB type. If we recognize the internuclear distance r_A- _B   and radius of the other atom. For instance the Si-C bond length in carborundum is 193 pm and covalent radius of C is 77, so you can analyze the covalent radius of Si as given:

 r_si-c = r_si+r_c or r_si  = r_si-c-r                       

 r_si  = 193 - 77 = 116 pm

The above relation holds good quality only if the bond between the atoms A and B is purely covalent. If there is dissimilarity in the electronegativities of the bonded atoms, it causes shortening of the bonds. Schoemaker and Stevenson have proposed the following relationship between the shortening of the bond and the electronegativity difference of the atoms;

r_A-B  =  r_A + r _B - 0.07 (X_A-X_B )²  

Now X_A and X_B are the electro negativities of A and B correspondingly. Multiplicity of the bond also causes a shortening of the bond. Generally a double bond is about 0.86 times or a triple bond about 0.78 times the single bond length for the second period elements. Covalent radii of the elements are listed.

Table: Covalent and van der Waals radii of elements

Van Der Waal's Radius:

In the solid state, non-metallic elements frequently exist as aggregates of molecules. The bonding within a non metal molecule is largely covalent. Though, individual molecules are held mutually via weak forces recognized as Van der Waal's forces. Half of the distance between the nuclei of 2 atoms belonging to two adjacent molecules in a crystal lattice is termed Van der Waal's radius. Values of Van der Waals radii of several elements. Figure illustrates the dissimilarity between the covalent or van der Waals radii of chlorine.

Fig: Covalent and van der Waals radii of solid chlorine

It is evident from the figure which half of the distance between the nuclei X and Xi of the 2 non-bonded neighboring chlorine atoms of adjacent molecule A and B is the Van der Waal's radii of chlorine atom. On another hand half of the distances between the two nuclei X and Y in similar molecule is the covalent radius of chlorine atom.

Therefore Van der Waal's radii symbolize the distance of the closest approach of an atom into the other atom it is in contact with, but not covalently bond to it. Values of Van der Waals radii are larger than those of covalent radii since van der Waals forces are much weaker than the forces working between atoms in a covalently bonded molecule.

Metallic or Crystal Radius:

Metallic or crystal radius is used to illustrate the size of metal atoms that are generally imagined to be loosely packed spheres in the metallic crystal. The metal atoms are supposed to touch one the other in the crystal.  Metallic radius is described as 1/2 of the distance between the nuclei of 2 adjacent metal atoms in the close packed crystal lattice. For instance the internuclear distance between 2 adjacent Na atom in a crystal of sodium metal is 382 pm so metallic radius of Na metal is 382 that is 191 pm.

The metallic radius depends to several extents on the crystal structure of the metal. Mainly metals adopt a close packed (hcp) and face close packed (ccp) lattice.

Fig kinds of metal lattices:

(a) Hexagonal;

(b) Face centered cubic

(c) Body-centered cubic

In both these structure, a given metal atom has 12 nearest neighbors. Though an important number of metals adopt a body centered cubic lattice (bcc) in that the number of nearest neighbors is 8. The number of nearest neighbors of a metal atom in a lattice is called as the coordination number of the metal. Experimental studies on a number of metals having more than one crystal lattice have shown that the radius of a metal in an 8 coordinate lattice is about 0.97 of the radius of similar metal in a 12 coordinate atmosphere.

The metallic radii are usually superior to the analogous covalent radii. Even though both involve a sharing of electrons this is since the average bond order of an individual metal- metal bond is noticeably less than one and thus the individual bond is weaker or longer than the covalent. This does not mean that the overall bonding is weak as there is a huge number of this bond, 8 and 12 per metal atom. On another hand, the metallic crystal lattices are stronger than the Van der Waals forces.

Ionic Radius:

Ionic radius is described as the distance between the nucleus of an ion or the point up to that the nucleus has influence on the electron cloud. In other words, it might also be named as the distance of the closest approach from the centre of ion via another ion. Ionic radius is frequently assessed from the distance determined experimentally between the centres of nearest neighbors. Therefore if we wish to estimate the ionic radius of Na+ we may compute the inter nuclear distance between Na⁺ and Cl^- ions in the NaCl crystal lattice. This distance is the sum of radii of Na+ and C^- ions. From the electron density maps gained via x-ray analysis, it has become probable, in various cases, to apportion the internuclear distance into the radius of cation or anion. A small member of ionic crystals has therefore been studied or the ionic radii of several of the elements have been determined. These radii have become the basis for assigning the ionic radii of most of another element.

Ionic radii are of two kinds, cation radii or anion radii. All general cations are smaller than all common anion except for rubidium and caesium cations (largest single atom cations). This is not as well surprising because not only is there a loss of electron(s) from a partially filled outer shell on cation formation, but there is also a raise in the overall positive charge on the ion.

Conversely, in anion formation the addition of an electron to an atom raises the size due to rise in inter-electronic repulsion in the valence-shell and decrease in effective nuclear charge. In common, there is a decrease in size of anions to covalent radii of corresponding atoms to cations therefore in the series of iso electronic species (example N³, O^2-, Na, Na⁺, Mg²⁺ and Al³⁺). The greater the efficient nuclear charge, the smaller is the radius of the species. Radii of several of the common ions have been listed.

Factors Affecting the Atomic Radii:

We shall now turn our attention to 2 of the factors which affect them.

(A) Principal Quantum Number (n): As the principal quantum number amplifies, the outer electrons get farther away from the nucleus or therefore the atomic radius usually increases.

(B) Effective Nuclear Charge (Z*): The magnitude of the effective nuclear charge establishes the magnitude of the force of attraction exerted via the nucleus on the outermost electrons. The greater the magnitude of effective nuclear charge. The greater is the force exerted via the nucleus on the outermost electron. Therefore the electron cloud of the outermost shell is pulled inward nearer to the nucleus or therefore its distance from the nucleus. That is, atomic radius reduces. Effective nuclear charge Z* is the amount of positive charge felt via the outer electrons in an atom. It is forever less than the actual charger Z of the nucleus of the atom. This is since electrons in inner shells partially shield the e^-s in the outer shell from nuclear attraction. The effective nuclear charge felt through the outer electron depends on the genuine nuclear charge or the number and type of inner screening electrons. It can be computed by subtracting him screening and shielding steady, S from the atomic number Z therefore Z* = Z-S.

We can estimate the charge of screening steady, S, with the help of Slater's rules in the given manner:

i)        Write out he electronic configuration of the factor in the following order and groupings;

(Is) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f)

(5s, 5p) (5d) (5f) (6s, 6p) etc.

ii)      Electrons in any group higher in this sequence than the electron under consideration contribute nothing to s. For example in Ti atom (electronic configuration 1s², 2s², 2p⁶, 3s², 3p⁶, 3d², 4s²). The 2 electrons in 4s orbital will supply nothing on the way to the screening for an electron in 3d orbital.

iii)    Then for an electrons in an ns and np orbitals

a-      All another electrons in the (ns, np) group contribute S =0.35 each except for the electron in that contribute S = 0.30

b-      All electrons in (n-1) shells contribute S = 0.85 each

c-      All  electrons in (n-2) and lower shells contribute S = 1.00 each

iv)    For an electron in an nd or of  orbital

(a) All electrons in similar group that is nd or nf contribute S = 0.35 each.

(b) Those in the groups lying lower in the progression than the nd or nf group contribute S =1.00 each.

In order to describe the application of Slater's rules, we shall now compute the Z* for an electron in N, K and Zn atoms.

a. Electronic configuration of N = (Is²) (2s^2, 2p³)

Grouping (Is²) (2s², 2p³)

Value of screening constant for an electron in 2p orbital will be

S = (4 x 0.35) + (2 x 0.85) = 3.10 hence

Z*=Z-S=7-3.10 =3.90

B   Electronic configuration of "K = Is², 2s^2, 2p⁶, 3s², 3p⁶, 4s¹" Grouping of orbitals will be (Is²) (2s², 2p⁶) (3s², 3p⁶) (4s¹) charge of screening steady for an electron in 4s orbitals will be S = 90.85 x 8) + (I x 10) = 16.80. Therefore effective nuclear charge Z* = Z - S = 19- 16.80 = 2.20

C  Electronic configuration of Zn = Is²2s²2p⁶3s²3p⁶3d¹⁰4s² Grouping of the orbitals gives (1s²) (2s² 2p⁶) (3s² 3p⁶)(3d¹⁰) (4s²) Value  of screening steady for S for an electron in 4s orbital will be S = (0.35 x 1) + (0.85 x 18) + (1 x 10) = 25.65 therefore the effective nuclear charge felt by 4s electron will be Z* = Z - S = 30 -25.65 = 4.35 If we think a 3d electron m Z_n the grouping is as above, but the effective nuclear charge felt through the 3d electron will be Z* = Z - S = 30 - [(9 x 0.35) = (18 x 1)] = 8.85. Therefore we can see an electron in 3d orbitals in Zn is more strongly old through the nucleus than that in 4s orbital

Nuclear charge for electron in valence shell in the first 30 elements analyzed through Slater's rules. We can see from the table that there is a constant raise in Slater's Z* across rows of the periodic table. Effective nuclear charge felt through electrons as well depends on the oxidation condition of an atom in a compound. The higher the oxidation condition of the atom, the higher will be the effective nuclear charge felt via the electrons or consequently, smaller will be the atomic radius. Therefore the ionic radius of Fe³⁺ ion will be smaller than that of the Fe²⁺ion. Likewise, covalent radius of bromine in Brcl₃ will be then that in Brcl.

Periodicity in Atomic Radii:

Now that we recognize the diverse kinds of atomic radii or the factors which affect them, we will consider the periodicity in them. Before doing that though, we would like to give emphasis to that trends studied in 1 type of radii (instance covalent radii) are usually found in another type of radii as well (instance ionic or metallic radii). Two general periodic trends are originated for all types of atomic radii. These are the atomic radii reduces along a period or usually rise down a group in the long form of the periodic table. These transforms in the atomic radii can be related to the charges in effective nuclear charge or the principal quantum number in the periodic table.

We will find out that there is a constant raise (by 0.65 units) in the value of Z* from alkali metals to halogens for the elements of period 2 and 3, but there is no change in the value of n since the electrons fill similar principal shell. As a consequence of this there is a constant reduce in the covalent radius from 123 and 165pm for Li or Na to 64 and 99 pm for F or Cl correspondingly. In relationship to the over, the reduce in covalent radii across the changes series is much smaller. As we know, electrons are successfully filled in the (n-1) d orbitals across a conversion series and therefore screen the dimension determining ns electrons from the nuclear charge more effectively. Therefore across a transition series, there is only small amplify in effective nuclear charge (by 0.15 units), consequently only a small enhance in effective nuclear charge reduce in atomic radius from one element to the other takes place.

In 3d series, covalent radius reduces from 144 pm for Sc to 115 pm for Ni. After that in copper or zinc due to completion of 3d sub shell, the electronic charge density in this sub shell becomes very high that raises the inter electronic repulsion. Consequently covalent radii of Cu and Zn rise slightly to 117 and 125 pm correspondingly. Therefore across the 10 elements of the first transition series, there is an overall reduce in covalent radius through 19 pm that is much less than which across 7 normal elements of period 2(59 pm) or period 3(57 pm). But due to this, the covalent radii of elements from Ga to Kr given Zn becomes much smaller than that expected through simple extrapolation of the values for elements of period 2 and 3 for instance, the covalent radii of Al or Ga are equal while the covalent radii of elements Ge, As, Se, Br are only slightly larger than those of analogous elements (Si P, and Cl) of period 3. The rate of reduce in the size across the Lanthanide series is even less than that across the first conversion series.

In the Lanthanide elements, filling of (n-2) f orbitals take place, whereas concurrently the nuclear charge rises. The electrons in the (n-2) f orbital protect the ns electrons, (which largely determine the size, from the raise in nuclear charge) approximately completely (S = 1.00) consequently of this, there is only a small reduce in the atomic radius from 1 element to the other. But there are 14 elements in the series. There is a total of contraction of 13 pm across the series from Ca (Z = 57) to Lu (Z = 71). This is recognized as lanthanide contraction, since of which the atoms of elements (Hf to Hg) given Lu are frequently smaller than

They would be if the lanthanide had not been built up before them. Lanthanide contraction approximately exactly cancel out the consequence of the last shell added in the 6^th period or consequently, the conversion elements of 4d and 5d series have approximately similar atomic radii.

On descending any collection of the periodic table, the number of electron in the valence shell remains steady but the number of shells around nucleus amplifies monotonically, so that the effective nuclear charge felt through valence electrons stays nearly similar. So with amplify in principal quantum number (n) of the valence shell, an raise in atomic radii is usually observed down any group of the periodic table. There is a raise in atomic radii of alkali or alkaline earth metals as we continue downward in the group.

The inclusion of 3d transition elements in period 4 raise in the radii of elements from Ga to Br is smaller than expected. Likewise, since of inclusion of Lanthanide elements in period 6, atoms of the conversion elements of this period ("Hf to Hg") are approximately of similar size as atoms above than in period 5 (Zr to Cd). Then, only a small amplify in size of elements of period 6 (tc to Al) as compared to the dimension of elements above them in period 5 ((In to I) is examined.

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