B.sc 1st year Book
(Page 2)

The atomic radii are sub-divided into three classes.

The covalent radius of an atom Is measured when two like atoms or unlike atoms are bonded together by a single covalent bond, It is defined as ‘one hall of the internuclear distance between the nuclei of two like atoms linked together by a single covalent bond as is called ‘single bond covalent radius‘: SBCA.

#### (i) In homonuclear diatomic molecules:

Let us consider a homonuclear diatomic molecule Y2 formed by a single covalent bond between two atoms Y and Y. It is in this molecule that the two. like atoms are considered to be two-sphere in close contact with each other, then according to the definition of covalent radius, the distance between these two nuclei is denoted by dy−y which is equal to the sum of the radii of the two atoms.
dY – y = rY + rY
=2rY
$$r_y=\frac{dY-Y}{2}$$
where rY is a single bond covalent radius of atom Y.
For example: In the Cl2 molecule, Internuclear distance,
dCl – Cl = 1.98A
$$r_{Cl}=\frac{d}{Cl-Cl}\:=\:\frac{1.98}{2}$$

#### (ii) In heteronuclear diatomic molecule.

In the case of two dissimilar atoms joint together by a single covalent bond like A- Y. The bond length between A and Y is dA-Y which is equal to the sum of the radii of A and Y When the electronegativity of these two atoms is nearly equal.

dA-Y = rA+rY….. (i)

But when the electronegativity values of these two atoms ‘A ‘ and ‘ Y‘ are not equal, then the experimental value of bond length, dA−Y between these two dissimilar atoms is always less than the sum of the radius value of both atoms.
dA-Y < rA+rY

### This deviation is arisen due to the following:

(i) electronegativity difference betweenA’ andY’ atoms or ionic character of the A−B, bond.
(ii) the multiplicity of the band between the atoms A and Y.
In order to compensate for the ionic character of the A- Y bond, Schomaker and Stevenson1941 suggested the following equation to calculate the covalent radius.

dA-Y = rA – rY – 0.09(xA – xY)
where dA−Y is the internuclear distance between A and Y-atoms, rA and rY are covalent radii, xA and xY are electronegativities of atom A and Y respectively, and −0.09, correction term. Later on, Pauling generalized the Schomaker and Stevenson equation as :
dA-Y = rA + rY – C(xA – xY) (Faulling Equation)…(iii)
where ‘C‘ is Schomaker and Stevenson coefficient which depends upon the atom involved In the molecule. The value of ‘ C ‘ is 0.08,0.06,0.04 and Å0.02ÅA for the p-block elements of the 2nd, 3rd, 4th, and 5th periods respectively. When we compare these two equations to calculate, dA−Y for the A-Y molecule. Pauling equation is found to be more reliable than that of the Sckormaker and Stevenson equation, because of the fact that the dA – Y calculated by the Pauling equation is approximately equal to the dA – Y observed.
 Table 2.1: Single bond covalent radii for s and p block elements in Å
 s Block p Block elements
 I A II A III A IV A V A VI A VII A Zero H = 0.32 He = 0.93 Li = 1.34 Be = 0.89 B = 0.80 C = 0.77 N = 0.75 O = 0.73 F = 0.72 Ne = 1.31 Na = 1.54 Mg = 1.36 Al = 1.25 Si = 1.11 P = 1.06 S = 1.02 Cl = 0.99 Ar = 1.74 K = 1.96 Ca = 1.74 Ga = 1.26 Ge = 1.22 As = 1.19 Se = 1.16 Br = 1.14 Kr = 1.89 Rb = 2.11 Sr = 1.91 In = 1.50 Sn = 1.41 Sb = 1.38 Te = 1.36 I = 1.33 Xe = 2.09 Cs = 2.25 Ba = 1.96 II = 1.55 Pb = 1.47 Bi = 1.46 Po = 1.46 At = 1.45 Rn = 2.14

### The covalent radii are three types:

Single-Bond, Double-Bond, and Triple-Bond covalent radii involved single, double, and triple bonds respectively. The C-C single bond covalent radius is equal to 0.77Å whereas in C=C double bond and C≡C triple bond, covalent radii are Å0.67Å and Å0.06Å respectively. The values of covalent radii in the case of single, double, and triple-bonded Nitrogen atoms are 0.75 A,0.60 A, and 0.55 A respectively.

In a metallic crystal, metal atoms are arranged in. closely packed spheres at the minimum distance possible between them. It is defined as ‘one hall of the distance between the nuclei of two adjacent metal atoms closely packet in the crystal lattice and the metal atom must exhibit the coordination number of 12′, eg. In the crystal of sodium metal, the distance between the nuclei of two adjacent atoms is equal to 3.80 A hence the metallic radius of a sodium atom is 3.8/2 i.e, 1.9 A. The metallic radii are 10 to 15% higher than the single bond covalent radii. (ref. Table of the metallic radius of s and p-block elements), and single bond covalent radi are smaller than van der Waals radius. This is due to the stronger binding forces in the metallic crystal as compared to van der Waal’s force. Also in a metallic crystal, the bond between metal atoms is not localized. whereas in the case of a covalent crystal, it is localized.
Table 2.2: Metallic radii of elements having a coordination number of 12inA

$$Hence\:covalent\:radius\:=\:\frac{a}{2}=\frac{1.98}{2}=0.99\:A^{\circ }$$
$$And,\:Van\:der\:waal\:radius\:=\:\frac{b}{2}=\frac{3.60}{2}=1.8\:A^{\circ }$$