Chapter 2:- Periodic properties of the elements

B.sc 1st year Book
(Page 2)

Atomic radii | Covalent radii, Metallic radii, Van der Waals radii

Atomic radii:

The atomic radii are sub-divided into three classes.
(a) Covalent radii
(b) Metallic or crystal radii
(c) van der Waals radii

(a) Covalent radius:

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.

Determination of covalent radii:

(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.

Homo Nuclear diatomic molecules, Homo Nuclear,

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

$$ r_{Cl}=\frac{d}{Cl-Cl}\:=\:\frac{1.98}{2} $$

$=0.99Å$

(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 d_A-Y which is equal to the sum of the radii of $A$ and $Y$ When the electronegativity of these two atoms is nearly equal.

d_A-Y = r_A+r_{Y….. (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.

d_A-Y < r_A+r_Y

This deviation is arisen due to the following:

(i) electronegativity difference between ‘ $A’$ and ‘ $Y’$ 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.

d_A-Y = r_A – r_Y – 0.09(x_A – x_Y)

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 = r_A+ r_Y– C(x_A – x_Y) (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 d_A – Y calculated by the Pauling equation is approximately equal to the d_A – 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 $C\equivC$ 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.

(b) Metallic radii or Crystal radii:

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 $12inA$

Metallic radii of elements having coordination number of

(c) van der Waals radius or Collision radius:

Most of the nonmetals are held together by a covalent bond in a molecule and each molecule in a solid state is held together by van der Waals forces. It is defined as ‘one-half of the internuclear distance between two adjacent atoms of two neighboring molecules of an element in the solid-state held together by van der Waal forces. These forces arise due to the mutual distortion of the electron cloud of one molecule with the other molecule and vice-versa. The van der Waal forces are absent in gaseous molecules because gaseous molecules are mobile and found farther away from one another. They are present when the atoms or molecular substance are considered in liquids and also in crystalline state at Jow temperatures. Thus, the van der Waal force is related to the effective packing size of the atom in the solid stale. It is determined by the X-ray studies of various elements in the solid state.

For example, in the $Cl2$ molecule, the distance between two nuclei of two adjacent chlorine of neighboring molecules is $3.60A$ and the distance between the nuclei of two bonded $Cl$ –atoms is $1.98A$ . where a and $b$ are internuclear distances between two atoms.

$$ Hence\:covalent\:radius\:=\:\frac{a}{2}=\frac{1.98}{2}=0.99\:A^{\circ } $$

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

radii, covalent radii, van der waal radii,

The above figure expresses the difference in the value of covalent and van der Waal’s radius. Noble gases do not form covalent molecules therefore it is impossible to determine their single-bond covalent radii. Hence, in the crystal of noble gas, no chemical bond is formed and we can measure only their van der Waals radii in the solid state. Thus, the atomic radii of noble gases are actually the van der Waals radii. It is the reason for the exceptionally high atomic radii of noble gases than the elements of their respective periods.

V A	VI A	VII A	Zero
		H = 1.20	He = 1.20
N = 1.50	O = 1.40	F = 1.36	Ne = 1.60
P = 1.90	S = 1.85	Cl = 1.80	Ar = 1.91
As = 2.00	Se = 2.00	Br = 1.95	Kr = 2.00
Sb = 2.20	Te = 2.20	I = 1.25	Xe = 2.20

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Atomic radii | Covalent radii, Metallic radii, Van der Waals radii

Atomic radii: