PERIODIC Property,Atomic Radius

 In the long form of the periodic table, several properties of elements such as atomic radii,ionic radii,ionization potential,electronegativity etc. vary in regular way in a group and in a period. Such properties are called periodic properties. These properties depend on electronic configuration of elements.


ATOMIC RADIUS:-

The distance between the centre of the nucleus and the electron cloud of the outermost shell is called atomic radius.

Types of atomic radius:-
  1. Covalent radius,
  2. Vander Waals radius or collision radius.
  3. Crystal radius (metallic or atomic radius).

Covalent Radius 

It is one half of the distance between nuclei of two like atoms joined by a single covalent bond.

example:- The distance between the nuclei of two chlorine atoms in a chlorine molecule is 1.98A⁰.

In a heteronuclear  Diatomic molecule AB, if both the atoms are linked by a single covalent bond and have nearly the same electronegativity , the bond length dA-B is equal to sum of covalent radii of the two atoms.

dA-B = rA+rB

example:- dH-Cl = rH+ rCl
                     1.36A⁰ = 0.37A⁰+rCl
                   rCl = 1.36A⁰ - 0.37A⁰
                              = 0.99A⁰.

This method is used for non metals.

The bond lengths in  free elements and in  other molecules  can be measured by X-ray  diffraction , electron  diffraction, infrared spectroscopy, nuclear magnetic resonance spectroscopy etc.

Schomaker and Stevenson(1941) proposed the following relation to calculate the covalent radius:-
               dA-B = rA+rB-0.09(XA-XB)

             where  XA and XB  are  the electronegativities of  the two atoms in A and  B.  Later on  Pauling  gave a general formula for same as :
   
dA-B = rA+rB - C(XA- XB).


vANDER WAALS RADIUS(COLLISION RADIUS):

One half of the distance between the nuclei of two nearest atoms of the two nearest atoms of two adjacent molecules of an element in the solid state.

"The distance at which the two atoms arre in contact without bond formation".


Covalent and vander Waals radii of chlorine atoms.

CRYSTAL RADIUS(MTALLIC OR ATOMIC RADIUS):-


It is defined as one-half of the distance between the nuclei of two adjacent metal atoms in the metallic close packed crystal lattice.


example :The intrnuclear distance between two adjacent sodium atoms in a crystals of the metal is 3.72A⁰. The crystals radius  of sodium is ,therefore 1/2*3.72 = 1.86A⁰.

"The crystal radii are about 10-15% higher than the single bond covalent radii"


The metallic radii can be calculated by knowing the density of metal and the nature of the unit cell,  i.e. the arrangement of other atoms around the central metal atom.


VARIATION OF ATOMIC RADII WITH ATOMIC NUMBER:-

In general, atomic radius depends upon two factors:-

1. Number of shells,

2.Nuclear charge.


VARIATION OF ATOMIC RADIUS IN A GROUP:-

In general, atomic radius increase in a group as the atomic number increases.

Li = 1.34A⁰, Na = 1.57A⁰, K = 1.96A⁰,Rb = 2.11A⁰,Cs = 2.25A⁰.


 



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