PERIODIC PROPERTIES

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 ATOMIC RADIUS

Atomic radius is defined as the distance from the center of the nucleus to the outer most shell of electrons. 

Probability of finding the electron is never zero even at large distance from the nucleus. Based on probability concept, an atom doesn't have well defined boundary. Hence it is very difficult to determine the atomic radius. 

Atomic radius is taken as the effective size which is the distance of the closest approach of one atom to another atom in a bonding state. 

The atomic radius can be determined as

(a) Covalent radius

(b) Vander waal's radius

(c) Metallic radius

(d) Ionic radius

Covalent radius

One half of the inter-nuclear distance between the two covalently bonded atom is called covalent radius. 

Covalent radius can be determined in case of the atoms which are attached to each other by covalent bond. 

r covalent = Inter-nuclear distance between two covalently bonded atoms / 2






(i) For homoatomic molecules

d A-A = r A + r A

Or,  d A-A = 2r A

Or,  r A = d A-A / 2

 (ii) For heterodiatomic molecules in which Electronegativity remains approximately same. 

d A-B = r A + r B

(iii) For heterodiatomic molecules in which Electronegativity of atom A is relatively larger than atom B. 

d A-B = r A + r B - 0.09 ( X A - X B ) 

Where X A  and X B Electronegativity values of high electronegative element 'A' and less electronegative element 'B' respectively. This formula is given by Stevenson & Schomaker. 

Vander waal's radius

One half of the inter-nuclear distance between two adjacent non-bonded atoms of the nearest neighbouring molecules of same substance. 

r vanderwaal = Inter-nuclear distance between two non-bonded nearest neighbouring molecules / 2






r van = d A-B /2


Comparison of covalent radius and Vander waal's radius. 

(i) The Vander waal's force of attraction are weak.Therefore, their inter-nuclear distances in case of atoms held by Vander waal's forces are much larger than those of between covalently bonded atoms. Therefore Vander waal's radii are always larger than covalent radii. 

(ii) A covalent bond is formed by the overlapping of two half filled atomic orbitals, a part of the orbital become common. Therefore, covalent radii are always smaller than the Vander waal's radii. 

Metallic radius

One half of the inter-nuclear distance between the nearest metal atom in a metallic crystal is called metallic radius. 







r metallic = d A-B /2


r metallic  = Inter nuclear distance between the adjacent atom in a metallic crystal / 2

Metallic radius of an element is always greater than covalent radius. It is due to metallic bond (electrical attraction between positive charge of an atom and mobile electrons) is weaker than covalent bond and hence the inter-nuclear distance between two adjacent atoms in a metallic crystal is longer than the inter-nuclear distance between the covalently bonded atoms

Vander waal's radius > Metallic radius > Covalent radius

Variation of Atomic Radius in a Group

  • As we move top to bottom in a group the atomic radius go on increasing because along a group the number of shells increases and the electrons are added to new shell. 
  • Also along the nuclear charge increase but here the increase in number of shells is more pronounced than that of the increase in nuclear charge. 
  • Here, when the electrons are added to new shells, screening effect increases . So, atomic radius increases along the group. 
Variation of Atomic Radius in a Period

  • As we move from left to right in a periods atomic radius go on decreasing along the period. Electrons are added to the same outermost shell and also there is increases in nuclear charge from left to right. 
  • The electrons get added to the same shell, so the added electrons don't screen the nucleus, so the attraction of nucleus towards the outermost electrons go on increasing  and hence atomic radius decreases along a period. 
Atomic radius in Transition elements:-
Atomic size of transition element decreases from left to right slowly upto Ni then increases upto zn. 
Cause:-  In the transition series the last electron enters into the inner ( n-1) d subshell. So,  the effective nuclear charge decreases due to inter electronic repulsion ( shielding effect). So, the size decreases slowly but from Ni to Zn atomic size increases, because effective nuclear charge can't over come the shielding effect. 

Elements   Sc    Ti     V     Cr     Mn     Fe     Co    Ni     Cu      Zn
Radius   1.44  1.32  1.22  1.18  1.17  1.17  1.16   1.15  1.17  1.25

Ionic radius
Distance between cation & anion in an ionic crystal. 
Radius of Cation
Radius of Cation is less than the radius of parent atom. 
Cause:-  In Cation electrons lose from Valence shell whether the nuclear charge remain same. 
Ex :- Radius of Na+  <  Radius of Na
Radius of Anion
Radius of anion is greater than radius of parent atom
Cause:-  Size of anion is greater than its parent atom due to the electron electron repulsion (inter electronic repulsion) is greater than effective nuclear charge. 
Ex :- r Cl-  >  r Cl 


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