Atomic radii

Atomic  radii  may be defined as  the distance between the nucleus and the outermost  electronic level of the atom. Since electrons are considered as the negatively charged electronic cloud there is no well defined boundary  for an atom.The diffused  nature of the electron cloud  makes it difficult  to give exact definition of  atomic size or atomic radii.

Introduction: Atomic radii

Thus  the atomic radii is an arbitrary  concept and is influenced by the nature of neighbouring atoms.

Types of atomic radii

As  there  is   no exact definition for the atomic radius, a number of radii have been defined for an atom. They are  Covalent radius, Crystal radius (otherwise called as metallic radius)  Vander Waal radius (otherwise called Collision radius). Let us learn one by one.

Covalent radius

 Covalent  Radius:
       Covalent radius  is used to measure the  atomic radii of  non- metals. The atomic  radius of  a non- metal is calculated from the  covalent bond length. In case of  homonuclear diatomic molecules ( type AA) , like F₂, Cl₂,Br₂ ....etc half of the covalent bond length is taken as atomic radius. For example the value of  Cl - Cl  bond idstance is 1.98 A^o  half of the distance 0.99 A^o is taken as the  atomic radius of  chlorine
       Another example: measuring the atomic radius of  carbon in diamond. The value of  C- C bond distance in the diamond is 1.54 A^o half of the  distance 0.77 A^o  is considered as the  atomic  radius of carbon atom.

Heteronuclear diatomic  molecule:
      In the calse of heteronuclear diatomic  molecule of  AB type (example CCl_{4 ,} SiC ..etc) bond length  distance d_(A-B) is given by
                   d _{(A -B)}    =  r_(A)  + r_(B)
      r_(A)   and  r_(B) are the  covalent radii of  A and  B  respectively.
     Example:    The experimental value of   d_(C-Cl)  in CCl₄  molecule is  1.76 A^o
                  d _(C-Cl)  =  r _(C) + r_(Cl)
                         r_(C) =  d_(C-Cl) - r_(Cl)
                         r_(C)       =  1.76 A^o -  r_(cl)
                         if  r_(cl)  is  given, then the covalent radius of carbon atom  can be calculated by subtracting the  covalent radius of  Cl from the  d_(C-Cl) bond length.The covalent radius of Cl atom can also be obtained, provided that covalent radius of C atom is known
Crystal Radius:
      It is otherwise called as  Atomic or Metallic radius, and defined as  one half of  the distance between the nuclei of two adjacent metal atoms in the metallic close-packed crystal lattice. For example  the internuclear distance between  two adjacent Na atoms in a crystal of sodium  metal is  3.80 A^oand hence the atomic radius of a Na metal is  half of the  distance, that is  3.80 A^o/ 2                  =  1.90 A^o
      since there  are weak  bonding forces between the metal atoms, the metallic radii are higher than the  single bond covalent  radii and at the same time  the metallic radii are smaller than  the vander Waal radii since the  bonding forces in the metallic crystal  lattice  are much staonger than the vaner waals forces
Vander Waal Radius:
      The name is  derived from theVander  Waal forces which is  found in noble gases.This  type of atomic radii is other wise  called Collision Radius. Tthe distance  between the two non-bonded  isolated  atoms  or the distacnce between  two non-bonded  atoms belonging to two adjacent molecules of an element  in the solid state is called Vander Waals distance  while half of  this  is called vader Waals Radius.
 Example :  The vander Waals distance of Cl₂ molecule =   3.6 A^o  half of  this value is  1.8 A^o  and  1.8 A ^o  is the Vander Waal radius of chlorine  atom.
                   It is to be noted  that the vander Waal radius  of an element  is higher than its covalent radius. Example the measured Vander Waal radius of chlorine is 1.8 A^o  and the  covalent radius  is  0.99 A^o
                  The variation in the atomic radii can be explained as follows.
                  When two chlorine  atoms are  just in contact with each other and  there is no bond between them,  now the distance between nuclei of those two chlorine atoms is called  the vander Waals  distance (3.6 A^o) and  half of it ( 1.8 A^o) is called  vander Waals radius.
                 where as when the electron clouds of the two chlorine atoms merge with each other to form chlorine molecule by forming covalent bond between them, the distance (covalent bond length) between them further decreases and  the distance become 1.8 A^o and half of it  0.99 A^o is the covalent radius.
                 Thus while describing  the atomic radii of various atoms, any of the radii described above can be used.