Explain Fajan's rules? Why are elements with electron configuration #(n−1)d^n ns^0 np^0# more polarizing in nature as compared to the cations having noble gas electronic configuration #ns^2np^6#?

Because the nucleus #(+)# is what acts to polarize another atom's electron density #(-)#, and orbitals that aren't as good at shielding don't restrict the positive nucleus from polarizing other negatively-charged electron clouds as much.

Fajan's rules focus on polarization either by or of the atom. This can get complicated to word...

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• If the atom is highly positively charged and small, it is regarded as having a hard electron cloud, and thus easily polarizes something else, but is not itself easily polarized.

That is, something approaching the atom would more easily feel a pull on its own electron density than it can manage to pull on the atom's electron density.

Examples are #"Ca"^(2+)#, #"Al"^(3+)#, etc.

• If the atom is highly negatively charged and large, it is regarded as having a soft electron cloud, and thus is easily polarized, but does not easily polarize something else.

That is, something approaching that atom would more easily pull on that atom's electron density than get its own electron density pulled upon.

Examples are #"I"^(-)#, #"S"^(2-)#, #"P"^(3-)#, etc.

EXTENT OF SHIELDING ON POLARIZING ABILITY

If an atom has a noble gas configuration but is not a noble gas itself, it must be an ion.

• If it is a cation, it is smaller than the noble gas in size, e.g. #r_("Ca"^(2+)) < r_("Ar")#.
• If it is an anion, it is larger than the noble gas in size, e.g. #r_("Cl"^(-)) > r_("Ar")#.

If it were to have #d# orbitals though, electron shielding becomes an issue. The order of penetrating ability of the electrons in each subshell towards the nucleus is

#s > p > d > f > . . . #

as seen in the radial density distributions below:

(That is, #s# electrons are more often near the nucleus, and #f# electrons are more often not near the nucleus.)

Something with valence configuration #(n-1)d^0 ns^2 np^6# rather than #(n-1)d^n ns^0 np^0# has valence #s# and #p# electrons, which function well to shield the nucleus (which is what acts to polarize) from outside interactions.

Since #d# and #f# electrons are not as good at shielding as #s# or #p# electrons, it allows the nucleus to polarize another atom's electron cloud more easily, and e.g.

#"Hg"^(2+)# (#[Xe] 4f^14 5d^10 6s^0#)

is more polarizing than

#"Ca"^(2+)# (#[Ne] 3s^2 3p^6 4s^0#).