Question

why does variable valency exist??? plz explain

Answer 1

valency related to number of valence electrons . we know that all elements have not equal number of valence electrons . example :-
Na has only one valence electron ,
if you see it's configuration ,
configuration of Na = 1s², 2s², 2p6, 3s¹
here only one electron in outer shell
so, number of valence electron = 1
so valency = 1
but if you see configuration of Oxygen
e.g 1s², 2s² , 2p4
here no of electrons in outer shell = 6
hence , its valency = 2

now, it is clear that valency of different elements have different , because their valence electrons different .

Answer 2

The number of atoms with which one atom of an element can combine is called it's valency.
Variable valencies exist as some metals can lose different number of electrons to form ions with different charges, that's why they exhibit variable valencies.
For example,
Copper = Cu +1 - Cuprous or copper (I)
                Cu+2 - Cupric or copper (II)
Iron = Fe +2 - Ferrous or iron (II)
          Fe +3 - Ferric or iron (II)
Thanks