Question

what is valency of an atom ? how does it varies?

Answer 1

Valency is the no. of electrons gained by an electron to become stable. means to complete its octet. 
If the no. of electrons is more than 4 then the valency is 8 - no. of electrons. 
If the no. of electrons is less than 4 or 4 then it is the valency.

Answer 2

of an atom. These electrons are called valence
electrons and thus determines the valency of the
atom (or element).
In representative elements, the valency is generally equal to either n or (8 - n), where n is number of valence electrons in the atom.
In a period valence electrons increase from 0 to 8
on moving from left to right. The valency of an
element w.r.t. H and Cl increases from 1 to 4 and
then decreases to zero. However w.r.t. oxygen,
valency increases from 1 to 7 and then becomes
zero in noble gases.
In a group, the number of valence electrons re¬f mains the same and therefore all elements in a
group exhibit same valency e.g., all elements of
group I have valency one and those of group 2
have valency two. However the transition elements
exhibit variable valency