For a given reaction, !!t_(1//2)= 1/(ka^2)!!. The order of this recation is:
The relationship between half life and initial concentration is given as:
!!t_(1/2) prop 1/(a\^(n-1))!!
Where n= order of reaction.
Here we have
!!t_(1/2) prop 1/(a^2)!!
Thus by comparing:
Hence it's a third order reaction.
Therefore option (b) is correct.