ratio of specific heat at a const. pressure and volume for hydrogen (Cp/Cv)=1.40. This indicates it is diatomic.How did we come to this conclusion? How do we find out the atomicity for other elements if the ratio of specific heat is given?

Basically you first need to know that  heat capacity ratio is depend on Degree of freedon of a particular gas and the Relation with degrees of freedom is :

The heat capacity ratio ( ) for an ideal gas can be related to the degrees of freedom ( ) of a molecule by:

Now, For a monatomic gas, with three degrees of freedom:

,

while for a diatomic gas, with five degrees of freedom (at room temperature: three translational and two rotational degrees of freedom; the vibrational degree of freedom is not involved except at high temperatures):

So, Now we can easily find out the atomicity of element or compound just by knowing its degree of freedom.