If the two atoms participating in a bond have an electron negativity difference of 1.9 , what type of of bond would they be participating in ?

Polar covalent bond.

Explanation:

When the bond is formed between the atoms by sharing the electrons the bond thus have covalent character.   The atom with larger electronegativity attract the electron pair more towards it self and becomes partial negative while the other atom becomes partial positive.  When the electronegativity difference is less than 0.4 the bond is non polar covalent.

When bonded atoms have greater electronegativity difference i.e 2 or greater than two the bond is ionic because electron is transfer from low electronegative atom to highest electronegative atom.

For example:

In water the electronegativity of oxygen is 3.44 and hydrogen is 2.2. That's why electron pair attracted more towards oxygen, thus oxygen becomes partial negative and hydrogen becomes partial positive.

In case of H₂, Cl₂, Br₂ the bond has very high covalent character because of zero electronegativity difference.