We investigate the Coulomb breakup of neutron rich nuclei 11 Be and 19,17,15 C within a theory developed in the framework of Distorted Wave Born Approximation. Finite range effects are included by a local momentum approximation, which allows incorporation of realistic wave functions for these nuclei in our calculations. Energy and angular as well as parallel momentum distributions of the fragments emitted in the breakup of these nuclei on heavy targets have been calculated using several structure models for their ground state. Comparison with the available experimental data shows that the results are selective about the ground state wave function of the projectile. Our investigations confirm that the nuclei 11 Be, 19 C and 15 C have a one-neutron halo structure in their ground states. However, for 17 C such a structure appears to be less likely. Calculations performed within our method have also been compared with those from an adiabatic model and the results are discussed. PACS numbers: 21.10. Hw, 24.10.Eq, 25.60.Gc Key words: Coulomb breakup, one-neutron halo nucleus, effects of projectile structure.