The ground state binding energy dependency of hydrogenic impurities on dielectric constant mismatch is investigated in cylindrical quantum wires as a function of wire radius and alloy concentration. The calculations are done for a cylindrical GaAs/Ga1-xAlxAs system with a uniform external magnetic field applied parallel to the wire axis using the effective mass approximation and variational methods for finite confinement potentials. According to the obtained results, one can ascertain that in calculating binding energies omitting the dielectric mismatch of the system is justified for large wire radii. However, there is a sign change in contribution for the binding energy for smaller wire radii. Furthermore, the magnitude of the contribution is more pronounced for smaller wire radii and larger alloy concentrations. (C) 2009 Elsevier B.V. All rights reserved.