The ground state densities of unstable neutron-rich 11Li and 12Be exotic nuclei are studied in the framework of the binary cluster model (BCM). The internal densities of the clusters are described by the single particle harmonic oscillator wave functions. The long tail performance is clearly noticed in the calculated neutron and matter density distributions of these nuclei. The structures of the two valence neutrons in 11Li and 12Be are found to be mixed configurations with dominant (1p1/2)2. Elastic electron scattering proton form factors for 11Li and 12Be are studied using the plane wave Born approximation (PWBA). It is found that the major difference between the calculated form factors of unstable nuclei [11Li, 12Be] and those of stable nuclei [7Li, 9Be] is the difference in the center of mass correction which depends on the mass number and the size parameter . The reaction cross sections for 11Li and 12Be are studied by means of the Glauber model with an optical limit approximation using the ground state densities of the projectile and target, where these densities are described by single Gaussian functions. The calculated reaction cross sections of 11Li and 12Be at high energy are in good agreement with experimental data. The analysis of the present study supports the halo structure of these nuclei.