A simple, parameter free model for nuclear E2 transition from 2ı^+ to 0ı^+ states for even-even nuclei has been proposed. Transition rates based on this model have been deduced and calculated. The lifetimes of the 2ı^+ states for 214 nuclei have been calculated and compared with experimental results. The ratios of these two values fail into a region from 0.2 to 1.67 for most nuclei. The deformation parameters for 49 vibrational nuclei have also been calculated. These values are found to consist with the experimental values to within 50%.