Our study consists of investigations of nuclear ground state properties and weak transition rates of eveneven waiting point nuclei. The calculation was performed for N = 50 and N = 82 nuclei. The Relativistic Mean Field (RMF) model was used to explore the nuclear ground state properties of selected nuclei. The proton-neutron quasi particle random phase (pn-QRPA) model was used for the computation of allowed Gamow Teller (GT) and unique first-forbidden (U1F) transitions of the selected waiting point nuclei. The RMF approach with different density-dependent interactions, DD-ME2 and DD-PC1, was used to compute potential energy curves and surfaces, quadrupole moments, deformation parameters, binding energies, proton-neutron separation energies, charge, and radii. The RMF computed deformation parameters were used in the pn-QRPA model, as a free parameter, for the computation of GT and U1F weak transitions. We investigated three different sets of deformation parameter for the calculation of electron emission rates. The rates changed considerably with change in deformation parameter. We later investigated contribution of allowed GT and U1F rates and competition between positron capture and electron emission rates at high stellar temperatures. The computed positron capture rates were significant especially at low densities and high temperatures. The contribution of U1F rates to allowed GT appreciably reduced the total calculated half-lives. The comparison of our results with previous calculations and measurement is also shown. The pn-QRPA calculation including U1F contribution is in good agreement with the experimental data. (c) 2021 Elsevier B.V. All rights reserved.