We examined the conditions of neutron density (n) and temperature (T9) required for the N =50,82,and 126 isotopes to be waiting points (WP) in the r-process.The nuclear mass based on experimental data presented in the AME2020 database (AME and AME ± Δ) and that predicted using FRDM,WS4,DZ10,and KTUY models were employed in our estimations.We found that the conditions required by the N =50 WP significantly overlap with those required by the N =82 ones,except for the WS4 model.In addition,the upper (or lower) bounds of the n-T9 conditions based on the models are different from each other due to the deviations in the two-neutron separation energies.The standard deviations in the nuclear mass of 108 isotopes in the three N =50,82,and 126 groups are about rms =0.192 and 0.434 MeV for the pairs of KTUY-AME and WS4-KTUY models,respectively.We found that these mass uncertainties result in a large discrepancy in the nn-T9 conditions,leading to significant differences in the conditions for simultaneously appearing all the three peaks in the r-process abundance.The newly updated FRDM and WS4 calculations can give the overall conditions for the appearance of all the peaks but vice versa for their old versions in a previous study.The change in the final r-process isotopic abundance due to the mass uncertainty is from a few factors to three orders of magnitude.Therefore,accurate nuclear masses of the r-process key nuclei,especially for 76Fe,81Cu,127Rh,132Cd,192Dy,and 197Tm,are highly recommended to be measured in radioactive-ion beam facilities for a better understanding of the r-process evolution.