Two parametric relations are proposed for calculating the level energies ofan electron bound in a screened Coulomb potential in a plasma. The firstrelation is between the energies of levels which have the same ℓquantum number. The second relation is able to represent the bound-stateenergies for 1s, 2p, 3d...levels as a function of the screeningparameter to a good degree of accuracy. These two relations taken togethercan give the energies of any level up to and including n = 8, and estimatedenergies for n = 9 and 10 for any value of ne and Te. Theseare relevant for at least three topics in plasma physics. The applicationof these relations for the calculation of the partition function of plasmasis discussed.