Theoretical computations of Rydberg energy levels series and atomic lifetimes for singly ionized boron (B II), silicon (Si II), and germanium (Ge II) have been performed. In the theoretical computation weakest bound electron potential model theory (WBEPMT) is employed. Regularities of changes in quantum defects for the following Rydberg states series: 2sns (1S0), 2snp ([Formula: see text]), 2snf ([Formula: see text], [Formula: see text], [Formula: see text]), 2snf ([Formula: see text]) of B II; 3s2ns (2S1/2), 3s2nd (2D3/2,5/2), 3s2nf ([Formula: see text]), 3s2ng (2G7/2,9/2) of Si II; and 4s2nf ([Formula: see text]), 4s2nf ([Formula: see text]), 4s2ng (2G7/2,9/2) of Ge II, up to n = 50 are presented. The atomic lifetimes of the following series: 1s22sns (1S0), 1s22snp ([Formula: see text]), 1s22snd (1D2) of B II; 3s2ns (2S1/2), 3s2nf ([Formula: see text]) of Si II; and 4s2ns (2S1/2) of Ge II are predicted with good accuracy. Some high-lying Rydberg energy levels and atomic lifetimes have been presented for the first time. The series for which Rydberg energy levels are computed in this work are unperturbed series.

Background Mathematical modeling provides grounds for understanding scientific systems theoretically. It serves as a guide for experimentalists in determining directions of investigation. Recently, the Covid-19 pandemic has caused disturbances in almost every walk of life. Scientists have played their role and have continued research on the effects of the pandemic. Various mathematical models have been used in different branches of science (Djilali et al. in Phys Scr 96 12 124016, 2021; Math Biosci Eng 18(6):8245–8256, 2021; Zeb et al. in Alex Eng J 61(7):5649–5665). Well-established mathematical models give results close to those obtained by experiments. The Weakest Bound Electron Potential Model is one such model, which explains hydrogen-like atoms and ions. This model has been used extensively for hydrogen-like atoms and ions to calculate energies of Rydberg levels and ionization energies. This model has been used extensively for hydrogen-like atoms and ions to calculate energies of Rydberg levels and ionization energies. Results This paper presents the energies of the Rydberg series, 2s2ns, and 2s2np of Li I, calculated using WBEPM. The energies are used to calculate transition probabilities from np to 2s, 3s, 4s, and 5s levels. The transition probabilities are compared with corresponding values in published data where available. The agreement with known values is good; most of the transition probabilities calculated in this work are new. A computer program was developed to find the value of the dipole matrix element. The calculations were further verified by calculating the lifetimes of some low-lying levels. Conclusions Four series of Li I have been studied, and energies of the Rydberg levels in the series were calculated. The energies then are used to calculate transition probabilities from np to ms transitions, where m = 2, 3, 4, & 5 and n = 1–15. The results are compared where available. An excellent agreement with previously published data shows the reliability of calculations. Most of the transition probabilities are new.