Decay modes in Pb isotopes within the range 176≤A≤266 are investigated by the calculation of half-lives using several empirical formulas. These formulas along with various theoretical treatments are first tested to reproduce experimental half-lives and known decay modes of Pb isotopes, which are in consequence applied to estimate half-lives and decay modes of unknown Pb isotopes. A comparison between α-decay and weak-decay from the stable to drip-line isotopes is canvassed which leads to the excellent match with experimental data and applicability of applied empirical formulas. In addition, the full chain of Pb isotopes is probed as potential daughter candidates of cluster emission from superheavy nuclei which ensued the predominant role of 208Pb and nearby isotopes in probable cluster emission.

The possibility of cluster emission from trans-lead (86≤Z≤96) region of periodic chart has been explored comprehensively by employing few empirical formulas which are modified by adding angular momentum (l) or isospin-dependent (I = (N − Z)/A) or both terms for the calculation of cluster decay half-lives. These modified versions of the formulas are found with lesser χ 2 per degree of freedom and root mean-square error, in addition to the smaller values of some other statistical parameters, while compared to their corresponding old versions on available 61 experimental data of cluster radioactivity. By applying the modified version of the formula given by Balasubramaniam et al. [PRC 70 (2004) 017301], the most accurate formula among these, half-lives of several clusters i.e. isotopes of Be, B, C, N, O, F, Ne, Na, Mg, and Si are predicted systematically for the several isotopes in the trans-lead region. The contest of cluster emission with α-decay has been investigated in form of branching ratio which brings several potential cluster emissions into the probable decay modes of these nuclei. The accurate prediction of half-lives of such clusters is expected to be crucial for the future experimental observations where α-decay is observed dominantly.