There are theoretical reasons to expect that a cluster of relatively long-lived nuclides will exist in the neighborhood of the doubly magic nucleus with Z = 126 and N = 184, the latter being the next magic number beyond 126 predicted by the shell model.
(a) Compute the mass of this exotic nucleus using Equation 11-14. 

(b) Computing the necessary masses of the nearby nuclei, predict the decay modes that would be available to the doubly magic nucleus.