This paper presents a simple approach using empirical data to determine a first-order phase change in nuclei. The study examines the relationship between χ (a Majorana parameter in Interacting Boson Approximation) and Grodzins systematic (E4+ * B(E2)↑), which serves as a signature of a quantum phase transformation from prolate to oblate nuclear structure. The observed transition zone at N~90 is explained through shape transformation in a two-level system. The X(5) model is particularly effective in describing rare earth transitional isotopes, with emphasis on Gd-Hf. We are pioneers in conducting this research, and our results substantiate the approach of accuracy of Grodzins systematic in portraying the transitions from spherical U(5) to deformed SU(3) and O(6) patterns within the framework of the Interacting Boson Approximation.