The energy characterization of an RF ion beam, generated by an inductively coupled plasma (ICP) RF ion source, has been conducted using a spherical electrostatic energy analyzer. The RF ion source, operating at an applied frequency of 13.56 MHz and a power level of 300 W, was assessed in both pulse and continuous modes. The ion energy spectrum of the hydrogen beam was meticulously measured under various conditions, with the extraction voltage ranging from 1 to 10 keV. The analysis revealed variations in the energy profiles under different operational conditions, providing insights into the ion source's performance and optimization. These findings contribute to a deeper understanding of RF ion beams for enhancing the design and efficiency of ion sources used in particle accelerators and related technologies. The importance of precise energy spectrum measurements in enhancing the efficiency and functionality of ion sources in advanced beam instrumentation is underscored by this research.