Rotationally resolved spectra of the H-3 Sigma(-)(u)-X-3 Sigma(-)(g) electronic transition bands of Si-2 have been experimentally studied using laser-induced fluorescence in the 380-520 nm range. Si-2 molecules are produced in a supersonically expanding planar plasma by discharging a silane/argon gas mixture. In total, 44 bands belonging to the H-3 Sigma(-)(u)-X-3 Sigma(-)(g) electronic transition system of the most abundant isotopologue (28)Si(2 )are experimentally recorded. With a spectral resolution of similar to 0.04 cm(-1), the triplet spin-splitting structures in individual rotational transition lines are fully resolved. Detailed analyses on the high-resolution spectra have yielded an accurate determination of spectroscopic constants for both X-3 Sigma(- )(g)and H-3 Sigma(-)(u) states. The spin-spin interaction constants for the two triplet states are found to be comparable (lambda approximate to 1.5 cm(-1)), which may originate from the 3p atomic orbital interaction in the triplet Si, molecule. The measured isotopologue spectra of Si-29 Si-28 and (SiSi)-Si-30-Si-28 indicate that the H-3 Sigma(-)(u)-X-3 Sigma(-)(g) transition system of S-29 S-28 and (SS)-S-30-S-28 can be reasonably reproduced by the isotope mass-scaling rule. Spectroscopic parameters, including the Franck-Condon factors, the Einstein coefficients, and the oscillator strengths, are also determined from the experimental results and the Rydberg-Klein-Rees (RKR) calculations. The agreement between the experimentally measured and calculated dispersed fluorescence spectra indicates that the RKR calculations with the molecular constants determined in this work can accurately reproduce the diatomic potentials of both states. These molecular data provide a benchmark in high-level theoretical studies on Si-2 and likely other small silicon clusters.