Silver nanoparticles (AgNPs) were prepared by using the reducing agent sodium borohydride with the precursor silver nitrate and stabilized by trisodium citrate. The increase in concentrations of Silver nitrate significantly changes the color from colorless to light yellow to brown due to their physical properties of silver nanoparticles in the starting reduction process begin. The color change observed in the synthesis process suggests the formation of silver nanoparticles. The resulting AgNPs were characterized by X-ray Diffraction, UV–Vis Spectrophotometry and Fourier Transform Infrared Spectroscopy techniques. In this study, the effects of concentrations of silver nitrate on the band gap energy, absorption, and transmission of the silver nanoparticles were investigated. It was found that the increasing concentration of silver nitrate resulted in an increasing absorption of silver nanoparticles, but its absorption peak observed at different wavelength, 414 nm, 411 nm, 409 nm, 395 nm, and 400 nm. The UV-Vis spectrum results showed the highest absorption peaks at 400 nm in solutions with a volume ratio of 5 mM,, which showed the localized surface Plasmon resonance (LSPR) characteristics of silver nanoparticles. The optical direct band gap energy was decreased from 2.72 eV to 2.5 eV as silver nitrate concentration increased from 1 mM to 5 mM. The optical direct band gap of silver nanoparticles calculated by the Tauc plot model, which indicates band gap of synthesized silver nanoparticles more than band gap energy of bulk silver. This higher value of band-gap might be due to a decrease overlapping of energy levels depend on its small number of atoms and also was known the crystalline size structure of silver nanoparticles used XRD was got 13 nm. Finally, from the FTIR measurements, we have observed that the transmission of infrared decreases as concentration increases. But the molecular vibration of the AgNPs shows the same functional group with increase the concentration of silver nitrate. Molecular vibration of the silver nanoparticles showed high coherency at different concentrations.