Two-dimensional molybdenum sulphide (MoS₂) has been synthesized by hydrothermal method, and for optical characteristics, absorption and photoluminescence spectra are recorded. Variation of refractive index, extinction coefficient, dielectric constant (both real and imaginary) and optical conductivity with wavelength have been plotted. The exciton energy has been calculated in the weak electron–phonon coupling regime. The temperature-dependent splitting energy of valance band is well explained by using simulation. Splitting energy is constant up to 50 K and then decreases with increase in temperature. Average lifetime (0.75 ns) of excited electrons have been calculated using time-correlated single photon counting. X-ray diffraction (XRD), Raman spectra and high-resolution transmission electron microscope (HRTEM) have been recorded to investigate structural properties of MoS₂ sample. XRD shows hexagonal crystal symmetry with well-defined crystallinity. In Raman spectra, three prominent peaks are found at 381, 407 and 453 cm^–1. HRTEM also confirms that the structure of MoS₂ is hexagonal with three layers of nano-sheet with inter-planner spacing of 0.58 nm