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We measure the optical absorption spectra and optical conductivities ofexcitons and trions in monolayers of metal dichalcogenide MoS$_{2}$ and comparethe results with theoretical models. Our results show that the Wannier-Mottmodel for excitons, with modifications to account for small exciton radii andlarge exciton relative wavefunction spread in momentum space, phase spaceblocking due to Pauli exclusion in doped materials, and wavevector dependentdielectric constant, gives results that agree well with experiments. Themeasured exciton optical absorption spectra are used to obtain experimentalestimates for the exciton radii that fall in the $7-10\AA$ range and agree wellwith theory. The measured trion optical absorption spectra are used to obtainvalues for the trion radii that also agree well with theory. The measuredvalues of the exciton and trion radii correspond to binding energies that arein good agreement with values obtained from first principles calculations.

Absorption of Light by Excitons and Trions in Monolayers of Metal Dichalcogenide MoS$_{2}$: Experiments and Theory