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First-principles and semi-empirical tight binding calculations were performed to understand the adsorption of oxygen on the surface of two dimensional (2D) and zigzag stanene nano-ribbons. The intrinsic spin-orbit interaction is considered in the Kane-Mele tight binding model. The adsorption of an oxygen atom or molecule on the 2D stanene opens an electronic energy band gap. We investigate the helical edge states and topological phase in the pure zigzag stanene nano-ribbons. The adsorption of oxygen atoms on the zigzag stanene nano-ribbons deforms the helical edge states at the Fermi level which causes topological (non-trivial) to trivial phase transition. The structural stability of the systems is checked by performing Γ-point phonon calculations. Specific arrangements of adsorbed oxygen atoms on the surface of zigzag stanene nano-ribbons conserve the topological phase which has potential applications in future nano-electronic devices.