We performed a scanning tunneling spectroscopy investigation of the electronic properties of the topological insulator Bi₂Te₃ in the energy range between -200 and +700 meV with respect to the Fermi level. For unoccupied states, tunneling into topological surface states dominates. Analysis of Fourier-transformed (FT) dI/dU maps allowed us to obtain their energy dispersion relation and to visualize the breakdown of the linear dispersion relation typical of massless particles. For occupied states, no signature of scattering events involving surface states can be detected. FT dI/dU maps reveal in this case two scattering vectors pointing along the ΓM and ΓK directions. Both are identified with scattering events within bulk states. Interestingly, vectors pointing along ΓK which correspond to bulk backscattering events have a length longer than the minimum distance necessary to match opposite pockets on a constant energy cut. Comparison with calculated spin-resolved constant-energy cuts shows that this is a direct consequence of the chiral spin texture present in bulk states when their energy and momentum are close to the resonances of the spin-polarized topological surface states.