Nanoparticles of Mg_0.5Zn_0.5Fe₂O₄ ferrite have been synthesized by co-precipitation method. XRD and Mössbauer spectroscopic results of Mg_0.5Zn_0.5Fe₂O₄ annealed at 200^oC, 500^oC and 800^oC are reported. It was observed that the crystallite size increases and the lattice parameter decreases with increase in annealing temperature. The observed decrease in lattice strain supports the increase in crystallite size. The Mössbauer spectra of the samples annealed at 200^oC and 500^oC exhibits superparamagnetic doublets whereas the Mössbauer spectrum of the sample annealed at 800 ^oC exhibits paramagnetic doublet along with weak sextet of hyperfine interaction. The values of isomer shift resemble the presence of high spin iron ions. The studied ferrite nanoparticles are suitable for biomedical applications. The results are incorporated employing core-shell model and cation redistribution.