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A rare earth metal and a rare earth metal alloy and a method for the preparation of these by molten salt electrolysis. In the method, the electrolyte is an alkali metal or the chloride-fused salt of an alkaline earth metal, the positive electrode is an inert electrode or graphite, the negative electrode is composed of a rare-earth metal oxide or a rare-earth metal oxide and the oxides of other alloy components and/or metal powders, and electrolysis is induced by the passage of a direct current. During the electrolytic process, the temperature of electrolysis is higher than the melting point of the rare earth metal alloy or of the rare earth metal produced, and lower than the melting point of the negative electrode; the surface layer of the negative electrode is in the first stage electrolyzed to a liquid metal film which accumulates to a certain volume before falling to the crucible at the bottom. The current density of the negative electrode is sufficient to separate out from said negative electrode the components of the rare earth metal alloy or the rare earth metal. The electrolysis voltage is lower than the decomposition potential of the electrolyte and higher than the decomposition potential of the oxides corresponding to each component of the rare earth metal alloy or to the rare earth metal. The rare earth metal alloy or the rare earth metal obtained through the present method is in a liquid state and is collected in a crucible. The present method is technically simple and environmentally-friendly, while featuring low energy consumption, high current efficiency, and low costs.