The Ellingham diagram is a graph that shows the change in Gibbs free energy with temperature for the reactions of oxides, metals, and oxygen. This diagram helps in understanding which metal can be used as a reducing agent to extract another metal from its oxide. The basic principle lying here is that a metal can reduce the metal oxide that lies above it on the Ellingham diagram.
In this question, we need to determine which metal can reduce alumina (\text{Al}_2\text{O}_3). From the Ellingham diagram, we must find a metal that can have a negative free energy change when it reduces alumina, meaning the line for the reducing metal is below that of alumina at the given temperature.
Let's evaluate the options:
Therefore, the correct answer is magnesium (Mg) because its position in the Ellingham diagram relative to alumina indicates it can reduce \text{Al}_2\text{O}_3 effectively.