The metal that can be purified economically by fractional distillation method is:

Fractional distillation is a purification method applicable to metals with relatively low boiling points, where the impurities have significantly different boiling points from the metal being purified. For this method to be economically viable, the metal must have a sufficiently low boiling point so that the energy cost of vaporising and redistilling the metal is not prohibitive.

Among the given options, zinc (Zn) has a boiling point of about $$907^\circ\text{C}$$, which is the lowest among the metals listed. Iron (Fe) boils at about $$2862^\circ\text{C}$$, copper (Cu) at about $$2562^\circ\text{C}$$, and nickel (Ni) at about $$2913^\circ\text{C}$$. The very high boiling points of Fe, Cu, and Ni make fractional distillation extremely energy-intensive and therefore not economically practical for these metals.

Zinc's relatively low boiling point makes it the metal that can be economically purified by fractional distillation. Zinc and its impurities (such as cadmium, which boils at $$767^\circ\text{C}$$) have boiling points different enough to allow effective separation. Zinc is indeed industrially purified by this method.

The correct answer is option 2 (Zn).