Iron can react with steam to form different oxides depending on the reaction conditions. The most likely oxide that would be obtained on prolonged reaction of iron with steam is Fe3O4 (iron(II,III) oxide), option C.

Here's an explanation of why Fe3O4 is the correct answer:

1. Reaction of iron with steam:
When iron reacts with steam, a redox reaction takes place. The iron is oxidized, while the steam is reduced.
The general equation for the reaction is:
Iron (Fe) + Steam (H2O) → Iron Oxide (FeOx) + Hydrogen Gas (H2)

2. Formation of Fe3O4:
Under prolonged reaction with steam, iron can form a mixture of FeO (iron(II) oxide) and Fe3O4 (iron(II,III) oxide). However, Fe3O4 is the more stable and predominant oxide that forms.

3. Fe3O4 structure:
Fe3O4 is a mixed oxide consisting of both Fe2+ and Fe3+ ions. It has a crystal structure where Fe2+ ions occupy one-half of the octahedral sites, while Fe3+ ions occupy one-eighth of the tetrahedral sites.
This arrangement gives rise to the formula Fe3O4, indicating the presence of both iron(II) and iron(III) ions.

4. Color and properties:
Fe3O4 is a black or dark brown solid. It is a magnetic material and has a high melting point. The presence of both Fe2+ and Fe3+ ions in the structure contributes to its unique properties.

5. Other options:
a) FeO (iron(II) oxide) is a possible product, but it is less likely to be obtained on prolonged reaction. FeO is a black solid and is less stable compared to Fe3O4.
b) Fe2O3 (iron(III) oxide) is not formed on prolonged reaction with steam. It is a red-brown solid and can be obtained through different reactions but not in this case.
d) A mixture of Fe2O3 and Fe3O4 is possible, but Fe3O4 would still be the predominant oxide formed.

In conclusion, Fe3O4 is the most likely oxide obtained on prolonged reaction of iron with steam due to its stability and the presence of both iron(II) and iron(III) ions in its structure.