Final answer:
The differentiation of Earth into layers occurred because it melted into a molten sphere, allowing dense materials to sink to the center and less dense ones to rise to the surface, a process known as differentiation.
Step-by-step explanation:
The correct answer to what allowed for the differentiation of Earth into a layered structure is: c. Earth melted into a molten sphere, and the more dense materials sank to the center, and less dense materials moved to the outer layers. This process is known as differentiation, which is the sorting of a planet's major components by density due to gravitational forces. During the formation of Earth, the heat generated by the accumulation of planetesimals and radioactive decay caused the entire proto-Earth to exceed the melting temperature of rocks, leading to the separation of materials based on density. The heavier metals like iron and nickel sank to form Earth's core, while lighter silicates rose to form the crust.
The other options offered do not accurately describe the processes involved in the differentiation of Earth into layers. The correct explanation recognizes the role of gravity in this process and the importance of the planet's early molten state.