Final answer:
The most rigid layer of Earth is the Inner Core, followed by the Mantle, then the Crust, and the least rigid is the Outer Core. The correct order of Earth's layers based on increasing rigidity is: Outer Core, Crust, Mantle, Inner Core. None of the provided options match this order.
Step-by-step explanation:
The student asked to arrange Earth's layers based on rigidity. Rigidity indicates the resistance to deformation and, in the context of Earth's layers, relates to whether the layer is solid or liquid and its ability to transmit shear waves (which can only travel through solids). Using this information, we can deduce the order from the most rigid (solid) to the least rigid (liquid or partially molten).
Inner Core is solid and thus the most rigid. Mantle is solid but can flow on geological timescales. The Crust is solid and rigid but less so than the mantle or inner core. The Outer Core is liquid and not rigid, as shear waves do not travel through it.
Therefore, the correct arrangement of the layers of Earth according to increasing rigidity is: Outer Core, Crust, Mantle, Inner Core. Looking at the options provided, option (b) Inner Core, Outer Core, Mantle, Crust represents this order from the most rigid to the least rigid correctly but inverted. So, there is a need to provide a corrected order that matches what is known about Earth's layers. Since none of the provided options directly match the scientifically accepted order, we might explain to the student the correct order, which is not listed among the choices, should be: Outer Core, Crust, Mantle, Inner Core.