Describe the layers of the Earth, including their composition, density, and physical state.

The crust is the outermost solid layer. It is primarily composed of silicate rocks, with an average density of about $2.7 \text{ g/cm}^3$ for continental crust (granitic) and $3.0 \text{ g/cm}^3$ for oceanic crust (basaltic). Its physical state is solid.

The mantle lies beneath the crust and extends to about $2,900 \text{ km}$ deep. It is composed mainly of silicate rocks rich in iron and magnesium (peridotite). Its density ranges from about $3.3 \text{ g/cm}^3$ in the upper mantle to $5.7 \text{ g/cm}^3$ in the lower mantle. The upper mantle is plastic (solid but flows slowly), while the lower mantle is solid due to immense pressure.

The outer core is a liquid layer extending from $2,900 \text{ km}$ to $5,150 \text{ km}$ deep. It is primarily composed of molten iron and nickel, with some lighter elements. Its density ranges from about $9.9 \text{ g/cm}^3$ to $12.2 \text{ g/cm}^3$. Its physical state is liquid, responsible for generating Earth's magnetic field.

The inner core is the Earth's innermost layer, a solid sphere from $5,150 \text{ km}$ to the center at $6,371 \text{ km}$. It is composed mainly of solid iron and nickel. Its density is the highest, estimated to be around $12.6 \text{ g/cm}^3$ to $13.0 \text{ g/cm}^3$. Despite extreme temperatures, the immense pressure keeps it in a solid state.