Final answer:
Inge Lehmann is the seismologist who discovered that the Earth has a solid inner core and a liquid outer core by analyzing seismic waves from earthquakes. The Earth's core temperatures are sustained by the radioactive decay of primordial elements, while the outer core contributes to generating the Earth's magnetic field.
Step-by-step explanation:
The seismologist who determined that the inner core of the Earth is solid and the outer core is liquid was Inge Lehmann. She made this discovery by interpreting seismic wave data from earthquakes. Shear or transverse waves are unable to travel through the Earth's liquid outer core, whereas compression or longitudinal waves can, thus confirming the differing states of the inner and outer cores. The solid inner core is surrounded by the liquid outer core, which is primarily composed of molten iron and nickel. Lehman's observations also suggested that the Earth's temperature should have cooled significantly since its formation, but radioactive decay of primordial elements is believed to help maintain its heat.
The Earth's inner core is very dense, composed of an iron and nickel alloy, while the outer core's liquid state is essential for the generation of the Earth's magnetic field. The density of the Earth's mantle increases with depth, and occasionally, when volcanic material is ejected, it provides samples for detailed analysis, revealing the chemistry of the upper mantle.