Which light elements make Earth's core less dense than iron?
In plain words
Earth's liquid core is about 10 percent less dense than pure iron-nickel would be at core pressure, so lighter elements must be dissolved in it. Which ones (silicon, oxygen, sulfur, carbon or hydrogen) and how much of each is unknown.
Precise statement
The outer core is roughly 10 percent less dense than Fe-Ni at the same P and T, the inner core a few percent, and the density jump at the inner-core boundary is about $0.5\ \text{to}\ 0.9\ \mathrm{g}/\mathrm{cm}^{3}$ depending on the normal-mode analysis. Determine the concentrations of Si, O, S, C and H in outer and inner core that reproduce density, compressional velocity and the boundary density jump, with solid-liquid partitioning from experiment or ab initio calculation and consistency with core-formation conditions. An answer is a composition with uncertainty of about 1 weight percent per element.
What would settle it
Static and shock measurements of density and sound speed of Fe alloys at core conditions combined with ab initio solid-liquid partitioning and normal-mode constraints on the inner-core boundary.