What percent of the Earth's core is uranium?
Good question! Geochemists and geophysicists agree to disagree, sometimes quite strongly. There are also disagreements within each group as well as between the two groups.
It's not just uranium. There are four isotopes whose half-lives are long enough that they can be primordial and whose half-lives are not so long that they don't produce much heat. These four isotopes are

Uranium 235, with a half-life of 0.703 billion years,
Potassium 40, with a half-life of 1.277 billion years,
Uranium 238, with a half-life of 4.468 billion years, and
Thorium 232, with a half-life of 14.056 billion years.

The consensus view amongst geochemists is that there is very little, if any, of any of these isotopes in the Earth's core. Potassium, thorium, and uranium are chemically active. They readily oxidize. In fact, they readily combine chemically with lots other elements -- but not iron. They are strongly lithophilic elements. Moreover, all three are &quot;incompatible&quot; elements. In a partial melt, they have a strong affinity to stay in the molten state. This means that relative to solar system abundances, all three of these elements should be strongly enhanced in the Earth's crust, slightly depleted in the Earth's mantle, and strongly depleted in the Earth's core.
Geophysicists look at the amount of heat needed to drive the Earth's magnetic field, and at the recent results from neutrino observations. From their perspective, the amount of residual heat from the Earth's formation is not near enough to drive the geomagneto. The growth of the Earth's inner core creates some heat, but not near enough to sustain the geodynamo. Geophysicists want a good amount of heat flux across the core mantle boundary to sustain the geodynamo, and to them the only viable source is radioactivity. Recent geoneutrino experiments appear to rule out uranium or thorium in the Earth's core, but not potassium 40. The neutrinos generated from the decay of potassium 40 are not detectable using current technology.