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In relation to a recent question of mine, this alternate Earth still has its core consisting of 84% iron, but the other 16% contains the greatest concentrations of all known species of heavy metals (defined by high atomic number and weight and a specific gravity greater than 5), including 100% of all 34 species of metals so unstable that they are radioactive, like plutonium, uranium and strontium.

There would be many questions to this scenario, but let's narrow it down to one focus--Earth's mantle. The mantle is where we find the action of convection, the reason why Earth's outer shell moves in several pieces, or plates.

enter image description here

In an alternate Earth where all of the radioactive metals are trapped inside the core, would this affect the process of convection in any way? If yes, how?

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The radioactive metals would not be in the core

The primary heavy radioactive metals are not chemically reactive with iron, but they are with oxygen. Therefore, most of them would form compounds that are not as heavy as the heavy metals in your definition.

Most of the heat you will get from the core would be from four metals (see this post on ES.SE for further details):

  • 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.

These metals will form compounds that are no longer as dense as heavy metals, thus falling into the 'rock' category of Gimelist's answer to your last question.

A repeated melt cycle as proposed in your question will in fact increase the concentration of radioactive minerals in the crust and decrease them in the core. So relative to our Earth, your planet will have less radioactive heat in the core. Thus there will be less temperature differential across the mantle, and less convection.

What effects this has on geomagnetism and plate tectonics are hard to determine, but they don't sound good for life on the planet.

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kingledion's answer is spot-on: the metals will not partition into the core. The only way to put radioactive metals (i.e. U, Th, and K) in the core, is to lower the oxygen fugacity of the planet as a whole. In layperson's terms: get rid of the oxygen.

It is well known that alkali metals (including the radioactive potassium), thorium and uranium will partition more to an iron and/sulfide rich liquid if there is a shortage of oxygen around. For example:

Experimental partitioning of uranium between liquid iron sulfide and liquid silicate: Implications for radioactivity in the Earth’s core

Depletion of potassium and sodium in mantles of Mars, Moon and Vesta by core formation

Here's an SEM image from one of my own oxygen-starved experiments, where you can see tiny iron "blobs" inside silicate melt (call it "rock"). This iron concentrates sodium, which is an analogue for potassium.

enter image description here

So in theory it is possible, but the lack of oxygen will cause two things to happen:

  1. Your core is going to be larger, because more iron will remain as "metal" and not be oxidised to "rock",

  2. You will not have free oxygen in your planet. This will have major consequences for the possibility of advanced life forms as we know it.

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