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Abstract Volatiles from the solar nebula are known to be present in Earth's deep mantle. The core also may contain solar nebula‐derived volatiles, but in unknown amounts. Here we use calculations of volatile ingassing and degassing to estimate the abundance of primordial³He now in the core and track the rate of³He exchange between the core and mantle through Earth history. We apply an ingassing model that includes a silicate magma ocean and an iron‐rich proto‐core coupled to a nebular atmosphere of solar composition to calculate the amounts of³He acquired by the mantle and core during accretion and core formation. Using experimentally determined partitioning between core‐forming metals and silicate magma, we find that dissolution from the nebular atmosphere deposits one or more petagrams of³He into the proto‐core. Following accretion,³He exchange depends on the convective history of the coupled core‐mantle system. We combine determinations of the present‐day surface³He flux with estimates of the present‐day mantle³He abundance, mantle and core heat fluxes, and our ingassed³He abundances in a convective degassing model. According to this model, the mantle³He abundance is evolving toward a statistical steady state, in which surface losses are compensated by enrichments from the core. 

We combine calculations of pebble accretion and accretion by large and giant impacts to quantify the effects of pebbles on the hafnium-tungsten system during Earth formation. Our models include an early pebble accretion phase lasting 4–6 Myr with a global magma ocean and core segregation, a 20–50 Myr phase of large impacts, and a late giant impact representing the Moon-forming event. We consider various mass additions during each accretion phase, vary the metal-silicate partition coefficient for tungsten over a wide range, and track (180)Hf, (182)Hf, (182)W and (184)W in proto-Earth and impactor models over time using standard chondritic values for these isotopes in the pebbles. We find that an early phase of pebble accretion is compatible with the tungsten anomaly of Earth's early mantle as well as the present-day Hf/W ratio, but under restricted conditions. In particular, the pebble mass of proto-Earth is limited to 0.7 Earth masses or less, the average metal-silicate partition coefficient for tungsten is 30–50, and because the metal-silicate equilibration efficiency for giant impacts is low, the equilibration efficiency must be high for the large impactors.