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Abstract The bulk of Uranus consists of a rock–ice core, but the relative proportions of rock and ice are unknown. Radioactive decay of potassium in the silicates produces⁴⁰Ar. If transport of argon from the core to the gaseous envelope is efficient, a measurement of⁴⁰Ar in the envelope will provide a direct constraint on the rock mass present (assuming a chondritic rock composition). The expected⁴⁰Ar concentrations in this case would be readily detectable by a mass spectrometer carried by a future atmospheric probe. For a given envelope concentration there is a trade-off between the rock mass present and the transport efficiency; this degeneracy could be overcome by making independent determinations of the rock mass (e.g., by gravity and seismology). Primordial⁴⁰Ar is a potential confounding factor, especially if Ar/H₂is significantly enhanced above solar or if degassing of radiogenic⁴⁰Ar were inefficient. Unfortunately, the primordial⁴⁰Ar/³⁶Ar ratio is very uncertain; better constraints on this ratio through measurement or theory would be very helpful. Pollution of the envelope by silicates is another confounding factor but can be overcome by a measurement of the alkali metals in the envelope.