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The combined effect of turbulent transport and radioactive decay on the distribution of <sup>222</sup>Rn and its progeny in convective atmospheric boundary layers (CBL) is investigated. Large eddy simulation is used to simulate their dispersion in steady state CBL and in unsteady conditions represented by the growth of a CBL within a pre-existing reservoir layer. <br><br> The exact decomposition of the concentration and flux budget equations under steady state conditions allowed us to determine which processes are responsible for the vertical distribution of <sup>222</sup>Rn and its progeny. Their mean concentrations are directly correlated with their half-life, e.g. <sup>222</sup>Rn and <sup>210</sup>Pb are the most abundant whereas <sup>218</sup>Po show the lowest concentrations. <sup>222</sup>Rn flux decreases linearly with height and its flux budget is similar to the one of inert emitted scalar, i.e., a balance between on the one hand the gradient and the buoyancy production terms, and on the other hand the pressure and dissipation at smaller scales which tends to destroy the fluxes. While <sup>222</sup>Rn exhibits the typical bottom-up behavior, the maximum flux location of the daughters is moving upwards while their rank in the <sup>222</sup>Rn progeny is increasing leading to a typical top-down behavior for <sup>210</sup>Pb. We also found that the relevant radioactive decaying contributions of <sup>222</sup>Rn short-lived daughters (<sup>218</sup>Po and <sup>214</sup>Pb) act as flux sources leading to deviations from the linear flux shape. In addition, while analyzing the vertical distribution of the radioactive decay contributions to the concentrations, e.g. the decaying zone, we found a variation in height of <sup>222</sup>Rn daughters' radioactive transformations. <br><br> Under unsteady conditions, the same behaviors reported under steady state conditions are found: deviation of the fluxes from the linear shape for <sup>218</sup>Po, enhanced discrepancy in height of the radioactive transformation contributions for all the daughters. In addition, <sup>222</sup>Rn and its progeny concentrations decrease due to the rapid growth of the CBL. The analysis emphasizes the crucial role of turbulent transport in the behavior of <sup>222</sup>Rn n morning concentrations, in particular the ventilation at the top of the boundary layer that leads to the dilution of <sup>222</sup>Rn by mixing with radon low concentration air.