Uranium-238 - Radium Series (or Uranium Series)

Radium Series (or Uranium Series)

The 4n+2 chain of 238U is commonly called the "radium series" (sometimes "uranium series"). Beginning with naturally occurring uranium-238, this series includes the following elements: astatine, bismuth, lead, polonium, protactinium, radium, radon, thallium, and thorium. All are present, at least transiently, in any uranium-containing sample, whether metal, compound, or mineral.

The mean lifetime of 238U is 1.41×1017 seconds divided by 0.693 (or multiplied by 1.443), i.e. ca. 2×1017 seconds, so 1 mole of 238U emits 3×106 alpha particles per second, producing the same number of thorium-234 (Th-234) atoms. In a closed system an equilibrium would be reached, with all amounts except for lead-206 and 238U in fixed ratios, in slowly decreasing amounts. The amount of Pb-206 will increase accordingly while that of 238U decreases; all steps in the decay chain have this same rate of 3×106 decayed particles per second per mole 238U.

Thorium-234 has a mean lifetime of 3×106 seconds, so there is equilibrium if one mole of 238U contains 9×1012 atoms of thorium-234, which is 1.5×10−11 mole (the ratio of the two half-lives). Similarly, in an equilibrium in a closed system the amount of each decay product, except the end product lead, is proportional to its half-life.

As already touched upon above, when starting with pure 238U, within a human timescale the equilibrium applies for the first three steps in the decay chain only. Thus, for one mole of 238U, 3×106 times per second one alpha and two beta particles and gamma ray are produced, together 6.7 MeV, a rate of 3 µW. Extrapolated over 2×1017 seconds this is 600 gigajoules, the total energy released in the first three steps in the decay chain.