Question

There are three radioactive decay series that begin with either uranium or thorium. Given the information on the chemical behavior of these elements and there half-lives:

Uranium (particle unreactive)

Thorium (strongly particle reactive)

Protactinium (strongly particle reactive)

Actinium (particle unreactive)

Radium (weakly particle reactive)

Radon (gas; chemically inert)

a) Describe the concept secular equilibrium using U-234 and Th-230 as an example. Explain why this pair deviates from secular equilibrium in the water column.

b) Considering these three decay series, for what pairs would you expect secular equilibrium to hold in the surface mixed layer (particle removal time-scale 10 days) and in the deep ocean (particle removal time-scale 100 year.

Answer 1

(a) secular equilibrium means the quantity of daughter nuclei stays constant

both U-234 and Th-230 are radioactive. And U-234 >> Th-230 upon decay. Th-230 will have a secular equilibrium if the quantity produced by U-234 decay is equal to radioactive decay of Th-230. this will happen when half life of U-234 is much greater than half life of Th-230 and also when we observe for short time (when compared to half life of U-234).

is the condition for secular equilibrium where is the decay constant.

Water column scavenges Th-230 (particle reactive) and thus does not allow buildup of secular equilibrium.

(b) In a surface mixed layer, Radon is not stable as time scale for removal is larger than half life.

Radium will have have secular equilibrium.

In deep ocean, Radon will be in secular equilibrium.