Problem 2

Dating historical events using

^{210}\ce{Pb}

. Nathan Thompson, an early settler of Lord Howe Island, planted European deciduous trees; the year is unknown. Pollen of European oak and elm (which pollinate in their first year) accumulated in lake sediment together with radioactive

^{210}\ce{Pb}

(half-life = 22.0 years). In 1995 a sediment core was taken: oak/elm pollen first occurs at 50 cm depth, where the

^{210}\ce{Pb}

activity is 1.40 Bq kg⁻¹, versus 356 Bq kg⁻¹ at the top of the core. (2.1) In what year were the seeds planted? (2.2)

^{210}\ce{Pb}

is a daughter of

\ce{^{238}U}

, which stays in the earth's crust:

\ce{^{238}U} \rightarrow \ce{^{234}U} \rightarrow \ce{^{230}Th} \rightarrow \ce{^{226}Ra} \rightarrow \ce{^{222}Rn} \rightarrow (\ce{^{218}Po}, \ce{^{214}Bi}) \rightarrow \ce{^{210}Pb} \rightarrow \ce{^{206}Pb}

(stable). Which step explains how

^{210}\ce{Pb}

reaches rainwater while its parent

\ce{^{238}U}

remains in the crust?

Step 2 of 2: The radon escape step

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\ce{^{226}Ra} \rightarrow \ce{^{222}Rn} + \alpha;\qquad \ce{^{222}Rn}\ (\text{gas}) \uparrow \text{out of soil} \rightarrow \ce{^{210}Pb} \rightarrow \text{rainout}

Analysis

All other chain members are solids locked in minerals, but $\ce{^{222}Rn}$ is a noble gas that diffuses from soil into the atmosphere. There it decays through the short-lived daughters to $\ce{^{210}Pb}$ , which attaches to aerosols and is washed out by rain.