A granite sample is analysed for uranium–lead dating

PHYSICS · Multi-part · A Level · Physics · Nuclear physics · Nuclear physics

Problem

A granite sample is analysed for uranium–lead dating. Assume that the rock originally contained no

^{206}\text{Pb}

. Laboratory measurements give the present atom ratio

^{206}\text{Pb}/^{238}\text{U}=0.70

. The half-life of

^{238}\text{U}

4.5\times10^{9}\,\text{y}

. (i) Derive an expression for the age of the rock in terms of the present ratio of daughter to parent nuclei. (ii) Using the given ratio, calculate the age of the granite. (iii) A parallel analysis using the

^{232}\text{Th}\,\to\,^{208}\text{Pb}

decay chain on the same rock gives the ratio

^{208}\text{Pb}/^{232}\text{Th}=0.20

. The half-life of

^{232}\text{Th}

1.4\times10^{10}\,\text{y}

. Calculate the age indicated by this second system and comment on the consistency of the two results.

Related theory

Radioactivity
Nuclear physics
Radioactive decay

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