A zircon crystal in a granite intrusion contains uranium-238 that decays to lead-206

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

Problem

A zircon crystal in a granite intrusion contains uranium-238 that decays to lead-206. Chemical analysis shows that for every

1.0\,\text{mol}

^{238}

U present there are

0.45\,\text{mol}

of radiogenic

^{206}

Pb. Assume that no

^{206}

Pb was present when the crystal formed and that the system has remained closed since crystallisation. The half-life of

^{238}

U is

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

. (a) Derive an expression that relates the present number ratio

\dfrac{N_{\text d}}{N_{\text p}}

of daughter to parent nuclei to the age

t

of the crystal. (b) Using the measured ratio, determine the age of the zircon crystal. (c) Comment briefly on whether this result is consistent with a hypothetical geologic age of the granite body of about

1\times10^{9}\,\text{years}

Related theory

Radioactivity
Nuclear physics
Radioactive decay

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