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Radiocarbon Dating

A sample of ...

Question

A sample of $^{238} U$ (half-life $= 4.5 \times 10^{9}$ yr) ore is found to contain $23.8$ g of $^{238} U$ and $20.6$ g of $^{206} P b$ . Calculate the age of the ore.

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^{238} U

= 4.5

\times 10^{9}

238 U

^{206} P b

U^{238}

4.5 \times 10^{9}

U^{238}

P b^{206} .

U^{238} ((h a l f - l i f e = 4.5 \times 10^{9} y r)

U^{238}

P b^{206}

_{92}^{238} U

_{82}^{260} P b

^{238} U

^{206} P b

6^{260} P b

^{238} U

T_{50}

^{238} U

4.5 \times 10^{9}

U^{238}

= 4.5 \times 10^{9}

23.8 g

U^{238}

20.6 g

P b^{206}

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A sample of 238U(half-life=4.5×109 yr) ore is found to contain 23.8g of 238U and 20.6g of 206Pb. Calculate the age of the ore.