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Introduction to Imperfections in Solids

In a sample o...

Question

In a sample of pitch blende, the atomic ratio of $P b^{206} : U^{238}$ is $0.23 : 1$ . Calculate the age of mineral if half life of uranium is $4.5 \times 10^{9} y e a r$ . All lead originated from uranium.

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Solution

$t = \frac{2.303}{0.693} \times t 1 / 2 \times l o g ⎛ ⎜ ⎜ ⎜ ⎝ 1 + \frac{23 / 206}{\frac{1}{238}} ⎞ ⎟ ⎟ ⎟ ⎠$
$t = \frac{2.303}{0.693} \times 4.5 \times 10^{9} \times l o g (1 + 0.263)$
$t = 15 \times 10^{9}$ years

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_{92} U^{238}

_{82} {Pb}^{206}

U^{238}

P b^{206}

P b^{206}

U^{238}

U^{238} = 4.5 \times 10^{9} y e a r s

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0.277 g

_{82} {P b}^{206}

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_{92} U^{238}

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_{92} U^{238}

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X \times 10_{9}

2 X

U^{238}

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P b^{206}

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