On analysis a sample of 238 U ore was found to contain 20-6 g of 82 206 Pb and 23-8 g of 92 238 U- The half-life period of 238 U is 4-50 - 10 9 years- If all the lead were assumed to have come from the decay of 92 238 U- what is the age of the ore-

t= 2.303 0.693 × 4.5× 10 ^ 9 × log( 1+ 20.6 20.6 #160; 23.8 238 #160; #160; ) t=4.50× 10 ^ 9 years ...

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Byju's Answer

Standard XII

Chemistry

Law of Radioactivity

On analysis a...

Question

On analysis a sample of $^{238} U$ ore was found to contain $20.6 g$ of $_{82}^{206} P b$ and $23.8 g$ of $_{92}^{238} U$ . The half-life period of $^{238} U$ is $4.50 \times 10^{9}$ years. If all the lead were assumed to have come from the decay of $_{92}^{238} U$ , what is the age of the ore?

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Solution

$t = \frac{2.303}{0.693} \times 4.5 \times 10^{9} \times l o g ⎛ ⎜ ⎜ ⎜ ⎝ 1 + \frac{\frac{20.6}{20.6}}{\frac{23.8}{238}} ⎞ ⎟ ⎟ ⎟ ⎠$
$t = 4.50 \times 10^{9}$ years

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