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Chemistry-

General

Easy

Question

There are $0.618 blank mu g blank$ of $blank to the power of 206 end exponent P b$ and $0.238 blank mu g blank$ of $blank to the power of 238 end exponent U$ in a rock. If $T subscript 50 end subscript$ of $blank to the power of 238 end exponent U$ is $1.5 cross times 10 to the power of 9 end exponent y r comma$ age of the rock is

$1.5 \times 10^{9} y r$
$3.0 \times 10^{9} y r$
$4.5 \times 10^{9} y r$
$0.75 \times 10^{9} y r$

The correct answer is: $3.0 cross times 10 to the power of 9 end exponent y r$

Based on rock-dating
$left parenthesis 1 plus fraction numerator open square brackets P b close square brackets over denominator open square brackets U close square brackets end fraction equals open parentheses 2 close parentheses to the power of n end exponent$
$open parentheses 1 plus fraction numerator fraction numerator 0.618 blank cross times blank 10 to the power of negative 6 end exponent over denominator 206 end fraction over denominator fraction numerator 0.238 blank cross times 10 to the power of negative 6 end exponent over denominator 238 end fraction end fraction close parentheses equals open parentheses 2 close parentheses to the power of n end exponent$
$open parentheses 2 close parentheses to the power of 2 end exponent equals open parentheses 2 close parentheses to the power of n end exponent$
$n equals 2$
$2 equals fraction numerator t over denominator T subscript 50 end subscript end fraction$
$t equals 2 cross times T subscript 50 end subscript equals 3 cross times 10 to the power of 9 end exponent y r$

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