Chapter 24: Q24.43 P (page 1104)

A rock contains_$μ$mol of $^{238} U (t_{1/2} {=4.5×10}^{9} yr)$ and110mol of $^{206} Pb$ Assuming that all the $^{206} Pb$ comes from decay of the , estimate the rock’s age.

Short Answer

Expert verified

The rock's age is _{$2.22 \times 10^{9} yr$}

Step by step solution

Radioactive decay

The radioactive decay follows the first order kinetics. The relation between half-life and rate constant “k” is:

$t_{1 / 2} = \frac{0.693}{k}$

Estimation of the rock’s age

- The half-life of_{$^{238} {Uist}_{1/2} {=4.5×10}^{9} yr$}

- Rock now contains $N_{t} {=270μmolof}^{238} U$ , and_{${110μmolof}^{206} Pb$} (which means that ${110μmolof}^{238} U$ decayed into_{$^{206} Pb$} )

Therefore, the rock initially contained

_{$N_{0} {=270μmol+110μmol}^{238} {U=380μmol}^{238} U$}

First, let us calculate the decay constant of _{$^{238} U$}

_{$\begin{matrix} t_{1/2} = \frac{ln(2)}{k} \\ k= \frac{ln(2)}{t_{1/2}} \\ = \frac{0.693}{{4.5×10}^{9} yr} \\ {=1.54×10}^{-10} {yr}^{-1} \end{matrix}$}

Calculation of the rock's age

_{$\begin{matrix} ln (\frac{N_{t}}{N_{0}}) =-kt \\ t= \frac{-ln (\frac{N_{t}}{N_{0}})}{k} \end{matrix}$}

_{$\begin{array}{l} = \frac{-ln (\frac{{270μmol}^{288} U}{{380μmol}^{28U}})}{{1.54×10}^{-10} {yr}^{-1}} \\ {=2.22×10}^{9} yr \end{array}$}

Hence the rock's age is _{$2.22 \times 10^{9} yr$}

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A rock contains_$μ$mol of $^{238} U (t_{1/2} {=4.5×10}^{9} yr)$ and110mol of $^{206} Pb$ Assuming that all the $^{206} Pb$ comes from decay of the , estimate the rock’s age.

Short Answer

Step by step solution

Radioactive decay

Estimation of the rock’s age

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A rock containsμmol of238U(t1/2=4.5×109yr) and110mol of206Pb Assuming that all the206Pbcomes from decay of the , estimate the rock’s age.

Short Answer

Step by step solution

Radioactive decay

Estimation of the rock’s age

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Chemistry Textbooks

Chemistry Branches

Nuclear Chemistry

Organic Chemistry

Making Measurements

Ionic and Molecular Compounds

Physical Chemistry

Study anywhere. Anytime. Across all devices.

A rock contains_$μ$mol of $^{238} U (t_{1/2} {=4.5×10}^{9} yr)$ and110mol of $^{206} Pb$ Assuming that all the $^{206} Pb$ comes from decay of the , estimate the rock’s age.