Q24.43 P A rock contains聽聽聽渭mol of聽2... [FREE SOLUTION]

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Chapter 24: Q24.43 P (page 1104)

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

Short Answer

Expert verified

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

Step by step solution

Radioactive decay

The radioactive decay follows the first order kinetics. The relation between half-life and rate constant 鈥渒鈥� is:

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

Estimation of the rock’s age

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

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

Therefore, the rock initially contained

_{$N_{0} {=270渭尘辞濒+110渭尘辞濒}^{238} {鲍=380渭尘辞濒}^{238} U$}

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

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

Calculation of the rock's age

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

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

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

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91影视

A rock contains_$渭$mol of $^{238} U (t_{1/2} {=4.5脳10}^{9} yr)$ and110mol of $^{206} Pb$ Assuming that all the $^{206} Pb$ comes from decay of the , estimate the rock鈥檚 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

Physical Chemistry

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Making Measurements

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91影视

A rock contains渭mol of238U(t1/2=4.5脳109yr) and110mol of206Pb Assuming that all the206Pbcomes from decay of the , estimate the rock鈥檚 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

Physical Chemistry

Chemistry Branches

Inorganic Chemistry

Kinetics

The Earths Atmosphere

Making Measurements

Study anywhere. Anytime. Across all devices.

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