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The decay of U-238 to Pb-206 can be used to estimate the age of inorganic matter. The half-life of U-238 is 4.5 X 100 years. In a particular rock sample, the ratio of the numbers of Pb-206 to U-238 atoms is 0.66. Assume all of the Pb-206 present is due to the decay of U-238. What is the age of the rock? -kt C=Co e .693 .693 -10 Ty2: K= = 1.54 X10 K 4.5 110

The decay of U-238 to Pb-206 can be used to estimate the age of inorganic matter. The half-life of U-238 is 4.5 X 100 years. In a particular rock sample, the ratio of the numbers of Pb-206 to U-238 atoms is 0.66. Assume all of the Pb-206 present is due to the decay of U-238. What is the age of the rock? -kt C=Co e .693 .693 -10 Ty2: K= = 1.54 X10 K 4.5 110

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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The decay of U-238 to Pb-206 can be used to estimate the age of inorganic matter. The half-life of U-238 is \(4.5 \times 10^9\) years. In a particular rock sample, the ratio of the numbers of Pb-206 to U-238 atoms is 0.66. Assume all of the Pb-206 present is due to the decay of U-238. What is the age of the rock? Equation: \( C = C_0 \, e^{-kt} \) Half-life equation: \( T_{1/2} = \frac{0.693}{k} \) Decay constant: \( k = \frac{0.693}{4.5 \times 10^9} = 1.54 \times 10^{-10} \)
Transcribed Image Text:The decay of U-238 to Pb-206 can be used to estimate the age of inorganic matter. The half-life of U-238 is \(4.5 \times 10^9\) years. In a particular rock sample, the ratio of the numbers of Pb-206 to U-238 atoms is 0.66. Assume all of the Pb-206 present is due to the decay of U-238. What is the age of the rock? Equation: \( C = C_0 \, e^{-kt} \) Half-life equation: \( T_{1/2} = \frac{0.693}{k} \) Decay constant: \( k = \frac{0.693}{4.5 \times 10^9} = 1.54 \times 10^{-10} \)
Expert Solution
Step 1: Calculation of decay constant

The decay of the U - 238  to Pb - 206 is used to estimate the age of the inorganic matter .

The half ife of U-238 is given to be  4.5 x 109  years 

Given the ratio of  the numbers Pb- 206  and U-238 atoms  is 0.66

Assuming  all the Pb - 206 present is due to the decay of U-238 

To Find 

Age of the rock 

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