Chapter 25, Problem 69IL

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# The age of minerals can sometimes be determined by measuring the amounts of 206Pb and 238U in a sample. This determination assumes that all of the 206Pb in the sample comes from the decay of 238U. The date obtained identifies when the rock solidified. Assume that the ratio of 206Pb to 238U in an igneous rock sample is 0.33. Calculate the age of the rock (t1/2 for 238U is 4.5 × 109 years_)

Interpretation Introduction

Interpretation: Age of the rock has to be calculated.

Concept Introduction:

Radiocarbon dating: The dynamic equilibrium exists in all living organism by exhaling or inhaling, maintain the same ratio of 12C and 14C that takes in. when the living organism dies, the intake of 14C stops and it’s the ratio no longer exhibits equilibrium; undergoes radioactive decay.

Half-life period: The time required to reduce to half of its initial value.

Formula used to calculate half-life:

t1/2=0.693kwhere,kis rate constant.(or)ln[N]t- ln[N]0= -kt

Explanation

Given info:

The ratio of Pb206â€‰toâ€‰U238 in an igneous rock sample is 0.33

t1/2â€‰forâ€‰U238â€‰isâ€‰4.5Ã—109â€‰years.

Calculation:

The given 0.33â€‰sampleâ€‰isâ€‰equalâ€‰toâ€‰13

Ratio of the lead-206 and Uranium-238 is 13

Pb206:â€‰U238<

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