Chapter 25.4, Problem 25.7CYU

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

A sample of the inner part of a redwood tree felled in 1874 was shown to have 14C activity of 9.32 dpm/g. Calculate the approximate age of the tree when it was cut down. Compare this age with that obtained from tree ring data, which estimated that the tree began to grow in 979 ± 52 BC Use 13.4 dpm/g for the value of A0

Interpretation Introduction

Interpretation:

The approximate age of the tree 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

The age is calculated from rate constant and Half-life is explained below,

Using first order integrated rate law,

ln[AAo]â€‰=â€‰â€‰-â€‰Kt

Here, A = final activity is Aâ€‰=â€‰9.32â€‰dpm/g

Ao initial activity given is Aoâ€‰=â€‰13.4â€‰dpm/g;Â  k is constant.

As known, the half-life of C-14 is 5730 years and using this calculate the constant â€˜kâ€™ as shown below,

kâ€‰â€‰=â€‰0.693t1/2â€‰=â€‰0.6935730â€‰yrsâ€‰=â€‰1.21Ã—10âˆ’4â€‰yrsâˆ’1

By substituting activity value and initial activity in integrated rate law equation,

ln(NN0)â€‰=â€‰âˆ’kâ€‰(t)ln(9

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