# 9-62 (Chemical Connections 9A) In a recent archeological dig in the Amazon region of Brazil, charcoal paintings were found in a cave. The carbon-14 content of the charcoal was one-fourth of what is found in charcoal prepared from that year's tree harvest. How long ago was the cave settled?

### Introduction to General, Organic a...

11th Edition
Frederick A. Bettelheim + 4 others
Publisher: Cengage Learning
ISBN: 9781285869759

### Introduction to General, Organic a...

11th Edition
Frederick A. Bettelheim + 4 others
Publisher: Cengage Learning
ISBN: 9781285869759

#### Solutions

Chapter
Section
Chapter 9, Problem 9.62P
Textbook Problem

## 9-62 (Chemical Connections 9A) In a recent archeological dig in the Amazon region of Brazil, charcoal paintings were found in a cave. The carbon-14 content of the charcoal was one-fourth of what is found in charcoal prepared from that year's tree harvest. How long ago was the cave settled?

Expert Solution
Interpretation Introduction

Interpretation:

How long ago the cave was settled should be found from the C-14 ratio of the cave painting and plant harvest of the year which is given as one fourth?

Concept Introduction:

C-14 being radioactive it undergoes decay process in dead sample. From the half life of C-14 and the ratio of C-14 in dead sample to that of living sample the age of the dead sample can be calculated using first order reaction kinetics.

### Explanation of Solution

Radioactive disintegration of C-14 is a first order reaction. If we consider the amount of C-14 during the cave paintings as 100% then amount of C-14 present in the cave painting when discovered was 25%

Half life of C-14 is 5730 years.

If we consider that the cave was settled t years ago and radioactive disintegration constant of C-14 as k then using first order reaction kinetics we can write that.

t=(2.303k)×log(N0N) where N0,N are initial and final atoms present in the radioactive sample i.e in the cave paintings. Now putting all the values we get,

t=(2.303k)×log(N0N)

For first order reaction,

k=0.6932t1/2=0

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