   Chapter 25, Problem 65IL

Chapter
Section
Textbook Problem

A piece of charred bone found in the ruins of a Native American village has a 14C/12C ratio that is 72% of the ratio found in living organisms. Calculate the age of the bone fragment (t1/2 for 14C is 5.73 x 103 years.)

Interpretation Introduction

Interpretation:

The age of the bone fragment 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, given by,t1/2=0.693kwhere,kis rate constant.(or)lnA- lnA0= -kt

According to first order reaction;

ln(A/A0)=-kt, where

A=activityA0=initialactivityt=time

Explanation

Given,

14C/12C ratio is 72%

t1/2for14C=5.73×103years.

According to first order reaction;

ln(A/A0)=-kt

The decay constant is calculated as follows,

k=0.693t1/2

Substituting the values in above equation,

k=0.6935.73×103=1

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