   Chapter 25, Problem 66IL

Chapter
Section
Textbook Problem

A sample of wood from a Thracian chariot found in an excavation in Bulgaria has a 14C activity of 11.2 dpm/g. Estimate the age of the chariot and the year it was made. (t1/2 for 14C is 5.73 X 103 years, and the activity of 14C in living material is 14.0 dpm/g.)

Interpretation Introduction

Interpretation:

The age of chariot and the year the chariot was made has to be estimated.

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:

Activity (A)=11.2min1g1

Initial activity (A0)=2.40min1g1

Half-life of carbon-14(t1/2)=5.73×103years

Calculation:

According to first order reaction;

ln(A/A0)=kt

The decay constant is calculated as follows,

k=0.693t1/2=0.6935.73×103=0.1209×103y1

The age of the chariot has been calculated as follows,

ln(A/A0)=kt

ln(11

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