   Chapter 25, Problem 60GQ

Chapter
Section
Textbook Problem

In June 1972, natural fission reactors, which operated billions of years ago, were discovered in Oklo, Gabon (page 1178). At present, natural uranium contains 0.72% 235U. How many years ago did natural uranium contain 3.0% 235U, the amount needed to sustain a natural reactor? (t½ for 235U is 17.04 × 108 years.)

Interpretation Introduction

Interpretation:

Period did the natural Uranium contain 3%, the amount needed to sustain a natural reactor 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:

Half-life of uranium-235(t1/2)=7.04×108years

Initial activity (A0)=3.0%

=0.03

Activity (A)=0.72%

=0.0072

Calculation:

Then k calculated as follows,

k=0.693t1/2=0.6937.04×108

=0.0984375×108yr1

The time is calculated as follows,

Formula:

ln(A/A0)=kt

ln(0

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