   Chapter 6.2, Problem 34E

Chapter
Section
Textbook Problem

Radioactive Decay In Exercises 29-36, complete the table for the radioactive isotope.Isotope Half-life (in years) Initial Quantity Amount After 1000 Years Amount After 10,000 Years 14 C 5715 _____ 1.6   g _____

To determine

To calculate: The initial amount of the radioactive isotope 14C and its total amount after 10,000 years.

Explanation

Given:

Half-life of the isotope 14C as 5715years and its amount after 1000 years as 1.6g

Formula used:

We can use the growth and decay model y=Cekt

Calculation:

Let us consider the given expression:

y=Cekt …… (1)

Let the initial amount of the isotope be C.

t=1000 for the amount after 1000 years and also given that y=1.6.

By putting t=1000 and y=1.6 in equation (1), we get:

y=Cekt1.6=Cek×10001.6e1000k=C

For half-life t=5715 and y=12C

By putting t=5715 and y=12C in equation (1), we get:

y=Cekt12C=Cek×571512=e5715kln(12)=ln(e5715k)

By simplifying further,

5715k=ln125715k=0

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