Show your work on a separate sheet of paper to show all details of how you derived your answer.An archaeologist student found the leg bone of a very large animal during the building of the newSEM building at Cypress College. The bone had a very small carbon-14 decay rate of 1.4 x 102dis/min/gC. Living organisms have a carbon-14 decay rate of 15.3 dis/min/gC. How old is the bone?The half-life of carbon-14 is 5730 years.The bone is approximately [ans1] years old.

Write the expression for first order kinetics as follows: A = A0exp-ktexp-kt = AA0kt= -lnAA0t =…

Answered: Show your work on a separate sheet of…

Introduction to Chemical Engineering Thermodynamics

8th Edition

ISBN:9781259696527

Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Chapter1: Introduction

Section: Chapter Questions

Problem 1.1P

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Question

Show your work on a separate sheet of paper to show all details of how you derived your answer.
An archaeologist student found the leg bone of a very large animal during the building of the new
SEM building at Cypress College. The bone had a very small carbon-14 decay rate of 1.4 x 102
dis/min/gC. Living organisms have a carbon-14 decay rate of 15.3 dis/min/gC. How old is the bone?
The half-life of carbon-14 is 5730 years.
The bone is approximately [ans1] years old.

Expert Solution

Step 1

Write the expression for first order kinetics as follows:

$\begin{array}{rcl} A & = & A_{0} e x p (- k t) \\ e x p (- k t) & = & \frac{A}{A_{0}} \\ k t & = & - \ln (\frac{A}{A_{0}}) \\ t & = & \frac{1}{k} \ln (\frac{A_{0}}{A}) . . . . . . (1) \end{array}$

Given,

Initial activity, $A_{0} = 15.3 dis / \min / gC$

Final activity, $A = 1.4 \times 10^{- 62} dis / \min / gC$

Half-life, $t_{1 / 2} = 5730 years$

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