Answered: An ancient wooden artifact was found in…

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Question

An ancient wooden artifact was found in 1960 from an archeological site in Clovis, New Mexico. A small amount of this sample was completely burned in O2 and the CO2 produced was bubbled through a solution of Ba(OH)2 to produce a precipitate of BaCO3. When the BaCO3 was collected by filtration, a 1.00-gram sample of the precipitate was found to show a C-14 activity of 4.0 x 10–3 Bq. (a) What is the C-14 activity in the sample expressed in dpm/gC? (b) What is the age of the wood sample at the time the analysis was carried out? (Assume that C-14 in the living organisms has an average activity of 15.0 dpm/gC and the half-life of C-14 isotope is 5730 years.)

Expert Solution

Step 1

Calculation of mass of 'C' in 1.00 g sample of BaCO₃:

$\begin{array}{rcl} Mass of' C' & = & No . of mol \times Molar mass \\ = & \frac{1.00 g}{197.34 g / mol} \times 12.00 g / mol \\ = & 0.06081 g \end{array}$

Step 2

1 Bq = 1 dis/sec

Conversion of 4.0 x 10^–3 Bq into dis/min:

$\begin{array}{rcl} 4.0 \times 10^{- 3} Bq & = & 4.0 \times 10^{- 3} dis / se c \times \frac{60 s}{1 \min} \\ = & 0.24 dis / \min \end{array}$

Calculation of per gram sample of 'C':

$\begin{array}{rcl} 0.24 dis / \min & = & \frac{0.24 dis / \min}{0.06081 g C} \\ = & 3.947 dpm / g C \end{array}$

Thus C-14 activity is 3.947 dpm/g C

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