Answered: Calculate the activity Carbon-14 in 2…

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

Calculate the activity Carbon-14 in 2 kg of carbon in a living organism. Express the activity in Bq. Note that the natural abundance of C-14 = 1.3e-12, Avogadro's number = 6.02e23, Activity R = 0.693*N / half-life-time. Write your answer in the form of an integer.

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Step 1

Mass of Carbon 14 = 2 kg = 2000 gms [1 Kg = 1000 gms]

Natural abundance of C-14 is 1.3 x 10^-12

Avogadro's number = 6.02e23 [Each mole contains 6.023 x 10²³atoms)

Total number of carbon atoms, Na = 1.3 x 10^-12 x 6.023 x 10²³ = 7.8299 x 10¹¹ nuclei/mol

Molar mass of C-14 = 12 g/mol

Number of moles of carbon nuclei atoms, N = Mass of C-14/Molar mass) x Na = (2000 g/12 g/mol) x 7.8299 x 10¹¹ nuclei/mol = 15.6598 x 10¹⁴/12 = 1.305 x 10¹⁴

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