Explanation Write the formula to find the activity R = λ N (I) Write the formula to find the number of nuclei per molecule N = m N A A (II) Write the formula for half-life T 1 / 2 = ln 2 λ (III) Here, R is the activity, λ is the decay constant, N 0 is the initial number of nuclei, N is the number of nuclei after time t , A is the atomic mass, N A is the Avogadro number and t is the number of hours for the activity. Conclusion: Substitute equation (II) and (III) in (I) to solve for m R = λ N = ln 2 T 1 / 2 m N A A m = R T 1 / 2 A N A ln 2 Substitute 45 decays / s for R , 1.265 × 10 9 yr for T 1 / 2 , 39.964 g / mol for A and 6.02 × 10 23 nuclei / mol for N A in the above equation to find the value of m 40 m 40 = ( 45 decays / s ) ( 1.265 × 10 9 yr ) ( 3.156 × 10 7 s / yr ) ( 39 .964 g / mol ) ( 6.02 × 10 23 nuclei / mol ) ( ln 2 ) = 1.721 × 10 − 4 g Thus, the mass of 19 40 K in a liter of milk is 1.721 × 10 − 4 g . From the abundance given in Appendix F, The number of 19 40 K nuclei in a liter of milk is N 40 = 0

Physics for Scientists and Engineers with Modern Physics

4th Edition

ISBN: 9780136139225

Author: Douglas C. Giancoli

Publisher: Prentice Hall

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Chapter 41, Problem 70GP

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The mass of 1940K and regular 1939K present in a liter of milk.

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Chapter 41, Problem 69GP

Chapter 41, Problem 71GP

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Physics for Scientists and Engineers with Modern Physics

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