Explanation Given data: Mass of the human body is 70 kg, Mass of potassium content is 140 g, Atomic mass of potassium is 39.1 u, The half-life of 40 K is 1.3 billion years, Natural abundance is 0.012%, and Energy deposited is 1 MeV. Formula used: Write the expression for number of nuclei decayed after time t. N = N 0 ( 1 2 ) t t 1 2 (1) Here, N is the number of atoms remaining after time t , N 0 is the number of atoms at the start t = 0 , t is the time, and t 1 2 is the half-life. Explanation: Calculate the number of atoms of 40 K . The chemical mass of 40 K is the product of its natural abundance and mass of its content, that is, ( 0.000012 ) ( 140 g ) . From appendix D the atomic mass of K is 39.1 g. 39.1 g → 1 mole of 40 K ( 0.000012 ) ( 140 g ) → 1 mole 39.1 g × ( 0.000012 ) ( 140 g ) Also, 1 mole 39.1 g × ( 0.000012 ) ( 140 g ) = 6.02 × 10 23 atoms 39.1 g × ( 0.000012 ) ( 140 g ) = 2 .59 × 10 20 atoms { ∵ 1 mole = 6.02 × 10 23 atoms } Subtract equation (1) with N 0 to get the number not decayed in one year. N 0 − N = N 0 − N 0 ( 1 2 ) t t 1 2 N 0 − N = N 0 ( 1 − ( 1 2 ) t t 1 2 ) Substitute 2

College Physics: A Strategic Approach Technology Update, Books a la Carte Plus Mastering Physics with Pearson eText -- Access Card Package (3rd Edition)

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Chapter 30, Problem 68GP

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The yearly dose in Gy a typical person receives from the decay of 40K in the body.

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Chapter 30, Problem 67GP

Chapter 30, Problem 69GP

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College Physics: A Strategic Approach Technology Update, Books a la Carte Plus Mastering Physics with Pearson eText -- Access Card Package (3rd Edition)

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