Explanation Given data: Carbon constitutes 12% of the body mass, and 100% of energy is absorbed of 49 keV of each 14 C decay. Formula used: Write the expression for activity. R = N τ (1) R = 0.693 N t 1 2 (2) Here, R is the activity, N is the number of nuclei samples, τ is the time constant, and t 1 2 is the half-life. Explanation: Consider the mass of the body to be m . The amount of carbon content in our body according to given question is 12% of m that is 0.12 m. The mass of 12 C is 12 u. Consider the conversion factor. 1 u = 1.66 × 10 − 27 kg Convert 12 u into kg by using conversion factor. 12 u = 12 × 1.66 × 10 − 27 kg The number of carbon atoms contained in the body can be calculated by dividing the mass of carbon contained in the body to the total mass of the carbon atom, that is N = ( 0.12 ) m 12 ( 1.66 × 10 − 27 kg ) The fraction of 14 C is 1.3 × 10 − 12 , so the number of 14 C atoms contained is , N = ( 0.12 ) m ( 1.3 × 10 − 12 ) 12 ( 1.66 × 10 − 27 kg ) The half-life of carbon is 5730 years. Substitute ( 0.12 ) m ( 1.3 × 10 − 12 ) 12 ( 1.66 × 10 − 27 kg ) for N , and 5,730 yr for t 1 2 in equation (2), R = 0.693 ( 0.12 m ) ( 1.3 × 10 − 12 ) 5 , 730 yr ( 12 ) ( 1.66 × 10 − 27 kg ) = 9.47 × 10 8 m yr ⋅ kg Rearrange equation (1) to solve for N . N = R τ Substitute ( 9.47 × 10 8 ) m yr ⋅ kg for R and 1 yr for τ , N = ( 9.47 × 10 8 ) m yr ⋅ kg ( 1 yr ) = ( 9.47 × 10 8 ) m yr ⋅ kg The dose can be found out by dividing the energy absorbed by mass That is, dose = Energy absorbed Mass (4) Consider the conversion factor for eV to J. 1 eV = 1.602 × 10 − 19 J Convert 49 keV into J by using conversion factor

College Physics: A Strategic Approach (3rd Edition)

3rd Edition

ISBN: 9780321879721

Author: Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field

Publisher: PEARSON

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Chapter 30, Problem 66GP

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The dose equivalent in Sv received each year from the 14C in the body.

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Chapter 30, Problem 65GP

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College Physics: A Strategic Approach (3rd Edition)

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The dose equivalent in Sv received each year from the 14 C in the body.

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Chapter 30 Solutions