Explanation Given Info: The mass of 88 226 Ra sample is 1.9 g . The molar mass of 88 226 Ra is 226 g / mol . The half-life of 88 226 Ra is 1600 yr . The formula to calculate value of decay constant of 88 226 Ra ( λ ) is, λ = 0.693 T 1 / 2 (1) Here, T 1 / 2 is the half-life of 88 226 Ra . The relation between year and second is, 1 yr = 3.154 × 10 7 s Use this relation to convert the calculated value of λ 1 . 1600 yr = 1600 × 3.154 × 10 7 s = 6928 × 10 7 s = 6.928 × 10 10 s Substitute 6.928 × 10 10 s for T 1 / 2 in equation (1) to find λ . λ = 0.693 6.928 × 10 10 s = 0.10 × 10 − 10 s − 1 Thus, the value of decay constant of 88 226 Ra is 0.10 × 10 − 10 s − 1 . The number of moles of 88 226 Ra ( n ) sample is calculated by the formula, n = m M (2) Here, m is the mass of 88 226 Ra sample. M is the molar mass of 88 226 Ra sample. Substitute 1.9 g for m and 226 g / mol for M in equation (2) to find n . n = 1.9 g 226 g / mol = 8.4 × 10 − 3 mol Thus, the number of moles of 88 226 Ra sample is 8.4 × 10 − 3 mol . The relation between the number of moles and nuclei is, 1 mol = 6.022 × 10 23 nuclei Use this relation to convert the calculated value of number of moles. 8.4 × 10 − 3 mol = 8.4 × 10 − 3 × 6.022 × 10 23 nuclei = 5.058 × 10 21 nuclei The formula to calculate number of disintegration per second ( d N d t ) of sample of 88 226 Ra is, d N d t = λ N (3) Here, N is the number of nuclei in 1

Physics, Books a la Carte Edition (5th Edition)

5th Edition

ISBN: 9780134020853

Author: James S. Walker

Publisher: PEARSON

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Nuclear Reactions

Nuclear reactions are processes in which the fundamental characteristics of a nucleus changes. They change into a completely different nucleus. These processes occur naturally in an unstable nucleus. Bombarding an energetic particle can induce nuclear re…

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Chapter 32, Problem 78GP

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The number of disintegration per second and activity of the given sample of 88226Ra in curies.

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Chapter 32, Problem 77GP

Chapter 32, Problem 79GP

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The number of disintegration per second and activity of the given sample of 88 226 Ra in curies.

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The number of disintegration per second and activity of the given sample of 88226Ra in curies.

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