Explanation Given info: Mass of sample 94 239 Pu is 50 g , mass of water is 4.75 kg time is 1 h . Write the equation for alpha decay of 94 239 Pu . 94 239 Pu → 92 235 U + 2 4 He The change in mass is calculated as, Δ m = m i − m f = m i − ( m U − m α ) Here, m i is the mass of initial sample. m f is the mass of final sample. Substitute 239.052158 u for m i , 235.043925 u for m U and 4.002603 u for m α to get Δ m . Δ m = m i − ( m U − m α ) = 239.052158 u − ( 235.043925 u + 4.002603 u ) = 0.00563 u Thus, the change in mass is 0.00563 u . Write the expression for energy per decay. E = ( Δ m ) c 2 Here, Δ m is the change in the mass of the sample. c is the speed of light ( 3 × 10 8 m / s ) . Substitute 0.00563 u for Δ m and 3 × 10 8 m / s for c in the above expression to get E . E = ( Δ m ) c 2 = 0.00563 u ( 931.5 MeV c 2 1 u ) × c 2 = 5.244 MeV Thus, the value of E is 5.244 MeV . Write the expression for first order decay. N = N ° e − λ t Here, N ° is the initial number of nuclei. N is the final number of nuclei. λ is the decay constant. t is the disintegration time. Write the expression for the number of decays. n = N ° − N Here, n is the number of decays. N ° is the initial number of nuclei. N is the final number of nuclei. Replace N by N ° e − λ t in the above expression to get n . n = N ° − N ° e − λ t Write the expression for the decay constant. λ = 0.693 T 1 2 Here, λ is the decay constant. T 1 2 is the half life. Replace λ by 0.693 T 1 2 to get n . n = N ° − N ° e ( − 0.693 T 1 2 ) t Replace N ° by m / M in the above expression to get n . n = N ° − N ° e ( − 0.693 T 1 2 ) t = N ° ( 1 − e ( − 0

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Chapter 32, Problem 88GP

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The increase in the temperature of water in 1 h .

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Chapter 32, Problem 87GP

Chapter 32, Problem 89PP

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

Ch. 32.1 - Prob. 1EYU Ch. 32.2 - A given nucleus can decay by alpha decay, beta...Ch. 32.3 - Prob. 3EYU Ch. 32.4 - Prob. 4EYU Ch. 32.5 - Prob. 5EYU Ch. 32.6 - Prob. 6EYU Ch. 32.7 - Prob. 7EYU Ch. 32.8 - Prob. 8EYU Ch. 32.9 - Prob. 9EYU Ch. 32 - Prob. 1CQ

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