Explanation Given: The four radioactive elements are W , X , Y , and Z ; and Z is the stable element. Calculation: Consider the series of decay as described below, W → − λ 1 X → − λ 2 Y → − λ 3 Z Here, decay constant for the W is − λ 1 , decay constant for the X is − λ 2 , and decay constant for the Y is − λ 3 . Consider the rate of decay of element W with respect to time. d w d t = − λ 1 w Here, amount of substance W is w . From the series of the decay shows that W is losing the atom and at same time X is gaining the decayed atom from the W . Consider the rate of decay of element X with respect to time. d x d t = λ 1 w − λ 2 x Here, the amount of substance X is x and Similarly from the series of the decay shows that X is losing the atom and at same time Y is gaining the decayed atom from the X

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 2.9, Problem 4E

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To construct: The mathematical model for a radioactive series of four elements W, X, Y, and Z.

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Chapter 2.9, Problem 3E

Chapter 2.9, Problem 5E

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Chapter 2 Solutions

Advanced Engineering Mathematics

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To construct: The mathematical model for a radioactive series of four elements W , X , Y , and Z .

Solution Summary: The author explains the mathematical model for a radioactive series of four elements W, X

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To construct: The mathematical model for a radioactive series of four elements W, X, Y, and Z.

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Chapter 2 Solutions