Homework2 - Homework 2 AMATH 383, Autumn 2009 Due: Monday,...

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Homework 2 AMATH 383, Autumn 2009 Due: Monday, October 26, after class 1. (6 points) Age of Cave Painting: The caves near Lascaux, France, contain multiple wall paintings of animals from ancient times. To determine the age charcoal found in the caves have been investigated using the C-14 dating method. The charcoal gave an average count of R measured = 0 . 97 disintegrations min gram of C-14 in a sample. Fresh wood measurements today give R fresh = 6 . 68 disintegrations min gram . Estimate the age of the charcoal and hence the possible date of the wall paintings. 2. (1+4+10+10+5+5+1 points) Reduced Thorium Chain: When restricted to the slowest compo- nents the Thorium chain reduces to Pu-244 τ 1 −→ U-236 τ 2 −→ Th-232 τ 3 −→ Pb-208 with half-lifes τ 1 , 2 , 3 around 10 8 years. In order to investigate this chain analytically we make the simplifying assumptions for the decay constants λ i = ln2 i λ 3 = 1 10 λ 1 and λ 2 = 10 λ 1 (a) Which decay is the fastest and which one the slowest in this chain? (b) Explain why the system y 1 ( t ) = λ 1 y 1 ( t ) y 2 ( t ) = λ 2 y 2 ( t ) + λ 1 y 1 ( t ) y 3 ( t ) = λ 3 y 3 ( t ) + λ 2 y 2 ( t ) y 4 ( t ) = + λ 3 y 3 ( t ) describes the above chain. What elements are the function y 1 , 2 , 3 , 4 refering to? (c) Write the system in matrix form. The general solution of the system is a superposition of solutions of the form y ( t ) = v exp ( α t ) with α R , v R 4 and y ( t ) = ( y 1 ( t ) , y 2 ( t
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This note was uploaded on 01/10/2010 for the course MATH 124 taught by Professor Walker during the Spring '08 term at University of Washington.

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Homework2 - Homework 2 AMATH 383, Autumn 2009 Due: Monday,...

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