5. Given the following system of radioactive decay equations and initial conditions, derive the solution for n3(t). Note

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5 Given The Following System Of Radioactive Decay Equations And Initial Conditions Derive The Solution For N3 T Note 1 (232.1 KiB) Viewed 45 times

5. Given the following system of radioactive decay equations and initial conditions, derive the solution for n3(t). Note I want you to work out this solution by hand. You can use a computer program to check your answer (but it may take you awhile to see that your answer matches the computer answer), but you must solve the coupled differential equations showing each step. Note that in this case the third isotope is also radioactive and decays. As you will see, starting off with non-zero amounts of n2 and n3 make this problem much more complicated. dni(t) - lini(t), ni(0) dt dne(t) = lini(t) – 12n2(t), n2(0) dt dn (1) 12n2(t) – 13n3(t), n3(0) = 130 dt = n 10 = = n20 = Hint: Try the method of undetermined coefficients for each equation in succession, use the Integrating Factor method for 1st order differential equations or solve using direct integration for each equation. For a harder way to do this you can try to solve the matrix differential equation. As you see there are many ways to work this. My recommendation is to use the first or second method given at the start of this hint.