Consider the decay of 235U → 231Th → 231Pa, with a half-life of 7.038x108 years for 235U and 25.5 hours for 231Th. Suppose you have a sample with 10 mCi of 235U. Calculate and plot the activities of the father and daughter as a function of time (assume the granddaughter is stable) between t = 0 and 1000 hours. If you find it convenient, use a logarithmic scale. What kind of balance is there and why? In the graph, indicate the time tm (remember tm = [1/( λ2 - λ1)] [ln(λ2 / λ1]) in which the daughter reaches her maximum activity and verify that it coincides with the analytical expression calculated in class.

Consider the decay of 235U → 231Th → 231Pa, with a half-life of 7.038x108 years for 235U and 25.5 hours for 231Th. Suppose you have a sample with 10 mCi of 235U. Calculate and plot the activities of the father and daughter as a function of time (assume the granddaughter is stable) between t = 0 and 1000 hours. If you find it convenient, use a logarithmic scale. What kind of balance is there and why? In the graph, indicate the time tm (remember tm = [1/( λ2 - λ1)] [ln(λ2 / λ1]) in which the daughter reaches her maximum activity and verify that it coincides with the analytical expression calculated in class.

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Question

Consider the decay of ²³⁵U → ²³¹Th → ²³¹Pa, with a half-life of 7.038x10⁸ years for ²³⁵U and 25.5 hours for ²³¹Th. Suppose you have a sample with 10 mCi of ²³⁵U. Calculate and plot the activities of the father and daughter as a function of time (assume the granddaughter is stable) between t = 0 and 1000 hours. If you find it convenient, use a logarithmic scale. What kind of balance is there and why? In the graph, indicate the time tm (remember tm = [1/( λ₂- λ₁)] [ln(λ_{2 /} λ₁]) in which the daughter reaches her maximum activity and verify that it coincides with the analytical expression calculated in class.