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A Guide to Microsofl Excel 2002 for Scientists and Engineers phần 7

Các chuỗi phân rã phóng xạ được thể hiện trong phương trình 9,7 xảy ra trong lò phản ứng hạt nhân. Khi lò phản ứng đang hoạt động thông lượng neutron phá hủy và Xe. Khi đóng cửa có một nồng độ còn lại của mỗi đồng vị. | 2. The radioactive decay sequence shown in Equation 9.7 occurs in nuclear reactors. When the reactor is operating the neutron flux destroys the 1 and Xe. When it is shut down there is a residual concentration of each isotope. Because the half-life of I135 is smaller than that of Xe135 the concentration of the latter reaches a maximum and then decays to zero. The reactor cannot be restarted until the Xe135 is well passed its maximum. The equations governing the production of the two isotopes are J135 6 68hrs vc135 9.l3hra - Xe Xe I 9.7 at where Xe and I denote concentrations and kXe and kị are the decay constants. The decay constant k of a radioisotope is related to its half-life Ằ by kẰ ln2. Your task is to model this system and show how the concentration of Xe varies with time for given initial concentrations of 1 and Xe. We will approximate the first equation in Equation 9.6 as A l - l Az giving 1 I 0 l -kt where I o is the initial concentration of I135 when the reactor is shut down and I is the concentration after time t. What condition is needed for this approximation to be justified The equation for Xe is treated similarly. Construct a worksheet similar to that in the figure below. Plot the data A7 C108. Experiment with the values in D3 D5 to observe the behaviour of the model. ỉ 88 A Guide to Microsoft Excel 2002 for Scientists and Engineers A B c D 1 Reactor Problem 2 half-life hrs k hr-1 Initial cone 3 Iodine 6.68 0.1038 2 4 Xenon 9.13 0.0759 0.001 5 Time interval 0.5 6 7 t I cone Xe cone 8 0.00 2 0.0010 9 0.50 1 8962 0.1047 10 1.00 1.7979 0.1991 100 46.00 0.0149 0.1565 101 46.50 0.0141 0.1513 3. Because microprocessors have limited memory their programs must be kept very small. The algorithm shown below has been suggested as a quick way to generate two cycles of a sine wave. The value of Quick 1 is an approximation to sin 90 Quick n approximates sin 90-5.625 - I . Start with q 1 128 and d 1 -1 Quick 1 q 1 128 For n - 2 to 129 d n d n-1 -1 when q n 0 d n-1