Solved: A random-number generator can be used to simulate the probability of a given

Chapter 24, Problem 24.146

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A random-number generator can be used to simulate the probability of a given atom decaying over a given time. For example, the formula _RAND() in the Excel spreadsheet returns a random number between 0 and 1; thus, for one radioactive atom and a time of one half-life, a number less than 0.5 means the atom decays and a number greater than 0.5 means it doesnt. (a) Place the _RAND() formula in cells A1 to A10 of an Excel spreadsheet. In cell B1, place _IF(A1<0.5, 0, 1). This formula returns 0 if A1 is <0.5 (the atom decays) and 1 if A1 is >0.5 (the atom does not decay). Place analogous formulas in cells B2 to B10 (using the Fill Down procedure in Excel). To determine the number of atoms remaining after one half-life, sum cells B1 to B10 by placing _SUM(B1:B10) in cell B12. To create a new set of random numbers, click on an empty cell (e.g., B13) and hit Delete. Perform 10 simulations, each time recording the total number of atoms remaining. Do half of the atoms remain after each half-life? If not, why not? (b) Increase the number of atoms to 100 by placing suitable formulas in cells A1 to A100, B1 to B100, and B102. Perform 10 simulations, and record the number of atoms remaining each time. Are these results more realistic for radioactive decay? Explain.