19-Feb-2018 15:13

Remember, we assume that the number of decays depends only on the number of pennies we have just before each toss. Now try to find the values of the variables that give the best "fits" to your data for the pennies.You'll see later how to make use of the specific number of pennies you started with. We can now extrapolate our observations by asking what would happen if we used dice instead of pennies, where a die is said to "decay" if it lands, say, with one dot showing up?Clearly the number of atoms decaying in one second depends on the number of atoms you start with, but the chance of any individual atom decaying in a given time period is always the same.These are the same conditions as for population growth (which assumes that everyone has the same chance for having babies no matter what particular time period we choose) except that here the population is decreasing rather than increasing with time.Obviously, you will have to see if you can find any values of m and b which fit your data.Compare your graphs to that of a straight line with the appropriate slope. Try finding whether a quadratic or cubic equation fits better. Scientists are often faced with the difficulty of fitting data coming from processes for which they do not have a quantitative prediction.The description of why atoms decay is quite complicated, involving quantum mechanics and nuclear physics.

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What do you predict the curve for an experiment of 100 dice would look like?This function is useful for describing many very different observations in science.In fact, any change in the number of objects which depends proportionally on the number of objects present will be described by an exponential.If a particular penny lands heads up on the first toss, the chance that it will land tails up on the second toss is still 50%.

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That's exactly the model we need for radioactive decay since the chance of any particular atom decaying in one second is unaffected by the fact that it did not decay a second ago.

Cover the container and shake for about ten seconds (each shake represents 8500 years), holding it tightly to avoid them flying out. Next, remove all the pennies which are now “tails-up.” Count these and put them aside.

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