Exponential Functions Of Decaying Dice: Mathematics And Applications

Mathematics of the decay of real radioactive nuclei

Discuss about the Exponential Functions of Decaying Dice.

The decay of the radioactive nuclear is slow hence the rate of the decay can be determined at some particular time. This is a result of the rate of the decay that is constant. Decay is a statistical process, this implies that there can be statistical analysis in determination of the rate of decay. Alternatively, the statistical method can also be used to determine the number of times a given die can roll. Therefore, an experiment is done to determine decay analogy of the radioactive nuclei. A die is thrown spontaneously where the sides showing specific numbers are regarded as decayed for example, a specific number such as five. The dice then are to be removed and counting is done to the remaining dice. Recording and representation of the remaining die are done within a range of time. The remaining dice are thrown and the recounting is also done. This process is done on and on until such a time when the number of dice that do not decay is reduced. A constant is used to represent the decay of the radioactive nuclei.in this experimentation, there is the assumption that dice have a single change in showing the specific number hence this gives an equivalent of real decay of a radioactive decay, thus this constant is given as 1/6.

with an assumption that one was to throw a dice at intervals of one hour and make counts on the same.by throwing 500 dice simultaneously at the end of every hour is the easiest way of starting the test[1]. This implies that at the end of one-hour one-sixth of this dice will be removed and with perfect statistics then the remaining dice will be 416.66667.

Generally, remaining number after that throw will be shown as;

N1 = 500(1 − 1/6).

When a throw is done for the second time we have;

N2 = 500(1 − 1/6) (1 − 1/6) = 500(1−1/6)2

General whilst when n number of mass is given as;

Nn = 500(1 − 1/6) n.

This is an indication that decay is a progressive geometry. The first twelve throws are the one that is used in the determination of the dice that do not decay. This method is indicated in the table below and a graph plotted as the number of the remaining die against the number of rolls as shown below.

Experimentation with Decaying Dice

The time interval presentation by each mass and the actual time elapse denoted by t is to be linked in this case. For the real nuclei decay is exponentially shown as;

Nt = N0e−λt

Where Nt number of dice that do not decay remaining at time t. By substituting the value of the constant of the decay with 1/6 h−1 and No is equated to nuclei of about 500.

Nt = 500 e−t/6.

Then the counting is done at an interval of every one hour. This value is indicated in the table below.

Alternatively, one can use 100 dice to do the test or the dice activity. For the first time, one needs to have a large number of the dice and also should have a cup that can be able to carry all the dice that you have for the operation. One should have the piece of paper for recording and some graph paper for showing some graphical results[2].

One should imagine having some supply of the radioactive isotopes with a sixth chance for decay for the time that follows. This is to be done for the next six minutes and a confirmation is done. It is done for the next 20 minutes. This continued until the half of the dice is used for the approximation on how long it takes for the decay of the half of the sample.

All the dice should be put in that cup and rolling to be done on the table. The separation of the dice should be done on the table and all that turned up to be separated these are regarded as the decayed particles. The counting should be done on the participles that decayed and remaining dice then is measured. Decayed particles then separated and then placed in a particular pipe for easy monitoring. This pipe should be good enough to carry the dice and easy to be supervised. Some dice are then placed in the cap.

This steps should be repeated for some time and measuring of this should be done for the decaying particles. Separation is then done to the batches that turned up perceived to be decayed. This process is done for the next 2 minutes. The rolling should be done for the next 3 minutes and repeated until all the dice are over. Lastly graphing is then done for the decaying dice. This should be done with respect to the minute of the rolling.stent ratio,  this decay can be employed in the real life to help in predicting the expectation for the impending losses or some case profits. It can as well be employed in real life to predict the market trends.  The exponential decay can also be employed in real life to determine the depreciation rate of commodities like houses and vehicle. In some cases, the government employs the exponential decay to predict the reduction in population, poll prediction and downwards trend in the markets.

Similarities Between Decaying Dice and Real Radioactive Decay

Checking on the function of the exponential decay is done with the calculator for the graphs or a program with the similarity of such. The plotting was done and had a constant of about 0.1666 that is equivalent to the sixth. Implying that the plotting was done with e-(1/6) this function was the description of the graph, with a proper software the plotting of the data was done and the software enabled to fit an exponential. Sketching done with a proper graph drawn later as indicated below. Since the process of this inherent randomness is the easiest way of the determining the nature of the exponential.                                        

Checking on the function of the exponential decay, with calculators for the graphs or a program with the similarity of such[3]. The plotting was done and had a constant of about 0.1666 that is equivalent to the sixth. Implying that the plotting was done with e-(1/6) this function was the description of the graph, with a proper software the plotting of the data was done and the software enabled to fit an exponential. Sketching done with a proper graph drawn later as indicated below. Since the process of this inherent randomness is the easiest way of the determining the nature of the exponential

Conclusion

The modification can be done accurately using the throwing of the six-sided dice to determine the decay of the radioactive nuclei. Most of the research indicates that obtained half-life by dice is different with that of nuclei hence the decay has a constant of 1/6. This divergence is as a result of the continuous exponential decay modeling done by the discrete geometric progression. There is a decrease in the number of the sides brought about by the degree of the divergence affected by the number of the sides. By going with the judgments from the internet, some works have indicated that most people have come to this conclusion. Most of the works have been done by the few pence per die.A useful analogy of the radioactive decay can be provided by the simple experiment. Where the random nature of the process is highlighted, the decay rate is varied with the number of the throw as shown by the graph produced and finally creates the room for the generation of data by the students in a safe and simple way

The modification can be done accurately using the throwing of the six-sided dice to determine the decay of the radioactive nuclei. research indicates that obtained half-life by dice is different with that of nuclei hence the decay has a constant of 1/6.this divergence is as a result of the continuous exponential decay modeling done by the discrete geometric progression. There is the decrease in the number of the side brought about by the degree of the divergence affect by the number of the sides.by the judgments of the internet, some works have indicated that most people have come to this conclusion. Most of the works have been done by the few pence per die. A useful analogy of the radioactive decay can be provided by the simple experiment[4]. Where the random nature of the process is highlighted, the decay rate is that varies with the number of the throw is shown by the graph produced and finally creates the room for the generation of data by the students in the safe and simple way

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