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Investigating the Concept of Half-Life in Radioactive Decay Using Coins.

Abstract

The main aim of the two experiments is to verify that 50% of coins will decay (heads-up) in the first throw. In the first experiment, 100 coins (tails-up) will be placed in a box with a cover then shaken thoroughly. Coins with heads –up will be removed to represent the decayed atom. It will be realized that 52% of the coins will decay within the first throw. Similarly, the second experiment will test the same concept. Eight coins will be used for the second experiment. Eight coins will be thrown for each decay cycle. The total numbers of pennies decayed and ...view middle of the document...

The coins are used in the experiment because the radioactive process is unpredictable. Tossing of coins to get the head and the tail is a perfect model to use because the probability is 50%. Another reason is that coins have the same shape and size so there is no bias in terms of the outcomes. Apart from that, coins are also readily available and easier to use. The two Lab experiments will be done in order to compare values when using large numbers and a few numbers of coins. The hypothesis for the two experiments is that approximately 50% of the coins will decay in the first throw. The second hypothesis for Lab 2 is that four of the eight coins will show their heads up.

Method for lab 1

To perform the experiment, hundred pennies and a box with cover were used.

All the pennies were placed with tails up in a flat box with cover. The box was then covered and shaken. After shaking, all the pennies with heads up were removed and their number recorded in a table. The number of pennies remaining was also recorded. The coins removed represents the number of atoms that had decayed in one half-life.

The steps above were repeated until all the pennies were removed from the box. The number of trials required to complete the process was recorded as well. Every trial entailed shaking the box and removing the pennies with heads up. The values were then used to plot a graph of the number of pennies used versus the number of trials. A graph of the number of coins left versus number of trials was also plotted for analysis.

Method for lab 2

For lab 2 experiment, eight pennies were thrown for every decay cycle. A decay cycle was completed when only one or no penny was left. Fifty decay cycles were done in this experiment. The values for each trial was recorded by recording the number of heads that showed up on the first throw. The number of throws, which was required to have one or no pennies left, was also done. A bar graph was drawn to represent the number of pennies which decayed on the first throw. Another bar graph showing the frequency of the number of throws needed to get one or zero pennies was done for analysis.

Data presentation

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Analysis

In the second experiment (lab 2), the total number of pennies that decayed on the first throw is given by adding the number that decayed the first time= (4x1)+(8x2)+(8x3)+(7x4)+(12x5)+(8x6)+(3x7)= (4+16+24+28+60+48+21)=201.

Total number of pennies thrown on the first throw is given by (50x8)= 400

The percentage of the number of pennies that decayed on the first time [pic]

Average time for three half-lives is given by the average of the number of throws for three for one or zero pennies to be left. It is equal to [pic]

Discussion

The results show that 50.25% of the coins decayed in the first throw. The value obtained is in agreement with our hypothesis that approximately 50% of the coins should decay in the first throw. A trial chosen...

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