The Probability of Tossing a Coin - Lab Report Example

Radioactive decay changes one nucleus to another or new element, this process is called transmutation; hence the main aim of the experiment is to determine radioactive process by determining the probability of tossing a coin a given number of times. The result obtained follows a normal distribution. The percentages of decay represent half-life of the decaying particle. Introduction Aims and Objective of the experiment To study radioactive decay and decay randomness of radioactive decay process by using probability from tossing a coin. Hypothesis Lab 1 1. Tossing coins is a good model for radioactive half-life. 2. Approximately 50% of coins should decay each trial. Lab 2 1. Should be able to see a normal distribution of the number of coins that decay on first throw of the coins. 2. Eight coins should decay most often on the first throw. 3. My prediction of the percentage decayed first throw calculation 53%. Background information Radioactivity is the process where particle or electromagnetic radiation are emitted or released from the nucleus. The particles which are mostly emitted are alpha, beta and gamma including the neutrons and protons and fission of atoms. Radioisotope has an unstable nucleus that does not have enough force or energy to hold the nucleus together Radioactive decay changes one nucleus to another or new element, this process is called transmutation. Nuclear decay process must satisfy several laws, the value of the quantity after decay must be equal to the nucleus before the decay. The probability that nucleus will decay does not depend on the age of the nucleus during a fixed length of time. Radioactive decay is a random process; it is impossible to predict or determine when a particular nucleus will decay. But some methods can be used to measure or calculate the rate of decay, the use of half-life. Half-life is the interval of time required for one-half of the atomic nuclei to decay into other nuclear by emitting the particles. It follows an exponential decay and is constant over the life time of the decaying quantity. Formula for half-life in exponential decay is given by the equation below. N (t) = No e-λt……………………………………………….. (1) No is the initial quantity of the substance that will decay N (t) is the quantity that remains after the decay process. Radioactivity can be modeled by using coins; the number of heads every 20 seconds was half the number of coins. Therefore the number of coins ejected will be half the number of coins remained or left. This matches what happens in real radioactive isotopes. This is only possible through probability. Method lab 1 Experimental procedure All coins were placed in a flat box with all head up. The box was covered and shacked thoroughly. The coins that were tails up were removed and the number recorded in the data table. That represented the number of atoms that have decay during one half-life. The accumulated number of coins decayed was calculated and recorded in the data table. The number of coins remaining in the box was recorded in the table. The process for steps 2 and 5 were repeated until all coins were removed from the box. Graph for lab 1 A graph was plotted the number of decayed coins (the accumulated number of tails up coins removed) for each trial against time. On the same graph, the number of coins that did not decay was plotted for each trial. Here the number will decrease from the maximum to 0. Method lab 2 Experimental procedure All the 16 coins were placed in the box. The box was covered and mixed thoroughly. The coins that were tails up were counted and removed on the first throw. This was recorded in the data table. The throwing was continued until two or less coin was left and the number of throws that was required to have two or less coins left was recorded in the table. The process was repeated 50 times. Graph lab 2 A bar graph of the number of coins that decayed was drawn on the first throw showing the number of trials. A bar graph was also drawn of the number of throws needed to get 2 or less coins left showing the number of trials. Data collected and results Trial (200) Number Decayed Accumulated Number Decayed Coins number left 1 91 91 109 2 49 140 60 3 28 168 32 4 16 184 16 5 10 194 6 6 4 198 2 7 0 198 2 8 1 199 1 9 0 199 1 10 1 200 0 Percentage decay 49/91*100 =53.85% Figure 1: A line graph of coins number left Figure 2: line graph of accumulated number decayed Data collected for lab 2 Number decayed first thrown Frequency ( y) 0 0 1 0 2 0 3 3 4 1 5 3 6 4 7 3 8 11 9 14 10 5 11 2 12 2 13 2 14 0 15 0 16 0 Number of throws to get 2 or less Frequency 1 0 2 10 3 21 4 15 5 3 6 1 50 Figure 3: bar graph of number decayed first thrown Figure 4: bar graph of number of throws to get 2 or less Discussion In lab one the result obtained are the one expected since approximately 50% of coins decayed for each trial. The graph of the number left is decreasing after every each trial. This shows that it has a negative gradient. As the graph ends it tries to have a straight horizontal line which makes it different from the starting of the graph. The graph of accumulated coins decayed is the reverse of graph of decay left since it has a positive gradient. (wilson and David) The result obtained in the lab 2 were the one expected since the graph shows a normal distribution as expected, and it also takes 6 throws to get 2 or less coins left. When a graph of number of decayed first is drawn the peak occurs at 14. (Rutherford and Earnest) In this lab report the probability of determining that an atom will decay is impossible but using the percentage from tossing a coin shows when the next decay can take place. Percentage is found to be 50% in every trial. This randomness can only be determined using the half- life equation following an exponential distribution. (Wroblewski and Andrej) There were some sources of errors that affected the result leading to incorrect data for example. Inaccurate counting of the number of heads decayed, different people shaking the box leading to confusion. Works Cited Rutherford and Earnest. Radioactive subtance and their radiation. Cambridge: Cambridge university press, 1913. wilson and David. Nuclear constitution of atoms. New York: MIT press, 1983. Wroblewski and Andrej. Prehistory of nuclear physics. Acta physica polonica, 2002. Appendix How to determine probability using coins 2H from 4 coins 4Cr2 = 6 2^4 = 16 Prob = 6/16 = 0.375 4H from 8 coins 8Cr4 = 70 2^8 = 256 Prob = 70/256 = 0.273 8H from 16 coins 16Cr8=12870 2^16 = 65536 Prob = 12870/65536 = 0.196 16Cr0=1 16Cr1=16 .. 16Cr15=16 16Cr16=1 Read More