The Radioactivity - Coursework Example

Radioactivity Lab Report by s s Table of Contents 1 3 2Introduction 3 3Hypotheses 43.1Lab 1 4 3.2Lab 2 4 4Method 4 4.1Apparatus 4 4.2Procedure 4 4.2.1Lab 1 4 4.2.2Lab 2 5 5Results 5 5.1Lab 1 5 5.1.1Figure 1: Graph of accumulated coins against the trial numbers 6 5.1.2Figure 2: Graph of the coins against the trial numbers 6 5.2Lab 2 6 5.2.1Figure 3: Graph of frequency against t he number decayed after first throw 6 5.2.2Figure 4: Graph of frequency against the number of throws to get 2 or less coins 7 6Discussion 7 7Conclusion 8 8Appendix 8 8.1Lab 1 8 8.1.1Table 1: Shows data for trials of 200 coins 9 8.2Lab 2 9 8.2.1Table 2: Shows the number of decays after the first throw 9 8.2.2Table 3: Shows data for the number of throws required to remain with 2 or less coins 11 8.2.3Table 4: Shows the frequency distribution of the number of throws required to get 2 or less coins 11 Radioactivity Lab Report 1 Abstract The objective of this experiment was to investigate the radioactive decay by using coins to simulate decaying nuclei by tossing a coin, which would decay when it came up tails. It also studied the radioactive decay process for small numbers and large numbers of coins, which gave more accurate results. In Lab1, 200 coins were tossed once. In Lab 2, 16 coins were used and tossed 50 times. 2 Introduction Unstable nuclei of atoms emit particles as a result of the instability of the nuclear. These particles are referred to as radioactivity. It results due to the lack of enough binding energy to hold the nucleus together when either the protons or neutrons are in excess numbers (Radioactivity n.d.). Radioactivity occurs in three types namely Alpha decay, Beta decay and Gamma radiation. In Alpha decay, the particle is composed of two neutrons and two protons and is thus identical to the helium nucleus. A particle will escape from the nucleus due to quantum mechanical processes and then repelled further by electromagnetism since both the nucleus and the alpha particle are positively charged. Beta decay occurs in two forms, the Beta positive and Beta negative decay. In Beta negative decay, one neutron nucleus is transformed into an electron, a proton, and an antineutrino. Beta positive decay process is similar but the proton changes into a positron, a neutron, and a neutrino. Gamma decay occurs after either alpha or beta decay (Radioactivity n.d.). This is because after either of the two decays, the nucleus is left excited and with excess energy. It will, therefore, loose this excess energy by emitting a gamma ray just as an electron moves to a lower energy state by emitting a photon between the ultraviolet and the infrared range. Radioactive decay is random or probabilistic and is thus determined by quantum mechanics (Radioactivity n.d.). It is, therefore, difficult to predict when an atom will decay, but predictions can be made based on the behavior of large numbers of atoms or coins in this case. Tossing a coin is also random since the probability of getting a head or tail is a half, and therefore using coins gives results relative to the radioactive decay process. It is also not possible to conduct a real radioactive experiment due to the health effects to humans after exposure to these radiations. The radiations kill body cells depending on the amount and time of exposure. Half-life, therefore, refers to the average time that half of the original matter takes to decay. After two half-lives, half of the material decays to become a quarter of the original. 3 Hypotheses 3.1 Lab 1 This lab modeled the decay process with 200 coins since the experiment was random and large numbers would help in getting more accurate results. At least 50% of the coins tossed should decay after each trial. 3.2 Lab 2 It modeled the process using 16 coins, which were then tossed 16 times. When 16 coins are tossed for 50 times, (216 = 65536 x 50) possible outcomes can be obtained. 4 Method 4.1 Apparatus 200 coins were used for conducting lab 1 and 16 coins for lab 2. 4.2 Procedure 4.2.1 Lab 1 All coins were placed in a flat covered box so that all the heads were up The box was then covered and shaken thoroughly All the coins that were now tails up were removed and the number recorded a data table. The number represented the atoms that had decayed after one half-life. The accumulated number of decayed coins was then calculated and recorded The number of coins remaining in the box was then recorded. The procedure was then repeated by covering the box and shaking thoroughly until all the coins were removed from the box and recorded. 4.2.2 Lab 2 16 coins were thrown and those with tails up counted and removed. This data was then recorded. The remaining coins were then thrown until 2 coins were left. The number of throws required to remain with 2 coins was also recorded. The procedure was repeated 50 times 5 Results 5.1 Lab 1 5.1.1 Figure 1: Graph of accumulated coins against the trial numbers 5.1.2 Figure 2: Graph of the coins against the trial numbers 5.2 Lab 2 5.2.1 Figure 3: Graph of frequency against t he number decayed after first throw 5.2.2 Figure 4: Graph of frequency against the number of throws to get 2 or less coins 6 Discussion The results show that six trials were conducted in order to remain with zero coins. Also approximately half of the coins decayed after each throw. The hypothesis that 50% of the coins would decay was also correct. The coins left after each throw decayed by more than half in their half-life. This shows that the coins experiment is a good representation of radioactive decay. The experiment produced more accurate results since large number of coins were used. The curve of the coins left against the trial numbers is similar to the radioactive decay curve and is also almost an inverse of the curve of accumulated coins against the trail numbers. Lab 2 was conducted to show that when a number of coins are tossed, it is not possible that half of that number will be tails or heads. This is because it is not the case for radioactive decay. The results show that half of the coins did not decay after the first throw. Therefore, to estimate the probability of half the coins thrown to decay, a calculation is used. The probability of 8 coins decaying after 16 coins are thrown is calculated using the equation 16Cr8. 16Cr8=12870, this is then divided by the number of possible outcomes, which is 216 = 65536. Therefore the probability getting 8 tails is . The peaks of the graphs are at almost the half the number of the coins decayed after first throw and at half the number of throws to get 2 coins. The experiment would have been tedious if it was continued until 0 coins were left instead of two. This is because the experiment is repeated 50 times. Lab 2 results do not give accurate results as Lab 1 because few numbers of coins was used. The experiments had few errors since they relied on probability to obtain the results. 7 Conclusion Tossing coins is a good model for radioactive decay since approximately half of the coins decayed after each throw. It, therefore, represents the half-life decay. Using large number of coins increases the probability of achieving accurate results. This is due to the randomness of the experiment. The larger the number of coins used, the better the experiment represents the radioactive decay process. The experiment was conducted fairly with the maximum amount of accuracy possible. The errors available cannot be eliminated since they were not affected by human or systematic errors, but can be reduced by using more coins. A better radioactive experiment would involve using weak radioactive sources and a radiation tube interfaced with a numerical machine to study the process as a function of time. 8 Appendix 8.1 Lab 1 Trial number Number decayed Accumulated number decayed Number left 0 0 0 200 1 98 98 102 2 58 156 44 3 30 186 14 4 7 193 7 5 5 198 2 6 2 200 0 8.1.1 Table 1: Shows data for trials of 200 coins 8.2 Lab 2 NUMBER DECAYED FIRST THROW FREQUENCY 0 0 1 0 2 0 3 0 4 2 5 4 6 8 7 12 8 13 9 5 10 3 11 2 12 1 13 0 14 0 15 0 16 0 total number 50 8.2.1 Table 2: Shows the number of decays after the first throw Trial number Number decayed first throw Number of throw to get to get 2 or less 1 10 2 2 10 3 3 7 2 4 9 2 5 8 4 6 6 2 7 7 3 8 7 5 9 7 2 10 11 2 11 12 2 12 8 3 13 6 3 14 7 3 15 5 3 16 8 3 17 8 4 18 6 4 19 8 3 20 7 4 21 10 3 22 11 2 23 9 3 24 8 5 25 7 4 26 7 2 27 8 3 28 5 2 29 4 2 30 6 3 31 8 4 32 8 3 33 8 5 34 8 3 35 9 5 36 7 4 37 6 2 38 8 2 39 9 2 40 6 3 41 5 3 42 7 3 43 4 2 44 8 2 45 6 2 46 9 2 47 7 5 48 5 2 49 6 3 50 7 3 373 148 373/800=0.46625 148/50=2.96 46.63% 8.2.2 Table 3: Shows data for the number of throws required to remain with 2 or less coins Number of throw to get to get 2 or less FREQUENCY 1 0 2 19 3 19 4 7 5 5 total number 50 8.2.3 Table 4: Shows the frequency distribution of the number of throws required to get 2 or less coins References Radioactivity. 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