Kittitorn KiatpipattanakunPhysics HL Period 6 How far is safe? Following Japan’s tsunami, crisis broke out at Japan’s Fukushima Daiichi nuclear powerplant. The gamma radiation contaminated the areas around the plant, making it uninhabitable foranother several decades. Several authoritative sources ordered evacuations at certain distances tothe reactor, but the question is, how far is safe? In this research, the relationship between theradiation intensity and its distance to the receiver will be investigated. For safety concerns, insteadof using a gamma ray emitter, a beta emitter will be substituted. Before going into the theory, the way in which the radiation is detected must first beunderstood. The Geiger counter, named after the Geiger-Marsden experiment or commonly knownas the gold foil experiment, is a type of particle detector that is use nowadays to measure radiation,resulting from particle ionization. The Geiger-Muller tube is what measures this, as seen in figure 1.The tube is prominently filled with neon and other mixture of halogen gasses. In the middle of thesurrounding negative electrode tube is an anode positive electrode wire. When radiation passesthrough the chamber and ionizes the gas, it generates a pulse of current turning it into the beepingsound. Figure 1: The left is a diagram of a Geiger-Muller tube, courtesy of Wikipedia. The blue circles inside the negative cathode tube are the gases, like neon. The charged ions and electron from ionized gas molecules causes the electric pulse. The causes of the ionizing radiation come from a radioactive material. This investigation usesStrontium-90 which undergoes β− decay since it is unstable. The neutron is converted into anelectron, a proton, and an ignored particle called an antineutrino. The decay energy in MeV ofStrontium is the Ionizing radiation–meaning the adequate energy to remove an electron from anatom–enters the mica window and ionizes the gas. An opening Figure 1.5: The left is a diagram of a Vernier Geiger counter. The X-ray diagram LCD shows where the Geiger- Mica window Muller tube is located, and stresses that there is an opening. Geiger-Muller tube
Kittitorn KiatpipattanakunPhysics HL Period 6 From several trusted sources, the relationship between the radiation intensity and distancewould have an inverse squared relationship showed in equation 1. The derivation to form thisequation can be found here. Equation 1Where is the radiation intensity in counts per minute, and is the distance between the plasticcover of the beta material and the Geiger counter in centimeter. To show a linear relationship, theequation 2 below is derived. √ Equation 2Thus, from equation 2, the square root of the radiation intensity is expected to increase linearly tothe inverse of distance.Works cited:http://imagine.gsfc.nasa.gov/YBA/M31-velocity/1overR2-more.htmlhttp://www.lndinc.com/products/711/http://www.scientrific.com.au/product.php?p=4015http://www.nytimes.com/interactive/2011/03/16/world/asia/japan-nuclear-evaculation-zone.htmlhttp://www.vernier.com/products/sensors/drm-btd/
Kittitorn KiatpipattanakunPhysics HL Period 6Design: Research Question: How does the distance between the Geiger counter and the radioactivematerial affects the intensity of the radiation. Variables: The independent variable is the distance between the Geiger counter’s sensor and the betamaterial source emitter, the sufficiency of this measurement will further be explained after theprocedure writing. The dependent variable is the counts per unit time received by the Geigercounter, which is the intensity of the radiation. The controlled variable is the type of beta source,which is Strontium-90, its position is also controlled by not moving it at all in the investigation. Thesame type of Geiger counter was used throughout, a Vernier Digital Radiation Monitor, with itssettings unchanged at CPM and audio on. The angle of the sensor to the beta source wasunchanged, only the distance to it was changed. The experiment was carried at the same place inthe corner of the room without moving anywhere else, so the background radiation was controlledto be at about 4 ± 1 counts per 10 seconds or 24± 6 counts per minute (cpm), from table 1. Thetemperature was controlled by turning on the air conditioner at 27± C without turning it off,however, temperature would not be such an important factor that would affect the radiation. Procedure: A safe area where few people pass by is firstly found. A metal support stand with severalextension clamps is use to hold the Geiger counter. The counter’s sensor is face downward and theLCD screen facing towards the experimenter. A ruler is attached to the metal stand, where at 0 cm,the top end tip of the clamp screw is at 0 cm mark, and when the Geiger counter touches the betaemitter. All of this can be seen in figure 2 down below. The Geiger counter is connected to thecomputer, and to the Vernier™ Logger Pro program. Then a lead apron shield is setup between theexperimenter and the beta source so it reasonably protects the emitting radiation as seen in figure 3below. A beta source, in this case, Strontium-90 is place directly perpendicular to the mica window,where the beta particle enters the Geiger-Muller tube, as seen in figure 2. When ready, the radiationcounts were collected for a period of 180 seconds, at 10 seconds per one sample. This would giveout 18 samples, or can be said, 18 trials. Then for each 60 seconds, the graph is analyze withstatistics, the whole graph is also analyze with statistic to see the mean radiation counts per 10second. This is repeated for several times for each distance away, the distances in this investigationrange from 0.0 ± 0.1 cm to 27.0 ± 0.1 cm.
Kittitorn KiatpipattanakunPhysics HL Period 6 Figure 2: The left photo shows the setup of the Geiger counter perpendicular to the beta emitter. The beta material is directly below a circular opening in the Geiger counter, where the beta particle will enter through this opening and into the Geiger-Muller tube where it would detect the beta, alpha, or gamma radiation. The tape as seen in the photo was purposely taped after 19 cm where this would be the highest distance from collecting the beta material’s radiation counts. Wire connecting to computer Tape at 19 cm Figure 3: The above photo is the setup for lead shielding, hanged by twoThe position of the extension clamps from a meter stick.detector’s opening The distance was about 25 ± 1 cm awaycalled the alpha between the lead shield and the betawindow, or the emitter.mica window
Kittitorn KiatpipattanakunPhysics HL Period 6Data Collecting and Processing:Beta material: Strontium-90 0.1 µC beta sourceInstrument: Vernier Radiation Digital Monitor; LND 712 halogen-quenched GM tubedDiameter of beta material’s plastic cover: 2.0 ± 0.1 cm Table of raw data and its average Seconds 0-60 61-121 121-180Measured Average countsDistance ± Raw Radiation Counts for each time interval per 10 second 0.1 cm 0.0 742 716 750 736 ± 20 1.0 280 288 285 285 ± 4 2.0 139 144 143 142 ± 3 3.0 77 76 77 77 ± 1 4.0 51 55 48 51 ± 4 5.0 42 41 35 39 ± 7 6.0 29 28 26 28 ± 2 7.0 22 20 19 20 ± 2 9.0 13 16 15 15 ± 2 11.0 9 8 11 9±2 13.0 9 8 10 9±1 15.0 8 7 8 8±1 17.0 7 6 6 6±1 19.0 5 5 6 6±1 27.0 4 4 3 4±1Table 1: This table shows the selected raw data collected. The selected data are from taking the radiation countfor every 20 seconds, instead of 10.Since the mean would be the same nevertheless. The raw radiation count isthe number of counts per 10 seconds. The distance is between the plastic cover of the beta material and theplastic surrounding of the Geiger counter, which leaves some distances to the mica window where the betaparticle enters. The last distance (27.0±0.1cm) is the background radiation. Sample calculations will be shown.Graph 1: This is a sample raw data graph at 1.0±0.1 cm distances apart, where the statistic is analyzed.
Kittitorn KiatpipattanakunPhysics HL Period 6 Table of actual distance and the average CPM Measured distance (± 0.1 cm) Real Distance (± 0.5 cm) Average counts per minute (CPM) 0.0 1.5 4400 ± 100 1.0 2.5 1680 ± 20 2.0 3.5 840 ± 20 3.0 4.5 438 ± 6 4.0 5.5 280 ± 20 5.0 6.5 210 ± 40 6.0 7.5 140 ± 10 7.0 8.5 100 ± 10 9.0 10.5 70 ± 10 11.0 12.5 30 ± 10 13.0 14.5 30 ± 6 15.0 16.5 24 ± 6 17.0 18.5 12 ± 6 19.0 20.5 12 ± 6Table 2: This table shows the actual distance between the approximated position of the beta material insidethe plastic cover, and the approximated distance inside the Geiger-Muller tube to where the gas actuallyionizes to create an electrical pulse. This will be extensively explained and discuss later in the evaluationsection. The second column is the actual average counts per minute, where it is subtracted by the backgroundradiation of 24 counts per minute. Sample calculations will be shown after graph 4.Graph 2: This graph shows the inverse square relationship between the average counts per minute and the realdistance between the Geiger counter and the beta material. The constant ‘A’ is about 9900 ± 80.
Kittitorn KiatpipattanakunPhysics HL Period 6 Table of the square root CPM and its inverse actual distance Measured distance (± 0.1 Square root Average CPM 1 / real distance (± 0.01 cm) cm) (CPM) 0.0 0.67 66.2 ± 0.8 1.0 0.40 41.0 ± 0.3 2.0 0.29 29.0 ± 0.3 3.0 0.22 20.9 ± 0.1 4.0 0.18 16.8 ± 0.7 5.0 0.15 15.0 ± 1.0 6.0 0.13 12.0 ± 0.5 7.0 0.12 9.8 ± 0.6 9.0 0.10 8.1 ± 0.7 11.0 0.08 6.0 ± 1.0 13.0 0.07 5.5 ± 0.6 15.0 0.06 4.9 ± 0.6 17.0 0.05 3.5 ± 0.9 19.0 0.05 3.5 ± 0.9Table 3: This graph shows the square root of the counts per minute to the inverse actual distance, mainly toshow a linearly relationship. The uncertainty for the square root of CPM is individually calculated. A samplecalculation will be shown after graph 4.Graph 3: This graph shows the data from table 3, where the highest square root counts per minute is the 0distance between the Geiger counter and the beta material. The slope is 103 and the y-intercept is -1.77.However, it is invalid when the inverse of a distance of 0 is calculated, and the square root of counts per minutecannot be less than 0 to a negative number.
Kittitorn KiatpipattanakunPhysics HL Period 6Graph 4: This graph shows the high-low fit of graph 3. The sample calculation will be shown below.Sample Calculations 1. Determining uncertainty for average counts per 10 second for 0.0±0.1 cm distance a. Highest: 750; Lowest: 716 b. (750 – 716)/2 = 17 = rounded to 20, Thus, 736 ± 20 counts per 10 seconds 2. Real distance (explain in evaluation section) a. Approximated distance of actual beta material (Strontium-90) to the plastic cover’s skin: 0.2 cm b. Approximated distance of the actual ionized gas position in the Geiger-Muller tube to the opening of the tube 1.3 cm c. Total distance apart = 1.3 + 0.2 = 1.5 cm d. Real distance at 0 cm = 0 + 1.5 = 1.5 cm 3. Average counts per minute a. Average counts per 10 seconds: 736 ± 20 b. Average counts per minute to significant figures = (736 ± 20) * 6 = 4400 ± 100 4. Square root of average CPM for distance of 0.0 ± 0.1 cm a. √ b. Uncertainty: (√ -√ )/2 = 0.75 = 0.8 c. Square root average CPM = cm 5. Uncertainty for inverse real distance at measured distance 5.0 ± 0.1 cm a. Real distance: 6.5 ± 0.5 cm b. Uncertainty: ( )/2 = 0.011 = 0.01 c. Inverse real distance = 1/6.5 = 0.15 ± 0.01 cm 6. Uncertainty for slope and y-intercept from graph 4 a. Slope & intercept from graph 3 respectively: 103 , -1.77 b. Slope: (109.1 – 95.0) / 2 = 14 = ± 10 c. y-intercept: (1.6 + 4.1) / 2 = 2.9 = ± 3
Kittitorn KiatpipattanakunPhysics HL Period 6Conclusion: From graph 2, it is clear that the results have support the hypothesis, in which it turned outto be an inverse square relationship. But to model this investigation’s results to be a linearrelationship, the final equation is found, with respect to significant figures: √ Equation 3Where is the radiation intensity without the background radiation in counts per minute, and isthe distance apart from the beta source to the detector’s opening. Equation 3 is a linear equationwhere when the higher the distances apart, the square root radiation intensity decreases. The level of confidence in this investigation is medium. The qualities of the data as seen ingraph 2, the average CPM’s error bar is relatively acceptable, and the real distance error’s bar is 0.5cm. The real distance is hard to determine because the exact position to where the beta materialreally is inside the plastic cover is not stated, we must assume it ourselves. Also, the exact point inthe Geiger-Muller tube, where the radiation ionizes, is very hard to determine. Since the tube isabout three centimeters, the reaction can occur anywhere. It is assumed that most of the radiationentering the tube starts reacting in the first half section. Further explanation of this will be discuss inthe evaluation. The validity of this relationship shown in equation 1 can be applicable universally.Any type of radiation whether it’s REMS or the sun’s intensity can be used with equation 1.However, equation 3 will only be applicable to this investigation only, since the distance will alsodepend on the materials and instruments given. The setting experiment of this research may alsolimit the equation 3. Nevertheless, further research must be done to confirm this relationship.Evaluation: One of the main causes of error in this experiment is determining the actual distance. Theactual distance between the beta material and the plastic cover skin is unknown, but it isapproximated to be 2 mm since the height of the plastic is 5 mm and the beta material assume tohave 1 mm thickness. Distance between beta material and skin of the plastic cover Beta material Figure 4.1: Sr-90 sample as beta sourceThe other approximated value is where the radiation actually ionizes the gas in the Geiger-Mullertube to generate an electrical pulse. So it is assumed that most of the reaction would occur about 1cm inside from the mica window. Approximated distance where most reaction occur (about 1 centimeter) Figure 4.2: LND 712 Neon filled Geiger-Muller tubeFrom all of these approximations, the data may be distorted from actual values. Some ways toresolve this issue is to directly contact the material supplier and ask for specific dimension. For the
Kittitorn KiatpipattanakunPhysics HL Period 6Geiger-Muller tube, a shorter and more precise instrument may be implemented if possible to findone. The second cause of error may have come from the Geiger counter itself, which can be seenin graph 1, the raw data. The standard deviation is up to 16 counts per 10 seconds. Even though theVernier Geiger counter is rated 1000 counts per minute for Cesium 137 laboratory standard,different detectors should be considered to confirm the validity. The last source of error that may affect the distance is the clamp. During the data collection,the extension clamp might slip by about a millimeter. Since the arm is protected with a fabric liketexture. Moreover, the extension arms might bend a tiny bit due to the weight of the Geigercounter. To fix this, a pulley mechanism should be considered, or using some kind of heightadjustment bar that have a height lock. In any method, the counter should have a fixed positionwhere it will not slip.