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Geun Ho Lee IB Physics HL Period 1 September 23, 2011 Mr. Eales Optical Activity Dependence on Temperature of a Sucrose SolutionIntroductionElectromagnetic waves are series of transverse waves oscillating at various axes. When these wavesare made so that they oscillate in one axis only, the wave is said to be polarized. The tool that allowsus to polarize the electromagnetic waves is called polarizer.In the spectrum of electromagnetic waves,different types of waves are named and arrangedaccording to their wavelength. For instance,visible light refers to electromagnetic wavesbetween 400 and 700 nanometers. And thesedifferent types of waves can have varyingeffects on living organisms. For gamma rays, ithas been proven that they exert enough power toalter living organisms’ DNA thereby likely tocause abnormal mutations. However, adequateamounts of visible light rays are essential formost living organisms to survive. For plants, Figure 1: This figure illustrates how optical activitysunlight is their main fuel to produce food is measured. In this diagram, d represents the lengththrough the process known as photosynthesis. of the immersed light path, c represents concentration, and represents the angle rotated byTo maximize the efficiency in photosynthesis, the optically active material.some proteins in some plant rotate the plane of (Principle of Physics. Kinetic Books. Chapter 34polarization of the light ray. The molecules Section 22)which do so are known as optically activemolecules. However, proteins are not the only optically active molecules. Table sugar, also known assucrose, is also optically active. And in this investigation, table sugar is used as the optically activematerial.It has experimentally been found that optical rotation or activity is dependent on the substance beingused. Each optically active material has a specific value called specific rotation. The specific rotationof a pure material is an intrinsic property of that material at a given wavelength and temperature.(http://en.wikipedia.org/wiki/Specific_rotation) This means that as temperature changes, the specificrotation will change. In this research, the relationship between temperature and optical activity ofsucrose will be investigated.The equation used to find the specific rotation of sugar is the following: T 3 (degrees cm ), Equation 1 0 l c g dmwhere represents observed angle from the vertical axis, l represents distance of immersed light path,c represents concentration of sucrose, and a0 represents specific rotation of sucrose.The optical rotation is also dependent on how much of the substance the light ray goes through.Concentration of the material and the length of the immersed light path go into consideration incounting this amount of substance the light went through. For this particular research, in measuring
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the concentration of the table sugar, mass of the sucrose per volume of water was computed. For theimmersed light path, the distance between one wall of a clear aquarium which the light was beingshined through and the other opposite wall was measured. Figure 1 is a clear diagram of this.(Principle of Physics. Kinetic Books. Chapter 34 Section 22)Then, an equation for calculating the rotation of light (optical rotation) can be found: T (l )(c)( 0 ) 100 l (m) c(kg T 3 3 ) (degrees cm ) m 0 g dm 100 l (m) c(kg T 2 3 ) (degrees m ) m 0 kg 100 l c T 0 (degrees) , Equation 2 100where represents optical rotation and other variables are carried through Equation 1.Thus, it is predicted that the optical rotation of sucrose will depend on the temperature of the solution,as Equation 2 presents. Indeed, it is not expected to show a proportional relationship becausetemperature is not directly correlated with the optical activity, but still is indirectly related. Design Research Question What is the relationship between the temperature and the optical rotation of 20% sucrose solution? Variables The independent variable was the temperature of sucrose solution and the dependent variable was the optical rotation of the solution. There were also several controlled factors that were kept constant Figure 2: This diagram is a simplified version of throughout the experiment. Only one light source the setup for this investigation. The grey cylinder (laser) and aquarium was used as changing the is the laser used in this investigation. The two wavelength of the light source or changing the black squares are two polarizers. The one closer aquarium, thereby changing the immersed light to the laser is called polarizer and the one behind path, would affect optical rotation of sucrose the aquarium is called the analyzer. The blue cuboid is the aquarium used in this investigation. solution. Also, the concentration of the sucrose The green rectangle is screen to enhance the solution was always kept at 20% to eliminate any experimenter’s vision of the laser beam. The red chance in changing the optical rotation of the line illustrates the path the laser light traveled. solution other than by varying temperatures. The method in measuring observed angles wascontrolled to minimize any inconsistency in the collection of data. By turning off the air conditioners,the temperature of the lab was controlled to minimize the difference in heat transfer with theenvironment when the solution was at high or low temperatures.As seen in Figure 2 on the left, the apparatus of this investigation was set up in such way. However, to
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increase precision in data, the laser and the polarizer was clamped onto a table. The analyzer wastaped onto a circular piece of paper to aid rotation, then clamped down onto the same table (SeeFigure 3 for clarification). θ Hypotenuse Base Figure 3: This picture is an image of how the Figure 4: This diagram represents the imaginary analyzer was fixed to its place. Notice that the dark triangle that was drawn to measure the observed angle line was drawn on the paper to indicate the during the experiment. The black circle represents the direction of the polarizing plane of the light that circular paper and the grey square represents the goes through the analyzer. The ruler shown is also analyzer. By a ruler, the values of hypotenuse and base clamped into place. This ruler acts as a base for was measured. Then, arccosine was used to compute which the trigonometry was applied to find the the angle θ. To clarify, the hypotenuse and base are observed angle. measurements from the center of circular paper to the end of the imaginary triangle.The method used to collect data in this experiment was by manually shining the laser beam throughthe polarizer, through the 20% sucrose solution in an aquarium, then through the analyzer which wasrotated until the laser beam has totally disappeared on the screen. Then, the experimenter used a rulerto measure the hypotenuse and base of an imaginary triangle formed as described in Figure 4. Theweaknesses of this data collection method will be discussed in the Evaluation section of this report.Data Collection and ProcessingData Table: Controlled Factors Wavelength of the laser ±nm Concentration of sucrose solution g 0.25 cm 3 Dimensions of aquarium Length: 10.5±0.3cm (Square base aquarium) Width: 10.5±0.3cm Height: 27.3±0.3cmTable 1: This table presents controlled factors in this experiment. The uncertainty of the concentration of sucrosesolution was omitted because it is negligible. Notice that the immersed light path is the same as length ofaquarium.
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Temperature vs. Hypotenuse and Base Trials Temperature of 20% (±0.3cm) sucrose solution 1 2 3 (±0.3℃) Hypotenuse Base Hypotenuse Base Hypotenuse Base 9.0 6.2 2.5 5.8 2.5 6.6 2.5 11.5 7.1 2.5 7.0 2.5 6.7 2.5 14.0 8.5 2.5 8.2 2.5 7.9 2.5 25.0 8.0 2.5 8.3 2.5 8.4 2.5 44.0 8.2 2.5 8.1 2.5 8.0 2.5 51.0 8.6 2.5 8.5 2.5 8.3 2.5 63.0 9.5 2.5 8.9 2.5 8.9 2.5Table 2: Imported from Excel spread sheet. This table shows measured values of hypotenuse and base of theimaginary triangle from Figure 4 for each trial at different temperatures. The uncertainty is instrumentaluncertainty. Temperature vs. Average Observed Angle Temperature of 20% sucrose solution Trials Average (±0.3℃) (±2 degrees) Observed 1 2 3 Angle (±2 degrees) 9.0 66 64 68 66 11.5 69 69 68 69 14.0 73 72 72 72 25.0 72 72 73 72 44.0 72 72 72 72 51.0 73 73 72 73 63.0 75 74 74 74Table 3: Imported from Excel spread sheet. This table shows observed angles at different temperatures. Theuncertainty was taken as half the range of 9.0°C. Notice that this angle is the observed angle, α in Equation 1.
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Temperature vs. Specific Rotation Temperature of 20% sucrose solution Average Observed Specific Rotation (±0.3℃) Angle 2 (±2 degrees cm g ) (±2 degrees) 9.0 66 25 11.5 69 26 14.0 72 27 25.0 72 27 44.0 72 27 51.0 73 28 63.0 74 28Table 4: Imported from Excel spread sheet. This table shows average observed angles and specific rotation ofsucrose solution at different temperatures. The uncertainty for specific rotation was taken as half the range in63.0°C. Temperature vs. Optical Rotation Temperature of 20% sucrose solution Specific Rotation Optical Rotation (±0.3℃) 2 (±0.06 degrees) (±2 degrees cm g ) 9.0 25 0.66 11.5 26 0.69 14.0 27 0.72 25.0 27 0.72 44.0 27 0.72 51.0 28 0.73 63.0 28 0.74Table 5: Imported from Excel spread sheet. This table shows specific rotation and optical rotation of sucrosesolution at different temperatures. The uncertainty for optical rotation was taken as half the range in 63.0°C.
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Data Processing:Figure 5: This is the graph of the raw data collected. This graph shows correlation between average observedangles and temperature. From the slope of the linear fit, it can be deduced that observed angle does change asthe temperature changes.Figure 6: This graph shows correlation between specific rotations and temperature. From the slope of the linearfit, it can be deduced that specific rotation does change as the temperature changes.
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Figure 7: This graph shows correlation between optical rotations and temperature. From the slope of the linearfit, it can be deduced that optical rotation does change as the temperature changes. It can be seen that linear is amuch better fit than a proportional just from the arrangement of the data points. However, it is difficult todecipher which relationship will fit this set of data the best.Sample calculation for Observed Angle using 9.0°C first trial data:Hypotenuse: 6.2 0.3cmBase: 2.5 0.3cm 2.5Actual Value of Observed Angle: cos 1 ( ) 66.2200 6.2 2.5 0.3cmMaximum Observed Angle: cos 1 ( ) 67.6073 6.2 0.3cm 2.5 0.3cmMinimum Observed Angle: cos 1 ( ) 64.7715 6.2 0.3cm 67.6073 64.7715Half range: 1.4179 1 2Observed Angle: 66 1Sample calculation for Specific Rotation using 63.0°C second trial data:Observed Angle: 74 2Immersed light path: 10.5 0.3cm gConcentration of sucrose solution: 0.25 cm 3
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66 2Actual Specific Rotation: 25.1429 cm g (0.25 g 3 )(10.5cm) cm (66 1) 2Maximum Specific Rotation: 26.2745 cm g (0.25 g 3 )(10.5 0.3)cm cm (66 1) 2Minimum Specific Rotation: 24.0741 cm g (0.25 g )(10.5 0.3)cm cm3 (26.2745 24.0741) cm2 2 2Half range: 1.1002 cm 1 cm 2 g g g 2Specific Rotation: 25 1 cm gSample calculation for Optical Rotation using 44.0°C third trial data: 2Specific rotation: 27 2 cm gImmersed light path: 10.5 0.3cmConcentration of sucrose solution: 0.25 g cm 3 (0.25 g 2 )(10.5cm)(27 cm ) 3 cm gActual Optical Rotation: 0.70875 100 (0.25 g 2 )(10.5 0.3cm)(27 1 cm ) 3 cm gMaximum Optical Rotation: 0.75600 100 (0.25 g 3 )(10.5 0.3cm)(27 1 cm ) 2 cm gMinimum Optical Rotation: 0.66300 100 (0.75600 0.66300)Half range: 0.0465 0.05 2Optical Rotation: 0.71 0.05ConclusionAccording to the results, this research has shown that the varying temperature has effects on theoptical activity or rotation of 20% sucrose solution. From Equation 2, it can be seen that therelationship between temperature and optical rotation is direct, because temperature is related tospecific rotation of any optically active materials. Thus, at the beginning it was predicted that theresults will not follow a proportional trend. Figure 7 clearly illustrates this, as no two data pointscould possibly lie on one proportional graph. Thus, no conclusive equation can be presented. However,it has been found by this research that as temperature increases, the optical rotation of sucroseincreases as well. This means that when sucrose solution is heated, the direction of polarization ofpolarized light rays will be rotated more going through the sucrose solution.
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Based on the fit on Figure 7, some level of confidence is gained, because the trend follows whatEquation 2 predicted; no proportional correlation between temperature and optical rotation. However,no strong confidence can be gained as not enough of research has been done on this topic to comparethe data with. Also, due to such lack of published knowledge, the actual trend the data should followis undetermined, thus lowering the level of confidence in the results of this investigation.Although no conclusive equation can be stated out of the results of this investigation, the data can stillprovide a useful knowledge with certain restrictions to applicability. First, the results gained onlyapply for sucrose solution of concentration 20% by mass. This is because both specific and opticalrotation are closely related to the concentration of the solution. Also, the results are only applicable totubing of 10.5±0.3cm. This tubing will act as the aquarium in this investigation and as defined inEquation 1 and 2, immersed light path is also a significant factor in determining optical rotation ofsucrose.The following document is a published document on the similar topic:http://www.standardbase.hu/tech/SITechPolar.pdfHowever, the results of this published document is based on 1 g 3 concentrated sucrose solution. cmThus, it cannot provide any reference point to the results of this document, as the concentration ofsucrose solution used in this one is 0.25 g 3. cmEven with these restrictions in applicability, the results of this investigation proves that 20% sucrosesolution will change its optical rotation as temperature changes. This knowledge can be applied inelectronics, especially in the areas of using screens. With the results from this investigation, it hasbeen concluded that 20% sucrose solution is not a good substitute for liquid crystals in our LCDscreens.EvaluationOne main source of error during the course of investigation was in the method of measuring observedangle. As described in Design section of this report, the method used to measure angle was usingtrigonometry. However, by using ruler and computing the angle measure using arccosine, quite a bitof accuracy of the measure was lost. This lost accuracy will certainly be improved if polarimeter wasused to measure the optical rotation in one step. This is because by going through four calculations toget to optical rotation, a lot of accuracy would have been lost, but polarimeter is a very accurateinstrument to measure specifically optical rotation of different materials.Also, the integrity of the data is questionable, because at lower temperatures, condensation occurredon the glass aquarium. This occurrence of condensation hampered the vision of the experimenter, thusleading to possible errors in detecting the true angles at which the light ray was totally blocked by theanalyzer. Although the experimenter had wiped the condensation off the walls of the aquarium, anerror could have occurred anywhere in that process. To improve on this problem, the experimentershould be testing in moister-free lab or a lab at low temperatures, close to what the solution is.Lastly, heat loss was another factor in error. Because the solution was not at all insulated, heat transferwith the environment occurred constantly at high and low temperatures. To minimize this effect, theenvironment’s temperature could be changed to the temperature of the solution or insulators can beput around the aquarium, only leaving small aperture for light ray to go through.
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