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IB Internal Assessment Example


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Physics IB Internal Assessment Example

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IB Internal Assessment Example

  1. 1. IB Internal Assessment Writers Per Hour WritersPerHour.COM
  2. 2. Running Head: BROGLIE’S RELATIONS Completed: Verifying the Broglie’s relations Name Institution Completed:
  3. 3. BROGLIE’S RELATIONS Completed: Verifying the Broglie’s relations Personal Statement To any physicist, the name Louis de Broglie is a prominent name because of his input on electron diffraction from crystals. I gained interest in this topic because in classical mechanics, motion is described through the assignment of momenta to point particles. It is described in quantum mechanics that a particle’s motion can also be described by waves using important parameters of two different points of view which are described through the equation by Broglie commonly known as the Broglie equation. The purpose of this paper was to verify the deBroglie’s relations for the dependence of the wavelength of an electron on energy. Research Statement The question to be answered is whether the electron respects the deBroglie’s relations. I will look for a linear relationship once the appropriate graph of Volts-1/2 against D meters is plotted. Background In his thesis in, Louis de Broglie, a French student in 1924 made a proposition that matter and light has dual character and in some circumstances has the behavior of particles and behaves like waves in others (Serway, Moses & Moyer, 2004). In his thesis, he made the suggestion that a particle, for example an electron, with momentum represented by p has a wavelength denoted by λ associated with it where;
  4. 4. BROGLIE’S RELATIONS Completed: " Equation 1 Where h is the Planck’s constant. Equation 1 can be rewritten as; " Equation 2 Where v is the velocity which can be obtained from the following equation; " Equation 3 After working out for v in equation 3 by making v the subject of the formula, the Broglie equation (Equation 1) becomes; " Equation 4 Where m and e represent the properties of the electron, that is, mass and charge respectively. In equation 4, λ = 1.23 V-1/2 nm. For small angles, the condition for diffraction is; " Equation 5 Where the angle denoted by θ can be obtained as follows; " Equation 6 p h =λ mv h =λ 2mv 2 1 eV = emV2 h =λ θ=λ d L2 D =θ
  5. 5. BROGLIE’S RELATIONS Completed: Therefore, from equation 4; " Equation 7 The relationship between momentum and wavelength for matter is the same relationship that is appropriate for light (Eisberg, Resnick & Brown, 1986). The ideas by deBroglie have been verified through the observation of interference patterns which are formed when a bean of 54 eV electrons was reflected from a single crystal of nickel. If the electrons have the behavior of waves, they will diffract into certain angles which are given by the Bragg’s Law. " Equation 8 Where θ represents a grazing angle, d represents the spacing between the Bragg planes and n is an integer, that is, " Graphite has a hexagonal structure with atoms which neighbor each other bonded to each other by a certain spacing. The experiment to test to verify the Broglie’s relations is done using the Electron Diffraction Tube. This tube has a gun which emits a converging electron beam which is narrow. The carbon target is penetrated by the beam which is then diffracted into two rings which correspond to carbon atoms separations of 0.123 and 0.213 nm (Kittel, 2005; Ashcroft & Mermin, 2005). 2/1 V23.1 L2 Dd − = θ=λ sind2n 3,...2,,1n =
  6. 6. BROGLIE’S RELATIONS Completed: Methodology Materials 1. Electron diffraction tube 2. DC power supply 3. High voltage supply 4. Cables Setting up 1. First, the electron diffraction tube sockets are connected to the power supply (This is shown in the diagram below). 2. The anode, G3 is then connected to the high voltage through a protective resistor (10 MΩ). " Diagram 1: The laboratory set up
  7. 7. BROGLIE’S RELATIONS Completed: " Diagram 2: The circuit diagram Procedure 1. First, the voltage of G1 was set to -50 V. This was done by making use of the second knob on the dc supplying power. 2. Secondly, the voltage of G4 was set to 0 V by making use of the third knob. 3. I then slowly increased the high voltage supply until a structure which was ring-like appeared on the fluorescent layer as shown in the diagram below. These rings depending on the intensity of light in the laboratory. When the voltage is increases to 4 kV, the rings start to appear.
  8. 8. BROGLIE’S RELATIONS Completed: " 4. I then measured the radius of the two rings from the graphite target for voltages between 2.5kV and 5kV.`A good way to do this is to place a masking tape across the tube face and mark the center and radii on the tape. Turn off the lights in the room to clearly see the rings. Variables Independent variable: Voltage Dependent variable: The inner and outer radii of the rings Safety 1. During operation, one should not touch the fine beam tube and cables because high voltage is used when conducting the experiment. 2. Due to danger of implosions, mechanical force should not be exerted on the tube.
  9. 9. BROGLIE’S RELATIONS Completed: 3. In the tube, the fluorescent layer can be damaged by the bright spot at the center of the screen. This is avoided by slightly reducing the intensity of light after each reading as soon as possible. Result After carrying out the experiment, I had to measure and write the values and made the raw data table as follows; Table 1: Raw Data I estimated the uncertainty in voltage to be about 0.1 kV. The uncertainties in the inner and outer radii were gotten by obtaining the difference between the maximum radii and the minimum radii and then dividing by 2, that is, For the inner radii; " or ± 0.007 m For the outer radii; V D meters kV Inner Outer 2.5 0.034 0.060 3.0 0.030 0.054 3.5 0.028 0.049 4.0 0.025 0.045 4.5 0.023 0.043 5.0 0.021 0.040 0065.0 2 021.0034.0 D = − =Δ
  10. 10. BROGLIE’S RELATIONS Completed: " or ± 0.01 m The uncertainties seem reasonable. Since the trial was only done once, I processed the data obtain V-1/2. I kept the values to four decimal places. The following table was obtained; Table 2: Processed Data Next, it was important to calculate the uncertainty for Volts-1/2. I did the calculations as follows; " or ± 0.003 Next, I constructed a graph of Volts-1/2 against D meters. Since the uncertainty for Volts-1/2 and D meters are relatively small, I ignore them and hence did not show the error bars on my graph. According to deBroglie’s relations, the graph of Volts-1/2 against D meters should give two straight lines. With the processed data, the graph of Volts-1/2 against D meters was plotted giving the following graph: 01.0 2 040.0060.0 D = − =Δ V V-1/2 D meters kV Volts-1/2 Inner Outer 2.5 0.0200 0.034 0.060 3.0 0.0183 0.030 0.054 3.5 0.0169 0.028 0.049 4.0 0.0158 0.025 0.045 4.5 0.0149 0.023 0.043 5.0 0.0141 0.021 0.040 00295.0 2 0141.00200.0 V = − =Δ
  11. 11. BROGLIE’S RELATIONS Completed: " From the above graph, it is evident that both set of points have a linear upward relationship. My research question said that the once the graph was plotted, there would be a linear relationship which has been proved by the relationship observed on the graph. Conclusion In my conclusion, I related what I obtained to what I was expecting to get. The experiment was to verify the deBroglie’s relations for the dependence of the wavelength of an electron on energy. It was expected that the plot of Volts-1/2 against D meters would give straight lines for the two radii. My graph showed this. Both lines were linear. Therefore, the de Broglie hypothesis was substantiated. The data had relatively high precision because after calculation of the uncertainties, they well small and insignificant. For the two lines of best fit, the lines passed through 4 of the 6 data points. However, systematic errors when taking the measurements could not be ruled out. Evaluation Volts-1/2 vs. D metresVolts-1/2 0.000 0.009 0.018 0.027 0.036 D metres 0.0000 0.0175 0.0350 0.0525 0.0700 Inner Outer
  12. 12. BROGLIE’S RELATIONS Completed: To improve data quality which would lead to the correct trend, I identified the possible weaknesses, their significance and ways to improve in the future. There was a limited range and amount of data. In this experiment, 6 measurements were taken for voltage between 2.5kV and 5kV. This is of high significance because a better line may have been obtained if more data was used. This can be improved by including voltages between 5.5 kV and 10.0 kV which would give a total of 16 data points and a would probably give a more accurate line. Another problem may have been the precision of the rule measuring the inner and outer radii. The uncertainty of the measurements was 0.001m which might have slightly shifted the lines for inner and outer radii. This was however insignificant because an uncertainty of 0.001m is a suggestion that the measurements were highly precise. Therefore, no improvement is needed.
  13. 13. BROGLIE’S RELATIONS Completed: References Ashcroft, N. W., & Mermin, N. D. (2005). Solid State Physics (Holt, Rinehart and Winston, New York, 1976). Google Scholar, 403. Eisberg, R., Resnick, R., & Brown, J. (1986). Quantum physics of atoms, molecules, solids, nuclei, and particles. Physics Today, 39, 110. Kittel, C. (2005). Introduction to solid state physics. Wiley. Serway, R. A., Moses, C. J., & Moyer, C. A. (2004). Modern physics. Cengage Learning.