Investigation #8 INTRODUCTION TO QUANTUM PHENONEMA

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1 Name: Investigation #8 Partner(s): INTRODUCTION TO QUANTUM PHENONEMA Near the end of the 19 th century, many practitioners of what was then known as natural philosophy (now called physics ) believed that the widespread success of Newtonian mechanics and Maxwell s theory of electromagnetism essentially completed our understanding of the operation and interactions of the physical world in terms of particles and waves. (O, human arrogance do you know no bounds?) While there were a few discoveries at the end of 19 th century, many scientists believed they would soon be explained in terms of the two well understood theories of the day. These included: the discovery of x-rays by Wilhelm K. Roentgen in 1895 the discovery of nuclear radioactivity by Alexandre-Edmond Becquerel in 1896 the discovery of the electron by Joseph J. Thompson in At that time, there were also some well-known phenomena whose explanation in terms of Newton and Maxwell remained a mystery. These included: the spectral distribution of wavelengths from hot glowing objects (first measured by Josef Stefan in 1879) the ejection of electrons from a metal surface by ultraviolet light (discovered on accident by Heinrich Hertz in 1887). Attempts to explain these observations in terms of the classical theories of Newton and Maxwell were either inadequate or led to predictions that contradicted experimental results. What appeared to be minor cracks in the foundation of physics, eventually led to the quantum revolution which completely altered our perception of nature. The purpose of this investigation and the next is to observe some of the phenomena that essentially led to the quantum revolution. First, you will examine the spectral distribution of wavelengths of a blackbody emitter and determine the relationship between absolute temperature and wavelength for such an emitter. Next, you will observe and measure the quantization of energy levels by bombarding gas atoms with electrons. In particular, you will determine the excitation energies of mercury and neon. Part I: Blackbody Radiation Spectrum One of the unsolved mysteries at the end of the 19 th century was the spectral distribution of wavelengths of blackbody radiation. A blackbody is the name given to describe a perfect absorber one that absorbs 100% of the radiation incident upon it. In the latter half of the 19 th century, Gustav Kirchoff was able to show that the most efficient absorbers of electromagnetic waves were also the most efficient radiators of this energy as well. Thus, a blackbody absorber would also be a perfect emitter. The startling 1

2 discovery made by Stefan in 1879 was that the total intensity (over all wavelengths) radiated from the interior of such a body depends only on temperature and is independent of the material. In other words, the spectral distribution for a blackbody emitter at a given temperature is the same regardless of the material. This implies that the emission of blackbody radiation must be a fundamental phenomenon. A blackbody (or a good approximation to one) can be constructed by making a small hole in a material that leads to a cavity with rough walls in the interior. Light that enters the hole has little chance of escaping. It is 100% absorbed. When the material is heated, the material begins to radiate until thermal equilibrium is achieved. This occurs when the rate of absorption equals the rate of emission. The radiation that does escape the hole can then be measured and analyzed. Early attempts to explain the observed spectrum met with failure. Ludwig Boltzmann tried to use a thermodynamic approach in terms of Carnot cycles. Wilhelm Wien built upon this and derived an expression that worked well at short wavelength, but failed at long wavelengths. At the turn of the century, Lord Rayleigh assumed the source of the radiation was the electric charges in the material. Behaving like little harmonic oscillators, a given temperature would set allow the oscillators to set up standing waves of radiation. Combining this with the equipartition theorem, Rayleigh and J. Jeans found an expression that worked well at very long wavelengths, but led to more severe discrepancies as the wavelengths got shorter. As l 0, the expression predicts infinite energy within the cavity. This result became known as the ultraviolet catastrophe. In 1900, Max Planck eventually solved the problem. He found the solution by pure mathematical reasoning. Contrary to the known laws of classical physics, Planck found that by assuming the energy of a harmonic oscillator could only take on integer multiples of the fundamental frequency of the oscillator he could bridge the gap between the Wien expression and the Rayleigh-Jean expression and remove the ultraviolet catastrophe. While Planck s results fit the data perfectly at all wavelengths, it is said that even he did not want to accept the implications of his own expression. Further background information for this section is provided in the computer file that you will use to acquire your data. Be sure to read the Introduction & Theory sections of the file when instructed in the procedure. Your group will need the following materials/equipment for this part: 1 blackbody apparatus containing the tungsten lamp, collimating slits, focusing lenses, dispersing prism, rotary sensor, and light sensor) 1 computer with PASCO Capstone TM software installed 1 PASCO Capstone TM laboratory interface and appropriate cabling 2

3 Procedure 1. Open the file Blackbody Radiation, which can be found in the PASCO Experiments alias on the computer desktop. 2. After the file has loaded, take the time to read the Introduction and Theory sections by clicking on the respective tabs. Note: Do not close any tabs. Otherwise you risk losing all of your data including the calibration run. 3. You can skip the Setup A and Setup B tabs, as the apparatus has already been configured for you. 4. Click on the Procedure tab. In general, you will follow the instructions provided under the Procedure tab. However, there will be a few changes: Start with Step 3 on the Procedure tab, as the sensors have already been configured for you. Continue through Step 8. You can skip Steps 9-13 as the calibration run has already been made for you. Continue at Step 14, however, instead of 4.0 V, 7.0 V and 10.0 V, you will collect data for nominal voltage values of 3.0 V, 6.0 V, and 9.0 V. Record the true filament voltages in Table 1 on the next page. 5. After completing the three runs, click on the Graph1 tab and select all three runs to display under the Data Select icon on the graph menu bar. The small peaks on the right side of the graphs correspond to the white light that passes over the prism and enters the light meter. Click on the Coordinate Tool and drag the cursor over the small peak. An arrow should point to the nearest data point. Do this for all three data sets. Note the angles of the small peaks. (These should be near 70. If the peak angle of one of the peaks differs by more that 0.1, it means you did not start with the light meter against the stop. You will have to repeat one or more runs until all of the small peaks occur at the same angle.) 6. Show your instructor your graphs on the compute. Upon instructor approval, print a copy of the graph for each member in your group. Checkpoint: Consult with your instructor before proceeding. Instructor s OK: Questions: Qualitatively, what change do you observe in the magnitude of the relative intensity of the spectra as the voltage across the filament is increased? Questions: Qualitatively, what change do you observe for the location of the peak of the spectra as the voltage across the filament is increased? 3

4 7. Locate the Coordinate Tool icon and determine the wavelength of where the maximum relative intensity occurs for each of the three runs. Complete Table 1-1 below. Nominal Voltage V nom (V) Table 1-1 Actual Filament Voltage V true (V) Wavelength of Maximum Intensity max (nm) 8. To find the temperature of the glowing lamp filament, click on the Appendix 2 tab. Using the true voltage across the lamp filament and taking the room temperature filament resistance to be 0.93, use equations A6 and A7 and calculate corresponding filament resistivity and temperature for your three trials. Complete Table 1-2. Nominal Voltage V nom (V) Actual Filament Voltage V true (V) Table 1-2 Tungsten Resitivity (x10-8. m) Filament Temperature (K) Question: Are your results consistent with higher voltages producing higher temperatures? Explain any discrepancies. Question: Are your results consistent with higher temperatures producing higher intensities? Explain any discrepancies. 4

5 Although Wien did not derive the correct expression for the spectral distribution of blackbody radiation, he did correctly identify a relationship between the wavelength of maximum intensity and the absolute temperature. This expression known as Wien s displacement law is given by max T = (constant). In the homework, you will use the wavelengths of maximum light intensity that occurred in your measurements and the corresponding temperatures that you determined for the lamp filament to calculate the Wien constant for each of your three datasets. Question: Does your data for the three filament temperatures appear to qualitatively follow this relationship? If not, what might account for any discrepancies? Checkpoint: Consult with your instructor before proceeding. Instructor s OK: Part II: Franck-Hertz Experiment Early experiments in spectroscopy demonstrated that atoms emitted electromagnetic radiation at discrete wavelengths. This observation is consistent with Planck s assertion that radiation is emitted in integer multiples of a particular frequency. In 1913, Niels Bohr proposed his model of the atom that explained (in one-electron atoms) the observed spectrum by assuming that the bound electrons in atoms can only exist in certain discrete energy states. For his work on this model of the atom, Niels Bohr was awarded the 1922 Nobel Prize for physics. Later experiments demonstrated that atoms in gases also absorb radiation only at discrete wavelengths. In particular, James Franck and Gustav Hertz verified this with mercury atoms in 1914 and were awarded the 1925 Nobel Prize for physics. The general layout for this experiment (depicted in the handout at your station) consists of bombarding gas atoms with electrons whose kinetic energies are adjusted by means of a variable accelerating voltage. As the kinetic energy of the electrons is increased, they will collide elastically with the gas atoms unless the electrons have sufficient energy to excite an atom. If so, they will give up an amount of energy equal to the excitation energy of the atom and therefore not have enough energy to reach the collector anode. The result is a dip in the measured current (and therefore the measured collector voltage). As the accelerating voltage continues to increase an electron that gave up its energy to a gas atom can once again gain sufficient energy to result in another excitation. As this process continues, the measured grid voltage will show peaks and valleys with increasing accelerating voltage. 5

6 By measuring the intervals between successive peaks (or valleys) in the accelerating grid voltage, the excitation energy of the gas atoms can be determined. In particular, you will do this for mercury vapor and for neon gas. Your group will need the following materials/equipment for this part: Mercury Franck Hertz apparatus (tube and heating chamber) Neon Franck-Hertz apparatus (tube) Franck-Hertz control unit High-temperature digital thermometer 2 digital voltmeters and/or 1 oscilloscope with appropriate cabling For computer data acquisition: 1 computer with LoggerPro software installed 1 universal laboratory interface (ULI) box and appropriate 2 shielded BNC cable and several banana leads 2 voltage probes CAUTION! The oven containing the mercury Franck-Hertz tube operates at a temperature around 200 C (~ 400 F). Do not touch the heating chamber! Procedure Because mercury is liquid a room temperature, it needs to be heated in order to produce a vapor of high enough density to observe the energy transitions. A schematic of the mercury tube and heating chamber is shown in the handout located at your station. Also provided is a description of the control unit and its components. If the apparatus is not already set up, start with Step 1 below. Otherwise, jump down to Step Confirm that the connections between the mercury Frank-Hertz tube and the control unit are consistent with Fig. 3 on the handout before energizing the oven or the tube: The anode (terminal A), the cathode (terminal K), cathode heater (terminal H), and the collector grid (terminal M) on the heating chamber are connected to their respective terminals on the control unit using the appropriate cabling. (Note that a shielded BNC cable must be used for the collector grid.) 2. Confirm that the control unit has the UB/10 x-out and F-H signal out connected to Channel 1 and Channel 2 (respectively) of the oscilloscope. 3. Insert the high-temperature digital thermometer through the small hole on the top of the oven and clamp it into place. 4. Set the rheostat to the desired temperature (200 C). Allow about 10 minutes for the oven to warm up. Again, be careful that you do not touch the hot oven! 5. In the meantime, check that all control knobs on the operating unit are turned fully counterclockwise to zero and the Reverse bias toggle is set to zero (in the center position). 6. Turn on the control unit and set the filament voltage to 6.5 V and allow about 90 s for the cathode to warm up. 6

7 7. Set the Man/Ramp switch to Ramp and slowly increase the accelerating voltage to 60 V. Note: The output for accelerating voltage measured at the UB/10 x-out jack is attenuated by a factor of ten. In other words, the values displayed on the oscilloscope are actually 0.1 times the true voltage. 8. Set the oscilloscope to XY mode with 1.00 V/div in each channel. You should observe a slowly rising curve with several peaks and valleys occurring along the horizontal axis. If this is not the case consult your instructor. Question: Observe the trace on the oscilloscope. What do notice about the spacing between consecutive peaks (or consecutive valleys)? To obtain a graph that you can analyze in more quantitatively, you will now replace the oscilloscope with the voltage probes connected to the computer using the universal laboratory interface (ULI). 9. Check that the ULI box is powered, properly connected to the computer and has the 2 voltage probes connected to CHANNEL 1 and CHANNEL Open the LoggerPro TM program on the computer desktop. The program should automatically identify the voltage probes. Once you have successfully opened the proper file, the computer should display, a graph showing both Voltage1 and Voltage2 on the vertical axis and Time on the horizontal axis. 11. Set up the axes so that only Voltage2 is displayed on the vertical and Voltage1 is displayed on the horizontal. (This is done by clicking on each axis label and selecting the desired variable.) 12. After zeroing your voltage probes, connect the voltage probes so that the accelerating voltage is Voltage 1 and the measured grid voltage is Voltage Confirm that the data collection time is set for 30 s. (On the menu bar, click on Experiment, drag down to Data Collection, and set the collection time to 30 s.) 14. On the control unit, dial the accelerating voltage back down to zero and flip the Man/Ramp switch to Man. 15. Start the data collection (click on the green Collect button) and slowly dial the accelerating voltage up to 60 V at a rate of about 2 V/s. 16. Click on the Examine button and measure the values of the accelerating voltage ( Voltage 1 on the horizontal axis) that correspond to the each of the peaks. You may or may not have enough peaks to completely fill the table. Don t forget that the Voltage1 values are actually 1/10 the true accelerating voltage. Be sure to record the true values of the accelerating voltage in Table 2-1 on the next page. 17. Print a copy of the graph for each member in your group. Note: The voltage probes max out at 6 V. This will result in a flat line at higher values. 7

8 Maxima Table 2-1 Accelerating Voltage (V) V between peaks (V) Question: Based on your quantitative data, how do the intervals (V s) between consecutive peaks compare? Calculate an average value. Average V: V Now you will repeat the measurements you just made only this time using neon gas. Furthermore, you will acquire quantitative results directly off the oscilloscope. As before, the apparatus is not already set up, start with Step 17 below. Otherwise, observe the oscilloscope trace and complete Table 2-2 below. Note: As a result of the manufacturing process, every tube is slightly different. This means that the voltage settings in Steps are approximate. It can take some time to find the optimal settings. Due to the time constraints, this has already been done for you. The tube should have a sheet or be labeled with all the proper voltage settings. If only the separate sheet is provided, be sure to verify that the tube number on the sheet is the same as the tube that you are using. If not, consult your instructor. 18. Confirm that the connections between the neon Frank-Hertz tube and the control unit are consistent with Fig. 2 on the station handout before energizing the tube. 19. In the meantime, check that all control knobs on the operating unit are turned fully counterclockwise to zero. 20. Confirm that the control has the UB/10 x-out and F-H signal out connected to Channel 1 and Channel 2 (respectively) of the oscilloscope. 21. Turn on the control unit and increase the filament voltage (U F ) until the filament just starts to glow a faint red (about 7 V). Then allow about 30 s for the cathode to warm up. 22. Set the Man/Ramp switch to Ramp and slowly increase the accelerating voltage to 80 V. 23. Set the grid voltage (U KG ) to 9 V. 8

9 24. Slowly increase the filament voltage until an orange glow appears between the filament and the grid. Then turn down the filament voltage until the glow disappears and only the filament itself is glowing. This should be around 8 V or so. 25. Set the oscilloscope to XY mode with 1.00 V/div in each channel. You should observe a slowly rising curve occurring along the horizontal axis with about three peaks and valleys. If this is not the case consult your instructor. 26. Slowly increase the decelerating voltage (U AE ) until the minima of the curve are nearly horizontal. Complete Table 2-2 below. Maxima Table 2-1 Accelerating Voltage (V) V between peaks (V) Question: Based on your quantitative data, how do the intervals (V s) between consecutive peaks compare? Calculate an average value. Average V: V Checkpoint: Consult with your instructor before proceeding. Instructor s OK: Now, take a step back and review the processes that are taking place in this experiment: A voltage is applied across a filament to create a cloud of electrons. Electrons are literally boiled off from the surface of the filament due to the high thermal agitation in the atoms of the filament. (The Ohmic heating due to the resistance of the filament increases the temperature of the filament to the point where the collisions among neighboring atoms can knock electrons out of the atoms.) This process is called thermionic emission. An accelerating voltage is applied between the filament and an anode grid to sweep away the electrons emitted from the filament. If this is not done, the negative space charge around the filament will inhibit further electrons from being emitted. The 9

10 electrons swept away from the filament accelerate toward the anode grid. If there is a vacuum between the filament and the anode grid, the electrons would acquire a kinetic energy (in ev) equal to the accelerating voltage (in Volts) at the anode grid. Electrons that pass through the anode grid would continue to a collector plate where a current can be measured. A reverse-bias voltage is applied between the anode grid and the collector plate to inhibit electrons from reaching the collector plate. A measureable current is detected only if the reverse-bias voltage is less that the accelerating voltage. With the presence of the gas in the tube, collisions occur between the electrons and the gas atoms. These collisions are elastic unless the electrons gain enough kinetic energy to match the excitation energy of the gas. When this occurs, the electron gives up its kinetic energy to the gas atom. The reverse-bias voltage then repels these electrons away from the collector plate. This results in a drop in the collector current. The purpose of the reverse-bias voltage is to observe this drop. As the accelerating voltage is increased, electrons can give up their gained kinetic energy to the gas atoms over a smaller distance. The increase in the accelerating voltage can allow electrons that would not have reached the collector to now do so. Thus, the collector current rises again. Further increases in the accelerating voltage will allow electrons that give up their kinetic energy to cause an excitation in the gas to acquire enough additional kinetic to cause a second excitation. Continual increase in accelerating voltage will thus show peaks and valleys in the measured collector current. The voltage intervals between successive peaks (or valleys) correspond to the excitation energy of that particular gas atom. The following observation is a rare opportunity to visually confirm that atoms absorb energy in discrete amounts. Be sure to take careful note of it. 1. On the control unit, dial the accelerating voltage back down to zero and flip the Man/Ramp switch to Man. 2. Look inside the tube and slowly increase the accelerating voltage until an orange glow appears near the anode grid. (You may have to use a magnifying lens and/or dim the lights to see this.) This glow is the result of the gas atoms emitting light as the gas atoms give up the excitation energy imparted to them by the accelerated electrons. 3. Very slowly, increase the accelerating voltage and observe the behavior of the orange glow inside the tube. (This is a subtle effect. You will have to observe carefully!) Question: Describe the behavior of the orange glow inside the tube as you increased the accelerating voltage. 10

11 4. Continue to slowly increase the accelerating voltage until a second orange glow appears inside the tube. This should be near where the accelerating voltage produced the second valley measured at the collector. Question: Why does a second glow appear inside the tube? 5. As in Step 3, increase the accelerating voltage very slowly and observe the behavior of the two glowing spots. Question: Why do you suppose the glowing spots behave the way they do? Checkout: Consult with your instructor before exiting the lab. Instructor s OK: 11

12 INTRODUCTION TO QUANTUM PHENOMONA Homework Part I Blackbody Radiation Planck s expression for the intensity of radiation per wavelength is given by I Planck (l,t) = 2pc2 h æ 1 ç l 5 è ( ) -1 e hc lk BT where c is the speed of light, h is Planck s constant, and k B is the Boltzmann constant. 1. Recall that the Rayleigh-Jeans radiation law worked well at long wavelengths, but failed to accurately reproduce the experimental findings at short wavelengths. Show that in the limit of long wavelengths (low energy) Planck s radiation law (shown above) reduces to the Rayleigh-Jeans expression: I Rayleigh-Jeans (l,t) = 2pck BT l 4. (Hint: Express the exponential function in a power series expansion and neglect the quadratic and higher order terms.) ö, ø 2. Wien s radiation law worked well at short wavelengths, but failed to accurately reproduce the experimental findings at long wavelengths. Wien s expression is given by I Wein (l,t) = C 1 l 5 e-c 2 lt, where C 1 and C 2 are constants. Show that in the limit of short wavelengths (high energy) Planck s expression reduces to the Wien expression and determine the values of C 1 and C 2 in terms of the constants given in Planck s expression. 12

13 3. As stated in the lab packet, Wien did not derive the correct expression for the spectral distribution of blackbody radiation. However, he correctly identified the relationship between the wavelength of maximum intensity and the absolute temperature. Recall that this expression (known as Wien s displacement law) is given by max T = (constant). Using the wavelengths of maximum light intensity that occurred in your measurements and the corresponding temperatures that you determined for the lamp filament, calculate the Wien constant for each of your three datasets. Complete Table HW-1 and calculate the average value of the Wien constant according the your data. Compare your result to the accepted value of x 10-3 meter-kelvin. Calculate your percent error. Nominal Voltage V nom (V) Wavelength of Max. Intensity max (nm) Table HW-1 Filament Temperature (K) Average: % Error: Wein constant (m-k) Part II Franck-Hertz Experiment 4. Compare your results for the average energy (in ev) for the transition in that you observed for both the mercury and the neon to the accepted values of 4.9 ev for mercury and 19.8 ev for neon. Calculate your percent error for each gas. 5. The first peak in your data likely did not occur at the transition voltage for mercury. If not, was the first peak at a higher voltage or a lower voltage? What is the magnitude of the difference between your transition voltage and the accelerating voltage at the first peak? What is the significance of this voltage? 13