Early in the last century, Robert Millikan developed

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1 Millikan s Oil-Drop Experiment: A Centennial Setup Revisited in the Virtual World Michel Gagnon, Université de Saint-Boniface, Winnipeg, MB Canada Early in the last century, Robert Millikan developed a precise method of determining the electric charge carried by oil droplets. 1-3 Using a microscope and a small incandescent lamp, he observed the fall of charged droplets under the influence of an electric field inside a small observation chamber. In so doing, Millikan demonstrated the existence of a fundamental unit of electric charge, and established its quantization. Now renowned as one of the most famous experiments of 20th-century physics, Millikan s oil-drop experiment has been reproduced with more or less success in most, if not all, high school and university physics classes. This has encouraged many improvements of the apparatus, now making this experiment much more accurate and easier to realize for advanced students. However, the required apparatus remains rather expensive, and for introductory college or high school students the experiment is still quite difficult to conduct. As an alternative to the traditional setup, a realistic computer-based simulator to replicate the Millikan oil-drop experiment has been developed. Using this software, students are able to undertake a complete experiment, obtain an accurate set of results, and thus gain a better understanding of the original experiment and its historical importance. Historical and beautiful, yet tedious and delicate The heart of the instrument consists of the chamber with a parallel pair of horizontal metal plates with a separation of 4 mm. By applying a potential difference to the two plates, a uniform electric field is created in the space between. Originally, a fine mist of oil droplets with very low vapor pressure was sprayed into the chamber. Today, the droplets are often replaced by tiny plastic beads. As they are sprayed, the beads acquire electric charges through friction with the nozzle; changing the voltage across the plates can make them rise or fall. A microscope and a small lamp allow observation of what is happening inside the chamber, as well as the graduation engraved on the reticle. Basically, to conduct the experiment, one has to spot a bead at the center of the viewing area and evaluate its velocity using a stopwatch and the graduation on the reticle. Of course, this process has to be repeated many times. Alternatively, one can try to immobilize a bead by varying the voltage to the terminals of the plates; however, in reality, this is close to impossible to achieve. Using variations of the original setup, generations of students have spent hours of observation and tricky fine-tuning to achieve final results that may have up to a 20% margin of error. 4 Difficulties associated with the experiment have led many laboratory instructors to attempt to render the oil-drop experiment more student friendly 4-6 or simply to replace it with something more accessible. 7 Moreover, recent innovations to available apparatus on the market have considerably decreased the inherent difficulties of the experiment. These successes have to be celebrated as the original setup has now evolved into an excellent training tool for advanced students. Indeed, they should now be ready to pay more attention to the details and be more careful when dealing with an experiment precise enough to measure a quantity as small as the fundamental unit of electric charge. Unfortunately, despite its beauty and historical importance, this delicate experiment remains costly and difficult to conduct at the introductory level. To overcome these problems, other instructors have developed computer-based simulations to mimic the Millikan apparatus. 8 However, these appear to be either more appropriate for a class demonstration, or almost as difficult to use as the real setup. Therefore, our software has been developed in order to greatly attenuate the many difficulties (fine-tuning, reading, etc.) associated with this particular experiment. This allows students to concentrate more on the scientific concepts than the difficulties associated with data acquisition. Of course, students using the software still have to perform measurements of times, distances, or voltages, giving rise to an uncertainty of about 1-2 % with no need to introduce an arbitrary uncertainty using the random number generator. Two methods of conducting the experiment Prior to discussing how to conduct the experiment using the software, it is useful to review its theoretical background. 9 There exist some variations of Millikan s original experiment using oil droplets; however, whatever the available apparatus, modeling the experiment requires the following four forces to be acting on free-falling particles in an electric field: 1. the weight of droplets: where r and r stand for radius and density; 2. the up-thrust due to the weight of air displaced by the droplet:, with r a as the density of the air; 3. the drag force described by Stokes law: F d = 6phrv, where h is the viscosity of the air and v the terminal velocity of the falling droplet; and 4. the electric force: F E = qe, where q is the charge on the droplet and E the electric field. 98 The Physics Teacher Vol. 50, February 2012 DOI: /

2 With this equation, it is possible to determine the radius of the droplet if one knows the viscosity of the air. The terminal velocity of the droplet is easily calculated using a stopwatch and the lines on the reticle. This is the usual path to follow when using actual oil-droplets, and it must be repeated in order for each droplet to be included in the data set. Of course, with modern apparatus, which uses plastic beads of known radius, this step became unnecessary. However, for pedagogical purposes, one can assume the viscosity of the air as being unknown; this can be easily calculated as: (2) Fig. 1. The main window of the Millikan oil-drop experiment software shows the observation area in black surrounded by the Millikan apparatus on the left, the power supply on the bottom, and virtual tools on the right. Next, the electric field is turned on. This introduces the fourth force, F E, which is proportional to the electric charge we want to discover. If the field force is upward, and sufficient to make the bead rise, then the drag force shifts downward, and the Newton law can be written: r e (3) where v e is the terminal velocity in the presence of the field, and has to be calculated. Using the expression found above for h, we get: g with the electric field given as E = V d where V is the potential difference across the apparatus chamber. The velocity v g has to be calculated only once. However, the velocity v e of the charged bead when the electric field is turned on has to be calculated for each individual bead in order to acquire an adequate data set. (4) Fig. 2. The heart of the software is the Millikan apparatus with its observation chamber, microscope, sprayer, lamp, and bubble-level. b) The Second Method An alternative approach is to adjust the electric field until the droplet remains steady. In that case, the null velocity disappears from the equations and with it the viscosity of the air. Consequently, there is no need to calculate r, h, nor v g, and thus we find: (5) Fig. 3. The power supply has two sliders for adjusting the voltage and a switch to reverse the polarity. a) The First Method In the absence of an electric field, the droplet will rapidly reach a constant velocity v g. When this is achieved, the total force acting on it must be zero, which means the three acting forces cancel out. This implies: (1) This steady state is very difficult to reach in practice with the real apparatus. However, using the magnifier to zoom in on a bead while it is rising, the simulator makes it possible to fine-tune the process and to achieve the determination of the stopping potential. This provides an alternate, simplified method to calculate the electric charge. The software As mentioned earlier, the software has been developed to alleviate the practical experimental difficulties, and to overcome the cost barrier of the equipment. The Physics Teacher Vol. 50, February

3 Table I. Raising velocities of beads under the influence of an electric field and the corresponding computed electric charge they carried. Data have been reorganized in ascending values of the electric charges. Prior to these measurements, the falling velocity of beads in the absence of electric field has been measured as m/s, and after this the voltage has been set to 40 V for the remaining experiment. Table I. First Method Velocity (10-4 m/s) Charge (10-19 C) Table II. Voltages used to immobilize beads and the corresponding electric charge carried by the beads. Data are reorganized in ascending values of the electric charges. Table II. Second Method Voltage (V) Charge (10-19 C) Fig. 4. The central part of the screen replicates what can be seen in the microscope. Tools are available to accurately measure the flight time and the distance traveled , The main screen of the software is divided into six sections (Fig. 1). The left one (in brown, Fig. 2) is meant to reproduce the apparatus itself, with the observation chamber (in green) surrounded by a droplet sprayer, a variable collimated lamp, and a small microscope with a slider to control the magnification (up to 32 ). The lamp and bubble level must be set correctly to enable spraying and zooming. By clicking on the sprayer, a single droplet with random speed and random electric charge is injected into the chamber. An option can be used to keep these parameters unchanged for subsequent droplets to be injected for as long as it is necessary for the student to complete the measurements. The power supply (in blue, Fig. 3) is on the bottom right. Apart from the main switch, there is a lever to allow reversing the polarity, and two sliders for coarse- and fine-tuning of the voltage. The central part of the screen is the observation area (black, Fig. 4) which reproduces what can be seen through Fig. 5. Data can be entered on a grid and saved in a file. the microscope. On the right side of the screen, a ruler (in millimeters) measures the distance covered by the droplet. Of course, zooming with the magnification ring resets the graduation accordingly. However, to make the required measurements (time and distance), it is better to use the provided tools: the chronometer (in gray) and the measuring tape (in yellow), on the right side of the screen. The measurements must be taken at constant speed. Therefore, one simply actuates the chronometer when the droplet s path is vertical, and stops it before the droplet reaches the bottom (or the top) of the observation area. This way, one obtains a mark on both ends of the path and may calculate the corresponding flight time. After that, it is sufficient to use the measuring tape. One click on both ending marks gives the distance traveled and makes it possible to compute the droplet s velocity. The grid s control center (Fig. 5) is below the stopwatch. The first button (grid) makes the grid appear or disappear over the observation area. The second button (pencil) is there to enter the voltage, the distance, and the duration of the last observed droplets on the grid. The last button (eraser) is used to erase the grid content. The buttons beside the grid allow for the erasing of single lines of data. 100 The Physics Teacher Vol. 50, February 2012

4 To conduct a complete experiment using the first method, students must follow these steps: 1. Prepare the apparatus (level, align the reticle, open the lamp). 2. Spray a bead. 3. Determine its velocity v g in the absence of an electric field using the virtual tools. 4. Turn on the virtual power supply and set to 40 V to actuate the electric field. 5. Spray beads until they get a rising one. If necessary, reverse the polarity. 6. Determine the velocity v e of the selected bead. 7. Repeat steps 5 and 6 until they have sufficient data. 8. Using the appropriate equation, compute the corresponding set of charges. 9. Organize the charges in ascending order of the computed electric charge. 10. Trace a graph. The second method does not require the calculation of velocities. Instead, students must adjust the voltage until the charged bead remains steady. The necessary steps are as follow: 1. Prepare the apparatus (level, align the reticle, open the lamp). 2. Spray a bead. 3. Adjust the voltage to stop the bead. 4. Zoom in using the magnifying slider to check if the bead is really immobile. 5. If not, repeat steps 3 and 4. The magnifying powers are 1, 2, 4, 8, 16, and Repeat steps 2 to 5 until they have sufficient data. 7. Using the appropriate equation, compute the corresponding set of charges. 8. Organize the charges in ascending order of the computed electric charge. 9. Trace a graph. Table I shows an example of a small set of data obtained with the first method: data have been arranged in ascending order of the computed electric charge using Eq. (4). The matching raising velocities v e are given in the first column and the falling velocity v g in the absence of an electric field has been computed to be m/s. On the corresponding chart (Fig. 6), one can clearly see that the electric charges carried by beads can be organized to exhibit a stair pattern with regular step height, or integer multiples of this height. Table II shows another set of data now obtained with the second method. This time, students have to determine the voltage to apply in order to stop the falling beads. Once again, data have been arranged in ascending order of the computed electric charge [Eq. (5)] and reported on a stair pattern chart (Fig. 7). Fig. 6. Data set obtained with the first method, organized in ascending order and showing a stair pattern. Fig. 7. Data set obtained with the second method and organized in ascending order. It still exhibits a stair pattern and moreover the lower value equates the fundamental unit of electric charge. If we analyze both sets of data, we find comparable uncertainties of less than 2% and 1%, respectively. The first method has the benefit of being closer to the real experiment. However, if we want to be able to make measurements with beads carrying only one unit of charge, we need a voltage of 120 V to get an electric force strong enough to raise beads. Unfortunately, such a voltage makes beads with more than three units of charge too fast to be measured. On the other hand, comparing Figs. 6 and 7, we realize that the second method is more suitable to observe a wider spectrum of carried charges. In particular, in the second example, the smallest value is equal to the step height and can be interpreted as the smallest indivisible electric charge. Moreover, we believe it may be of interest to students to realize that the same result can be obtained with two different kinds of data: time and distance for the first method and voltage for the second one. Conclusion By using a computer simulation to replicate circuit laboratory in a large-scale introductory physics course, we have demonstrated 10 that the use of computers appears to enhance learning for science students. After using the Millikan apparatus simulator in our introductory laboratories for two years, we too have noticed a significant improvement in students ability to deal with the Millikan experiment and related physical concepts. In particular, students obtain more accurate results, which, in turn, make analysis easier and more enlighten- The Physics Teacher Vol. 50, February

5 ing. Based upon our experience, this appears to be an effective way to make physics more accessible to all students, increase their interest, and improve their learning. A Windows compatible (98 and later) copy of the software (in English and French) is available as a free download at cusb/physique/nos_simulateurs-maison/telechargement/ or upon request from the author. Acknowledgments I would like to express my appreciation to my colleagues, Petra Franzen and Bryan Rivers, for having kindly helped me to improve the quality of this text. References 1. R. A. Millikan, The isolation of an ion, a precision measurement of its charge, and the correction of Stokes s law, Phys. Rev. (Series 1) 32, (April 1911). 2. R. A. Millikan, On the elementary electric charge and the Avogadro constant, Phys. Rev. (Series II) 2, (Aug. 1913). 3. A. Franklin, Millikan s oil-drop experiments, The Chem. Educ. 2 (1), 1 14 (1997). 4. Anthony Papirio, Jr., Claude M. Penchina, and Hajime Sakai, Novel approach to the oil-drop experiment, Phys. Teach. 38, (Jan. 2000). 5. Steve Brehmer, Millikan without the eyestrain, Phys. Teach. 29, 310 (May 1991). 6. Ray C. Jones, The Millikan oil-drop experiment: Making it worthwhile, Am. J. Phys. 63, (Nov. 1995). 7. Lowell I. McCann and Earl D. Blodgett, The nut-drop experiment Bringing Millikan s challenge to introductory students, Phys. Teach. 47, (Sept. 2009). 8. Dan MacIsaac, Websites for teaching high school and introductory college modern physics topics, Phys. Teach. 45, 124 (Feb. 2007). 9. R. A. Millikan, The Electron: Its Isolation and Measurement and the Determination of Some of its Properties (University of Chicago Press, 1917). 10. N. D. Finkelstein et al., When learning about the real world is better done virtually: A study of substituting computer simulations for laboratory equipment, Phys. Rev. ST - Phys. Educ. Res. 1, (2005). Physics teachers... get your students registered for the preliminary exam in the U.S. Physics Team selection process. All physics students are encouraged to participate in the American Association of Physics Teachers Fnet=ma Contest! The Fnet=ma Contest is the United States Physics Team selection process that leads to participation in the 43rd Annual International Physics Olympiad (IPhO) in Tallinn/Tartu, Estonia, July 15-24, The U.S. Physics Team Program provides a oncein-a-lifetime opportunity for students to enhance their physics knowledge as well as their creativity, leadership, and commitment to a goal. For program information and registration visit: (Registration is open now through January 3, 2012) Michel Gagnon joined the Université de Saint-Boniface in 1996, where he is an associate professor of physics. He received a PhD in theoretical highenergy physics in 1994 from Université Laval in Quebec City, following this with postdoctoral research and a science teaching certificate. His current interests include the design and development of computer simulations of scientific experiments, as well as the history of single lens reflex photography through its technical evolution. MiGagnon@ustboniface.mb.ca American Astronomical Society 102 The Physics Teacher Vol. 50, February 2012