Millikan Oil Drop Introduction Towards the end of the 19th century a clear picture of the atom was only beginning to emerge. An important aspect of this developing picture was the microscopic nature of electric charge. In 1897 J. J. Thomson demonstrated interactions of cathode rays with electrical charge. Thomson proposed that these rays were composed of small particles (now known as electrons), much lighter than atoms. He was ultimately able to determine the charge to mass ratio of the the particles in the cathode rays. In 1909 Robert Millikan devised an ingenious experiment to determine the electronic charge. The basic layout is illustrated in figure 1. He observed tiny oil drops (created in a fine mist using a device much like a perfume sprayer) with small amounts of excess charge as they fell and rose in a controllable uniform electric field. Using rise and fall times, as well as some basic mechanics, he was able to determine the amount of excess charge on numerous drops. The measured charges were always integer multiples of a particular value which we now refer to as the electronic charge, e. Oil Drop Physics Figure 1: Millikan's Apparatus The vertical motion of the oil drops follows from Newton's Laws and three basic forces: the weight of the drop, the air resistance due to the motion of the drop and the electrical force on the drop. The drops are observed moving under two conditions: falling (when the electric field is turned off) and rising (when the electric field of appropriate strength and direction are turned on). The equation of motion is given by F y =m a y =q E y m g k v y where the parameters are identified in the following table: m mass a y acceleration q charge E y electric field g acceleration of gravity k friction coefficient velocity v y F G = F E =qe y F f = kv y mg Figure 2: Free Body Diagram for Oil Drop
Whether falling (under the influence of gravity and friction alone) or rising (under the influence of gravity, friction and a non-zero electric field), the drops quickly reach their terminal velocity. At terminal velocity, the acceleration of the drops is zero. The equation of motion can then used to relate the physical parameters to the falling terminal speed v f and rising terminal speed v r so that: k v f =m g and k v r =q E m g. The friction coefficient is determined from Stokes's Law: k=6 a where a is the radius of the oil drop and η is the viscosity of air. The mass of the drop is related to its size by: m= 4 3 a3 where ρ is the density of the drop. The Electric field is determined from the voltage V applied to the conducting plates above and below the observation region and the separation d between the plates: E= V d. The rising and falling terminal speeds are determined by directly observing the motion of the oil drops through a microscope. The falling terminal speed then allows a determination of the radius of a particular drop: a= 9 v 1 f 2 g With the rising terminal speed, charge of a drop can be determined: 2. q= k v r m g E which can be rewritten as q=6 9 v 1 f 2 v 2g r v f V / d.
Procedure For this exercise, students will use video analysis of simulation videos to determine the charges on a number of oil drops. Each clip will contain a number of drops in motion. The each drop's motion should be analyzed using two separate tracks: one track for the falling motion (with the voltage off) and one for the rising motion (voltage on). Each data file is labeled md####.avi where the #### represents a number (from 1 to 6 digits). For each data file there is a text file with the same digits in its filename. The text file contains ancillary physical data (in MKS units) necessary to complete the analysis of that video. For example, video file md1702.avi has an associate text file millikan 1702ssng.txt which contains the following: rho: 886.000000 eta: 18.240000E-6 g: 9.805000 d: 0.010000 V: 200.000000 tape measure tool marked drop tracks player slider The video analysis program Tracker will be used for this lab. Start Tracker then Video:Import and select the video clip to be analyzed. Use the tick marks to set the length scale for each video. The major tick marks are 0.500 mm apart. Select Tracks:tape measure to make sure the tape measure tool is visible, drag the ends of the tool until the tool is vertical and the length goes from the top to the bottom major tick marks. Double click on the tools length indicator to set it at.005 (using MKS units).
Play the clip from beginning to end. Depending upon the particular clip, not all drops will rise after the voltage is turned on. Those oil drops which do not rise may not be suitable for this exercise. Choose an oil drop to track, use the player slider to set the clip at its beginning, and select Track:New:Point Mass. Shift click with the cursor carefully aligned with the drops location to mark its position in that frame. Use the player slider to pick the last frame before the voltage turns on, and mark the drops location in this frame. If the drop falls briefly out of view, choose the last slide the drop is visible before the voltage turns on. Another 4 to 6 frames between these two need to be marked to get an accurate estimate of the drop's falling terminal speed. Select Window:Right View to open the data window. The default graph is x versus t, so click on the vertical scale label and choose y to produce a y versus t graph. Right click on the graph and select Analyze... to open the dataset tool window.
In the Dataset Tool window, select the Fits check box. The default curve fit is linear, which is what is need for this exercise. The magnitude of the a parameter is the falling terminal velocity; record this value. A new track is needed to determine the rising terminal velocity, but the process basically is the same. Select Track:Mass A and uncheck visible to hide the falling track. Select Track:New:Point Mass. and use the player slider to pick the first frame after the voltage turns on, and mark the drop's location in this frame. Use the player slider to determine the last frame that the rising drop is visible (this may be the very last frame) and mark the oil drop's location on this frame. Again, 4 to 6 additional markings will be needed between these two frames. Get the y versus t plot of the new track, and use the Dataset Tool to obtain the rising terminal speed. Note that if you chose a drop that actually keeps falling after the voltage is turned on (not recommended) you should record the rising terminal speed as a negative number. A spreadsheet (millikan.xls) has been set up to facilitate the data analysis. Common parameters are the plate separation d, the viscosity of air η, the drop density ρ and the local acceleration of gravity g. Make sure the correct values for your video clips are specified. For each drop, the voltage (which will be common for all drops in a given clip), the falling terminal speed and the rising terminal speed are needed in the appropriate spots on in the spreadsheet. The calculation of the drop's radius and net
charge are already set up (you need to show complete sample calculations for your report). After at least three clips have been analyzed and the charge measurements have been determined, copy the column of charge values (q) into a separate sheet of the spreadsheet, using the past special > values option. Sort the column to see if there is any pattern to the magnitudes of the charges. You should be able to discern the minimum charge magnitude or the minimum step of in the value clusters, corresponding to the electronic charge. Use this estimated value of the electronic charge to determine the integer multiple n of e for each charge value, and make an additional column of the ration q/n for each charge. Each value of this ratio provides a measurement of e. A sample table of the values obtained from a single clip is shown below for illustration. Note that this table only contains one clip's worth of observations, so your data table will be much more extensive. charge q multiple e 1.62559E-19 smallest, e? 1 1.62559E-19 1.62659E-19 1 1.62659E-19 4.88817E-19 about 3x smallest 3 1.62939E-19 9.69274E-19 about 6x smallest 6 1.61546E-19 9.75801E-19 6 1.62633E-19 1.14142E-18 about 7x smallest 7 1.6306E-19 1.46199E-18 about 9xsmallest 9 1.62444E-19 1.79033E-18 about 11 times smallest 11 1.62757E-19 1.79938E-18 11 1.6358E-19 avg e 1.62686E-19 Anomalous Data: As a separate exercise, each group will be assigned to analyze one of the mdfc####.avi files, determine the values of the charges in their assigned clips and post those values to the class discussion board. As a result, each individual will analyze and report on all the anomalous data. Is charge quantized in the anomalous data? Is there any potential explanation for this data from accepted physics? Credits: Figure 1 drawn by Theresa Knott, and obtained from http://en.wikipedia.org/wiki/millikan_oil_drop_experiment Tracker is open source software from Doug Brown http://www.cabrillo.edu/~dbrown/tracker/