Millikan Oil Drop Experiment

Transcription

1 [International Campus Lab] Objective Determine the charge of an electron by observing the effect of an electric field on a cloud of charged oil droplets. Theory Reference Young & Freedman, University Physics (14 th ed.), Pearson, Electric Potential Problem (p.807) The droplets can be observed through a viewing scope with illumination by the bright light of a lamp. The scope has reticle marks spaced to 0.1mm, so the velocity of the falling or rising drop can be calculated. In 1909, Robert Millikan conducted the oil drop experiment to determine the charge of an electron. He suspended tiny charged droplets of oil between two metal electrodes by balancing downward gravitational force with upward electric force. The density of the oil was known, so he could determine the droplets masses from their observed radii. Using the known electric field and the value of gravity and mass, he determined the charge on oil droplets in mechanical equilibrium. By repeating the experiment, he confirmed that the charges were all multiples of some fundamental value. He proposed that this value was the charge of a single electron. The figure 1 shows a simplified scheme of Millikan s oil drop experiment. A fine mist of oil droplets is sprayed into the chamber and some droplets enter the space between the plates. The droplets become electrically charged by an ionizing radiation source such as an X-ray. By applying a potential difference across a parallel pair of horizontal metal plates, a uniform electric field is created in the space between them. The electric field can be controlled by changing the voltage across the plates. Fig 1 (a) Simplified scheme of the Millikan oil drop experiment. (b) Forces on a falling drop. (plates not charged) (c) Forces on a rising drop. (plates charged) 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA ( ) Page 1 / 19

2 Figure 1(b) shows the forces acting on a droplet when it is falling in air. The velocity of drop has reached its terminal velocity vv ff in a few milliseconds for the droplets used in this experiment. The frictional force FF fr = kkkk is proportional to the velocity of the drop, where kk is the coefficient of friction between the air and the drop. Since the gravitational force FF gg = mmgg and the frictional force FF fr are equal and opposite, mmgg = kkvv ff (1) Figure 1(c) shows the forces acting on the drop when it is rising under the influence of an electric field. The electric intensity is given by EE = VV dd, where VV is the potential difference across the parallel plates separated by a distance dd. If the charge on the droplet is qq then there is an additional electric force FF e = qqqq on it. If the sign and magnitude of the field are such to make the droplet rise, it will quickly acquire a terminal velocity vv rr and the frictional force FF fr = kkvv rr acts on it. Adding the forces vectorially yields The velocities vv ff and vv rr of the equation (5) can be measured experimentally and only the radius rr of the oil droplet remains unknown. The frictional force FF fr = kkkk in figure 1 actually results from the viscosity between the oil and the air. The viscous force on a small sphere moving through a viscous fluid is given by FF = 6ππππrrrr (6) Equation (6), known as Stokes law, is the frictional force acting on the interface between a fluid and a particle, where ηη is the viscosity, rr is the radius of the spherical object, and vv is the flow velocity relative to the object. (For accurate analysis, Millikan suggested the corrected form of Stokes law with effective viscosity ηη eff = ηη(1 + bb pppp) 1, where bb is a constant and pp is the atmospheric pressure. We will neglect this correction factor here.) Now Equation (6) can be substituted for FF fr = kkvv in equation (1). Substituting equations (4), (6) into equation (1) yields qqqq = qqqq dd = mmgg + kkvv rr (2) 4 3 ππrr3 ρρgg = 6ππππrrvv ff or rr = 9ηηvv ff 2ρρgg (7) In both cases, there is also a small buoyant force exerted by the air on the droplet. Since the density of air is only about 10 3 of that of oil, this force may be neglected. Substituting equation (7) into equation (5) yields Eliminating kk from equations (1) and (2) and solving for qq yields qq = mmggdd VV 1 + vv rr (3) vv ff To eliminate mm from equation (3), we use the expression for the volume of a sphere mm = 4 3 ππrr3 ρρ (4) where rr is the radius of the droplet, and ρρ is the density of the oil. Substituting equation (4) into equation (3) yields qq = 18ππ dd 3 vv ff VV ηη3 2ρρgg 1 + vv rr (8) vv ff qq : Charge carried by the droplet (C) VV : Potential difference across the plates (V) dd : Separation of the plates of the capacitor (m) ρρ : Density of oil (kg m 3 ) gg : Acceleration of gravity (m s 2 ) ηη : Viscosity of air (Pa s = N s m 2 ) (See appendix.) vv ff : Velocity of fall without E-field (m s) vv rr : Velocity of rise without E-field (m s) The most precise value of the charge of an electron is qq = 4ππ 3 ρρrr 3 ggdd VV 1 + vv rr (5) vv ff ee = (40) C. 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA ( ) Page 2 / 19

3 Equipment 1. List Item(s) Qty. Description Millikan Apparatus 1 Measures the elementary electric charge using a classical method of Millikan. Power Supply (Power cord included) 1 Supplies voltage for the capacitor plates. Produces regulated DC power up to 50mA in a voltage range 0 to 500 volts. Power Adapter (for LED lamp) 1 Supplies voltage for the LED lamp. Patch Cords (High Voltage) (with safety shrouded banana plugs) 2 Connect the power supply to the capacitor plates of the Millikan apparatus. Patch Cords (with banana plugs) 2 Connect the multimeter to the thermistor of the Millikan apparatus. Atomizer 1 Sprays oil droplets of density ρρ = 886 kg m 3 Multimeter 1 Measures voltage, current, and resistance. A-shaped Base Support Rod (600mm) 1 2 Provide stable support for experiment set-ups. Vernier Caliper 1 Measures external or internal diameter of an object with a precision to 0.05mm. 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA ( ) Page 3 / 19

4 2. Details (1) Millikan Apparatus (2) Power Supply (4) Vernier Caliper The power supply provides regulated DC power up to 50mA in a voltage range 0 to 500 volts. The Vernier caliper measures external, internal diameter or depth of an object with a precision to 0.05mm. (3) Multimeter The multimeter measures voltage, current, and resistance mm is to the immediate left of the zero on the vernier scale. Hence, the main scale reading is 22 mm. 2 Look closely for and alignment of the scale lines of the main scale and vernier scale. In the figure, the aligned (13 th ) line corresponds to 0.65 mm (= ). 3 The final measurement is given by the sum of the two readings. This gives mm (= ). 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA ( ) Page 4 / 19

5 Setup Setup 1. Equipment Setup (3) Reassemble the chamber. (1) Adjust the height of the platform. Mount the apparatus on two support rods on the A-shaped base with the viewing scope at a height which permits the experimenter to sit erect while observing the drops. (2) Measure the plate separation distance. Disassemble the chamber by lifting the Housing straight up and then removing the upper capacitor plate and spacer plate. Measure the thickness of the spacer (which is equal to the plate separation distance) with vernier calipers. Be sure that you are not including the raised rim of the spacer in your measurement. dd = (m) Caution The flat cut (with black painted hole) of the spacer ring must face the viewing scope. Make sure fit the electric discharge terminal into the groove on the underside of the spacer, and leave no gap between the spacer and capacitor plates. To prevent electric shock, do not touch the plates inside the chamber while the power supply is turned on. Prior to disassembling the chamber, you should be sure to turn off the power supply and rotate the plate charging knob to the Plate Grounded (middle) position. Caution Be careful not to lose any parts of the chamber assembly, especially the droplet hole cover. 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA ( ) Page 5 / 19

6 (4) Turn on the LED lamp. Connect the 12V DC adaptor to the lamp power jack. Adjust the position of the lamp by using two lamp position knobs. (5) Focus the scope and adjust the position of the lamp. The light is best focused when the right edge of the wire is brightest (in highest contrast compared to the center of the wire). Remove the droplet hole cover. Unscrew the focusing wire from its storage place on the platform and carefully insert it into the hole in the center of the top capacitor plate. Return the focusing wire to its storage location on the platform. Bring the reticle into focus by turning the reticle focus ring. View the focusing wire through the viewing scope and bring the wire into sharp focus by turning the droplet focusing ring. Complete the reassembly of the chamber by placing the droplet hole cover on the upper plate and the lid on the housing. (If you do not cover the droplet hole of the plate, the hole could be clogged with oil.) 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA ( ) Page 6 / 19

7 (6) Realign the optical system while observing the droplets. (8) Connect the power supply to the plate voltage connectors. Move the air vent lever to the OPEN positon. Place the nozzle of the atomizer into the hole on the lid of the chamber and squeeze the atomizer bulb with quick squeeze. While viewing a shower of drops through viewing scope, realign the optical system. Caution To prevent electric shock, use ONLY safety patch cords with shrouded banana plug. Do not apply voltage to the thermistor connectors. (7) Determine the temperature of the chamber and calculate the viscosity of the air. (9) Set the output voltage of the power supply. Prior to turning on the power supply, set the plate charging knob to Plate Grounded (middle) position and rotate voltage adjustment knob fully counterclockwise (VV = 0 V). Turn on the power and increase SLOWLY the output voltage to 300 V. Connect the multimeter to the thermistor connectors and measure the resistance of the thermistor. Refer to the Sutherland s Formula and the Thermistor Resistance Table (see appendix) to find the viscosity of air. ηη = (Pa s) 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA ( ) Page 7 / 19

8 Setup 2. Stopwatch Software (2) How to use the Watchy. (1) Run Watchy software. [Start] or [F5] : Start the clock. [Stop] or [F6] : Stop the clock. [Reset] or [F7] : Reset the stopwatch to zero. Clear the log. [Lap] or [F10] : Add a lap time without stopping the clock. [Split] or [F11] : Add a split time without stopping the clock. [Split] records overall time at any given point, whereas [Lap] records elapsed time between splits. Procedure Note (2) Rotate the plate charging knob of the power supply to the Plate Grounded (middle) position. It is recommended you do not use any air conditioner or fan while performing your experiment. The airflow outside the chamber could affect the motion of oil droplets. The high velocity stream of air creates a region of lower pressure above the chamber lid, compared with standard atmospheric pressure inside the chamber. This pressure difference results in a net force pushing droplets up. The plate charging knob changes the direction of the electric field between the plates. We will introduce the droplets into the chamber with no electric field by setting the knob to the Plate Grounded position. Step 1. Setting the Plates Voltage (1) Set the potential difference across the parallel plates. Set the output voltage of the power supply to 300 V or any desired value. (Do not exceed 400 V.) VV = (V) 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA ( ) Page 8 / 19

9 Step 2. Introducing Droplets into the Chamber Step 3. Charging the Droplets (1) Move the air vent lever to OPEN position. Move the air vent lever to the OPEN position to allow air to escape from the chamber during the introduction of droplets into the chamber. The apparatus uses the piezo igniter to charge droplets. An applied mechanical stress on piezoelectric ceramic in the igniter generates a high voltage. The voltage produces an electric field in the gap between the end of the connected wire and the lower plate in the chamber. (2) Introduce the droplets into the chamber. Note The object is to get a small number of drops, not a large, bright cloud from which a single drop can be chosen. 1 To make oil droplets, squeeze the atomizer bulb with one quick squeeze. Free electrons in the gap are accelerated by the electric field. As they collide with air molecules, they create additional ions and newly-freed electrons. The exponentially increasing electrons and ions cause regions of the air in the gap to become electrically conductive in a process called dielectric breakdown and finally an electrical discharge or an electric spark occurs. The ions or electrons produced during this process could be captured on the falling oil droplets. (1) Charge the droplets by pressing the piezo igniter. 2 Then squeeze it slowly to force the droplets through the hole in the droplet hole cover, through the droplet hole in the top capacitor plate, and into the space between the two capacitor plates. Excessive use of the atomizer can cause too many drops to be forced into the viewing area and prevent observation of drops. Besides, repeated squirts of the atomizer can cause the plate hole to be clogged and fail to produce any drops in the viewing area. In such cases, turn off the power supply, disassemble the chamber, and then clean them with a soft tissue. The droplets are charged with unknown charge. Some could have many electrons (or positive ions), some a few, and some could have no charge. If you find too few droplets have net charges, press the piezo igniter again. (3) When you see a shower of drops, move the air vent lever to the CLOSE position. 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA ( ) Page 9 / 19

10 Step 4. Selection of the Drop (1) Select an appropriate droplet for your measurement. The following charts shows the graphs of Eq. (8) computed with conditions of VV = 300 V, dd = m, ρρ = 886 kg m 3, ηη = Pa s (TT = 25 ), and fall/rise dist.= 0.5 mm.. (Notice that graphs could be altered when your experimental conditions vary.) For example, if you select a droplet which requires 15 seconds to fall 0.5 mm when the plates are not charged, and if the droplet has 2, 3, 4, or 5 excess electrons, the droplet will rise the same distance in the 15.7, 7.7, 5.1, or 3.6 seconds when the plates are charged. If it has only 1 excess electron, it will never rise. The droplets which have more than 6 excess electrons are almost indistinguishable since there are small differences in rise time. A droplet which requires 5 seconds to fall 0.5 mm when the plates are not charged, is good sample for measuring the charge of 6ee, 7ee, 8ee, 9ee, or 10ee. It will take about 38.4, 15.7, 9.9, 7.2, or 5.7 seconds for the droplet to rise 0.5 mm again. Thus, it is recommended to select the droplet for which it takes 5-20 seconds to freely fall 0.5mm (plates not charged), and for which it takes more than 5 seconds to rises 0.5mm (plates charged). If you have enough time for observations, you had better set the moving distance at 1.0mm because you can decrease measurement errors. However, you should also notice that a long-time observation is not always good, since your droplet could disappear from view during observation, or uncontrollable factors could disturb your observation. If too many droplets are in view, charge the capacitor plates and wait until many of them get out of sight. If you find that too few droplets have net charges to permit the selection of an appropriately sized and charged drop, press the piezo igniter again. When you find an appropriately sized and charged oil droplet, fine tune the focus of the viewing scope. (The oil droplet is in best focus when it appears as a pinpoint of bright light.) 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA ( ) Page 10 / 19

11 Step 5. Collecting Data on the Rise and Fall of the Droplet (4) Repeat step (2)~(3) 5~10 times. Measure the rise (plates charged) and fall (plates not charged) velocities of the selected droplet about 5-10 times. The greatest accuracy of measurement is achieved if you time from the instant that the droplet passes the reticle line A to the instant that the droplet passes the reticle line B (or C). The distance between the reticle lines is 0.1 mm, so A and B are 0.5 mm apart, and A and C are 1.0mm apart average distance(m) Fall time (s) Rise time (s) (5) Calculate the average fall and rise velocities of the selected droplet. vv ff = (m/s) vv rr = (m/s) (1) With the plates not charged, start the stopwatch at the moment the falling drop passes the line A. (2) At the moment that the droplet reaches the line B or C, record the lap time by clicking the [Lap] button of the stopwatch, and apply electric fields at the same time. (6) Calculate the charge on the droplet. qq = 18ππ dd 3 vv ff VV ηη3 2ρρgg 1 + vv rr (8) vv ff (3) At the moment that the rising drop reaches the line A, record the lap time again and stop applying electric fields at the same time. qq : Charge carried by the droplet (C) VV : Potential difference across the plates (V) dd : Separation of the plates of the capacitor (m) ρρ : Density of oil (886 kg m 3 ) gg : Acceleration of gravity (m s 2 ) ηη : Viscosity of air (Pa s = N s m 2 ) (See appendix.) vv ff : Velocity of fall without E-field (m s) vv rr : Velocity of rise without E-field (m s) If the result of this first determination for the charge on the drop is too great, you should use slower moving droplets in subsequent determinations. 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA ( ) Page 11 / 19

12 Step 6. Changing the Charge of the Droplet It is desirable to observe as many different charges on a single drop as possible. If the droplet is still in view, attempt to change the charge on the droplet and measure the new rising velocity many times, if possible. (1) Bring the droplet to the bottom of the field of view using the plate voltage switch. The following chart shows an example of the measured charges of 200 oil drops. Red dots are measured values and blue lines represent theoretical values of nnnn. Because of random errors, your measurements may be deviated from an expected value in every trial. Usually random errors follow a normal distribution, so the assumption of normality can be a good first approximation. (2) Rotate the plate charging switch to the charging position to the droplet to rise. (3) Change the charge on the droplet by pressing the piezo igniter as described previously. If the rising velocity of the droplet changes, make as many measurements of the new rising velocity as you can. (4) Repeat Step 5. (5) If the droplet is still in view, repeat Step 6 as many times as you can. A histogram is a good tool giving a rough sense of the density of the underlying distribution of the data. In the process of dividing the entire range of charge values into series of intervals, and then counting how many values fall into each interval, we can get the following histogram. As the histogram shows, the example data have a distribution that is nearly normal at several peaks. Curve fitting can be used to find the best fit curve, and finally the elementary charge is obtained. Step 7. Additional Measurement Repeat step 1 to 6 with other droplets. Repeat the experiment with at least 20 different charge through the steps 5~7. It is desirable to get as many data as you can. Step 8. Analysis Consider appropriate analysis methods to find the elementary charge with your experimental data. For example, the following statistical approach can be considered when lots of data collected. See appendix for more instructions. 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA ( ) Page 12 / 19

13 Appendix 1. Viscosity 3. Analysis Sutherland s formula can be used to derive the viscosity ηη of an ideal gas as a function of a temperature TT 0 + CC ηη = ηη 0 TT + CC TT 3 2 TT 0 CC : Surtherland s constant TT : input temperature (K) TT 0 : reference temperature (K) ηη 0 : reference viscosity (Pa s) at reference temperature TT 0 Surtherland s constant and reference values for dry air are CC = 120 TT 0 = K ηη 0 = Pa s 2. Thermistor A thermistor is a specialized resistor, intentionally designed to be thermally sensitive and its primary characteristic is its ability to alter its electrical resistance in response to changes in case temperature. The resistance of a 10 kω thermistor at TT( ) follows the table below. TT ( ) RR (kω) TT ( ) RR (kω) TT ( ) RR (kω) The following table is an example of 200 observations of the droplet charge. We now consider a statistical approach to find the elementary charge using the data. No. qq ( ) No. qq ( ) No. qq ( ) No. qq ( ) No. qq ( ) Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA ( ) Page 13 / 19

14 The following chart shows the distribution of the measured charges of 200 oil drops as in the previous table. X-axis is sequential number of droplets and y-axis is charge. Red dots are measured charges of each oil droplet. Theoretical values of nnnn are plotted in blue lines. You can easily carry out the previous process using any spreadsheet application such as Excel, which providing automated function to generate frequency table and histograms. To create a histogram in Excel (the following guide applies to Excel 2013 or prior versions), you need to load [Analysis ToolPak] ( 분석도구 ). Click [File] ( 파일 ) tab, click [Options] ( 옵션 ), and then click [Add-Ins] ( 추가기능 ) category. In the [Manage] ( 관리 ) box, select [Excel Add-ins] (Excel 추가기능 ) and then click [Go] ( 이동 ). To create a histogram, we need a frequency distribution table which contains the counts of the occurrences of values within particular intervals or bins. The theory of statistics introduces several rules for how to choose the optimal bin size. However, in this example, we simply set it to ( ) which is 1/10 of the elementary charge. Divide the range into as follows and count how many values fall into each bin. Now we have the following distribution table and histogram. Bin Frequency In the [Add-Ins] ( 추가기능 ) box, check the [Analysis Tool- Pak] ( 분석도구 ) checkbox, and then click [OK] ( 확인 ). Now you can use [Data Analysis] ( 데이터분석 ) in the [Analysis] ( 분석 ) group on the [Data] ( 데이터 ) tab. 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA ( ) Page 14 / 19

15 In one column, type bin numbers (evenly distributed intervals) in ascending order. These represent the intervals by which you want to measure the frequency. A frequency table and a histogram will be automatically generated as follows. Click [Data] ( 데이터 ) tab, click [Data Analysis] ( 데이터분석 ) and then select [Histogram] ( 히스토그램 ). The next step requires data analysis applications such as Origin or MATLAB, since Excel does not provide complex curve fit models such as Gaussian curve or multi-peak fitting. When any data analysis app is not available, we recommend the lightweight application, MagicPlot. (You can download the free version of it at magicplot.com.) In the [Input Range] ( 입력범위 ) box, enter the cell reference for the data range that has the droplet charges. In the [Bin Range] ( 계급구간 ) box, enter the cell reference for the range that has the bin numbers. Under [Output Options] ( 출력옵션 ), choose an output location. Check [Chart Output] ( 차트출력 ) to shows an embedded histogram chart. (Continued) 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA ( ) Page 15 / 19

16 Run MagicPlot application and click [Create new Table] icon. Type bin numbers in A column and frequency data in B column. (Or, use keyboard shortcuts such as Ctrl+C and Ctrl-V to copy and paste data from Excel to MagicPlot.) To customize your plot, click [Line & markers] tap of [Curve properties] window. Select [Vert Bars] for line type and check [Fill] the lines. To create a Fit Plot, select your B column in Table, then click [Create Fit Plot] button in the toolbar. Select [Line & Marker]. To add a Fit Curve, click [Add] button in the [Fit Curves] tab and select [Gaussian]. Now the following plot is generated. 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA ( ) Page 16 / 19

17 Fitting process assumes that certain initial values of parameters are set before fitting. So you have to approximately locate peaks before fitting. Using two circles on the fit curve, drag the fit curve on corresponding position in data plot. Click [Fit by Sum] button. Then MagicPlot will fit the data with the sum of each fit curves. You can find the parameters of each Gaussian curves in the [Fit Curves] tab. Add additional Gaussian curves and rearrange them. In the example, the data plot has 7 peaks, so we added 7 fit curves. 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA ( ) Page 17 / 19

18 Result & Discussion Your TA will inform you of the guidelines for writing the laboratory report during the lecture. End of Lab Checklist Please put your equipment in order as shown below. Delete your data files from your lab computer. Turn off the lab computer. With the voltage adjustment knob set at zero, turn off the power supply and unplug the power cable. Unplug the dc adapter of the LED lamp. Assemble the chamber. (Be careful not to lose any parts of it.) Screw the focusing wire to its storage location on the platform. Place the atomizer into the holder on the platform. (Handle the atomizer with care. It is very fragile.) Do not unplug the high voltage patch cords. 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA ( ) Page 18 / 19