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an experiment of the Electron topic Measuring Fundamental charge by Millikan’s Oil Drop Apparatus Instructor: 梁生 Office: 7-318 Email: [email protected] Introduction Measuring the Fundamental charge is a milestone of investigating on Electron. Millikan’s experiment is effective and with artful ideas, which is an illumination for design and development of instrumentation. Purposes There are two purposes in this experiment as follow: 1. To master measuring fundamental charge by Millikan’s oil drop apparatus; 2. To measure the fundamental charge and validate the discontinuity of electric charge. Experimental instruments Millikan oil drop apparatus. 1 Principle The tiny oil droplet is sprayed between the two parallel plates with a distance of d, then, the droplet obtains an electric charge of q due to the friction. When a voltage of V between the two parallel plates are operated, an electric field E is generated, therefore, the oil droplet is affected by both of the electric force and gravity. By tuning the value of the voltage V, balancing the gravity and the electric force on the oil droplet can be realized. And the oil droplet can be suspended between two parallel plates. Then, we have: mg = qE = q V d (1) where, V and d are physical constants easy to measure, by further measurement of the mass of the oil droplet m, the electric charge of the droplet can be obtained. It can be found that, the charge of the oil droplet is always an integer multiples of the smallest charge observed, namely, q=ne, n=±1, ±2 ……, which validates the discontinuity of the electric charge, and the smallest unit of electrical charge, is defined as the value of the fundamental charge e. By supposing the density of the oil droplet is ρ, the mass of oil droplet m can be expressed as: 4 m = π r3ρ 3 (2) To measure the radius of oil droplet r, remove the voltage between the two parallel plates to make oil droplet fall by the gravity, at the same time, resistance is generated by the air viscosity. Viscous force is proportional with the fall velocity, and it obeys Stokes’ law: f r = 6π rη v (3) where η is the viscosity of the air, r is the radius of the droplet, and v is the droplet 2 4 velocity, respectively. Furthermore, the oil droplet gravity is m = π r 3 ρ g . 3 When the oil droplet falls some distance in the air, the viscous resistance increases, two forces reach balance, then, the oil droplet fall with a constant velocity. In this case, it can be found that: 4 3 π r ρ g = 6π rη v 3 (4) To solve the radius of the droplet from (4), it is can be expressed as: r= 9η v 2ρ g (5) Because oil droplet’s radius is less than 10-6 m, the air medium cannot be considered evenly continuous, so we need to rewrite the η to η ′ = η b 1+ pr , where b is a correction factor and b=8.22×10-3 mPa, p is the atmosphere pressure, so we can get r= 9η v 1 ⋅ 2ρ g 1 + b pr (6) and ⎛ 4 ⎜ 9η v 1 ⋅ m= π⎜ 3 ⎜ 2ρ g 1 + b ⎜ pr ⎝ 3 ⎞ 2 ⎟ ⎟ ⋅ρ ⎟ ⎟ ⎠ (7) Above expression still contains radius r, but it is only in the correction item, it doesn’t need quite accurate. Considering the velocity of the oil droplet equal with the ratio of fall distance l to the time t, V=l/t, we can get: 3 ⎛ 4 ⎜ 9η l 1 m= π⎜ ⋅ 3 ⎜ 2 ρ gt 1 + b ⎜ pr ⎝ 3 ⎞ 2 ⎟ ⎟ ⋅ρ ⎟ ⎟ ⎠ (8) Substitute above formula into (1): ⎛ 18π ⎜ η ⎜ q = ne = 2ρ g ⎜ 1 + b ⎜ pr ⎝ 3 ⎞ 2 ⎟ ⎛ l ⎞32 d ⎟ ⎜ ⎟ ⎟ ⎝t ⎠ V ⎟ ⎠ (9) Formulas (5) and (9) are the basic formulas in this experiment. Procedures 1. Apparatus regulation Put the work voltage select switch on “fall” block, at this moment the upper and lower plates are short circuit without electric, and the oil droplets are easy to be sprayed in. Remove the drop chamber, check the insulation ring and the plates. Install the drop chamber back, and keep spray aperture towards the front right side, open it for droplet spraying. Make the apparatus steady, adjust the two level screws to make the level bubble indicate level. Turn on the power switch, tune the focus for CCD to make clear vision in the monitor. 2. Observation and controlling of droplet Spray oil droplets into the drop chamber (only a little) by the atomizer, tune the focus hand wheel of microscope to make the oil droplets clear in the monitor, then the oil droplets in the sight field seems to be like just stars in the night sky. If the scale is not brilliant enough, or the luminosity of up and down visual field is not uniform, it is 4 necessary to adjust the direction of the light emitting diode (LED) to make the visual field and the oil droplets clear. Keep the work voltage switch on “fall” for safety while removing drop chamber. Put working voltage switch to “Balance” to put 250 V working voltage to the two parallel plates, to observe the motion of the oil droplets; choose a clear oil droplet (not too large), adjust the voltage, observe the velocity changes of the oil droplet till it stops keeping balance; put the work voltage switch to the “rise”, let the oil drop in the top of visual field. Then put the switch to the “fall”, the oil droplets begin to fall, measure the time for falling through this distance. Repeat above operation to be skilled in controlling the oil droplet. 3. Measurement From formula (9), it is found that we just need to measure two parameters, one is the balance voltage V, the other is the time t for falling through the distance l. To measure the balance voltage we need adjust carefully. Put the oil droplets near the cross hair on the scale for judging whether it is balanced. Choose the right size droplet is the key point to this experiment. For large, bright oil droplet, due to its large quality and charge, the time of falling a distance is shorter, which increases the measurement and data processing errors. However, the little oil droplets is difficult to observe due to Brownian motion. It is better to choose the oil droplet which takes about 20 s to fall 2 mm at the balance voltage from 200 V to 300 V. For guaranteeing the oil droplet fall uniform, we should measure time after the oil droplet fall a distance. The selected measurement distance should be in the middle of the two parallel plates. If the distance is too near to the up plate, it will influence the result for the airflow near the hole and the electric field is not uniform yet. It will influence repeat measurement for easily missing of the oil droplet because of the distance is too near the down plates. After the oil droplet is balanced, put the oil drop on a proper place through adjusting “rise” voltage. Let oil droplet fall a distance then 5 start timing and measure the time t while the oil droplet falling distance l. Then increase the balance voltage again, otherwise the droplets will soon disappear. 4. Data processing The known data in this experiment are as follow: density of the oil ρ=981 kg/m3 viscosity of air η=1.83×10-5 kg/(ms) acceleration of gravity g=9.80 m/s2 fixed constant b=6.17×10-6 m cmHg air pressure p=76.0 cmHg distance between two parallel plates is d=5.00×10-3 m. Put above data into formula, we can get the charge of the oil droplet: q= 1.6 ×10−10 × l 3 2 ⎡ ⎛ ⎞⎤ −4 t ⎢t ⎜ 1 + 8.76 ×10 ⎟⎥ l ⎠ ⎥⎦ ⎢⎣ ⎝ 32 ⋅ 1 V (10) Obviously, as the density of the oil droplet, the viscosity of air η is the function of temperature, gravity and air viscosity force will change during in experiment. However, in general condition, this calculation just brings 1% relative error. Repeat the measurement operation 6~10 times for one oil droplet, adjust the balance voltage for each measurement, and record it. Achieve measuring 6 to 8 different oil droplets. 6 Table 1. Data Record Droplet 1 Droplet V(V) Time Droplet 2 t(s) V(V) Droplet 3 t(s) V(V) t(s) Droplet 4 V(V) t(s) Droplet 5 V(V) t(s) Droplet 6 V(V) t(s) 1 2 3 4 5 6 Ave. Table 2. Data Processing Droplet 1 Electric charge Ratio Approximate Integer Measured e Relative Error Droplet 2 Droplet 3 Droplet 4 Droplet 5 Droplet 6 q (C) q/e n e′ e − e′ e Attentions 1. The experimental report need to be achieved in English. 2. Do not lose droplets after timing, keep the droplet static before the eyes leave the microscope. Keep watching CCD monitor during droplets moving. 3. After choosing oil droplet, close the electrode into hole in time until beginning to measure. 4. For the accuracy of the measurement balance voltage, it should be appropriate to 7 extend the observation time of balance state of droplet. 5. Tune and record the balance voltage continuously in every measurement. If the voltage changes obviously, this oil droplet should be considered as a new one. 6. Due to that oil droplet is very difficult to control and measure, therefore, to get better results, it is necessary to have rigorous scientific attitude, experimental operation and data processing. Basic requirements 1. Observe and control the movement of the charged oil droplets in electric field. 2. According to the formula (10) for calculating charges more than 6 different oil droplets. Note: the selected droplet’s balance voltage and the falling velocity should be different, otherwise all the droplets are with the same charge, which can not validate discontinuity of the electric charge. 3. Measure the fundamental charge, and verify the discontinuity of the charge. 4. In order to verify the charge is always an integer multiple of the charge of the electron and get the value of fundamental charge e, we should seek the common denominator to every measured q. and the common denominator is the fundamental charge. For data processing, you can use “reverse validation” approach. Use the recognized fundamental charge e=1.602×10-19 C to divide the measured charge q, get a data close to an integer (if has a large difference to an integer, delete it), take the integer, and this integer is the basic charged number n of droplet. Then, the measured charge q is divided by n, the fundamental charge e can be obtained, find and compare it with the recognized value. 5. Tables for data record and processing should be designed by yourself. Tables should be clearly to illustrate the measured data and calculated results. Here Table 1 and 2 are presented for references. 8 Discussions 1. What are the causes of that droplets fall too fast or too slow without work voltage? What are the influences on the experimental results? 2. If the oil droplet’s balance voltage is too high or too low, what does that mean? 3. We find a significant change in balance voltage during the measurement, what is the matter? If the balance voltage decreases in a small range, what does that mean? 4. The droplet’s image is found to be dark during observation. What is the problem? How to deal with it? 5. According to your experimental results, calculate the radius and mass of two droplets that the fall time is maximum and minimum for the same distance, respectively. What is the cause for the differences of time. 6. Use the experimental data of one of the oil droplets to calculate the buoyancy that effects on the droplet. Compare the calculated buoyancy with the gravity, viscous force and electric force. 9 Appendix: MOD-5 Millikan’s Oil Drop Apparatus MOD-5 oil drop apparatus is shown in Fig. 1. It mainly consists of oil drop chamber, illumination system, leveling system, measuring microscope, timer, power supply, atomizer and CCD image monitor. Fig. 1. MOD-5 Millikan Drop Apparatus. 1. Oil droplets chamber As shown in Fig. 1, oil droplets chamber consist of two fine grinding parallel plates (upper, lower electrodes, respectively) with insulation ring composition among cushion, the distance between the parallel plates is 5 mm. There are apertures for LED and microscope on insulation ring. Oil drops chamber is located in the organic glass wind covering. There is a hole with diameter of 0.4 mm in the middle of upper plate. The oil droplets from the chamber fall between the upper and lower electrodes through this hole and lighted by LED. You can use level screws to adjust the level of the oil droplets chamber, and check with level bubble. There is a microscope in the front of oil droplets chamber wind covering, you can observe oil drops between the parallel plates through the observation hole on the insulation ring. There is a reticle in the ocular, the total vertical length is equivalent to 0.300 cm (each division is 0.050 cm), which is used to measure the distance l of the oil droplets falling. The falling time of oil droplets can be measured by the digital timer. By the regulation of 10 microscope, reticle and oil droplets can be seen clearly. Put CCD camera close to the ocular of microscope, rotate and move CCD lens appropriately, and then you can see the reticle and the oil droplets clearly on the monitor. Sometimes you can also omit the CCD imaging lens and the ocular of microscope, make the view directly imaged in the CCD sensitive surface through a microscope objective lens. Sensitive surface of CCD transforms imagine signal in every sensitive unit into a video signal and transmit it to the monitor, which shows the original image on the screen. 2. Power supply There are four different voltages supplied by the power supply system. (1) A 500 V DC working voltage is added to parallel plates to produce electric field between the two plates. The voltage can be continuously tuned. Voltage value can be read on the digital voltage meter, and controlled by work voltage switch. Switch has 3 states: “BALANCE” provides balance voltage; “FALL” removes balance voltage, makes oil droplets fall; “RISE” provides balance voltage plus a rise voltage of about 200 V to make the oil rise to repeat the measurement of the same oil droplet. (2) 200 V RISE voltage. (3) 5 V voltage as the power supply for digital voltage meter, digital timer and LED. (4) 12 V voltage as power supply for CCD. 3. Microscope and monitor The amplified imagine of oil droplet can be realized by the microscope and shown on the monitor. It is easy to observe, control and measure the oil droplet by the monitor. There is a reticle on the screen. Every small grid is 0.050 cm and total 4 grids are 0.200 cm, which is employed to measure the fall distance and calculate the fall velocity of the oil droplet. 11