Millikan Oil Drop Experiment PDF

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Determining the Charge of an Electron: The Millikan Oil Drop Experiment Trent H. Stein, Michele L. Stover, and David A. Dixon Department of Chemistry, The University of Alabama, Shelby Hall, Tuscaloosa, AL, 35487-0336

Millikan’s original apparatus Introduction: A key elementary quantity is the actual charge of the electron. In 1897, J. J. Thomson showed that cathode rays are what we now call electrons. He measured the charge to mass ratio of the electron by using crossed electric and magnetic fields. In addition, he showed that the mass of the electron was small, more than 1000 times smaller than the hydrogen atom. This means that atoms were composed of negative charges and positive charges. Thomson envisioned that the electrons were embedded in a “pudding” of positive charge to make an atom. For this work, Thomson received the Nobel Prize in Physics in 1906. Thomson also invented the mass spectrometer. E. Rutherford shot alpha particles at a gold foil and showed that only a few back scattered. This led to the nuclear model of the atom in 1911. Rutherford had already won the Nobel prize in Chemistry in 1908 for his studies of the disintegration of the elements and the chemistry of radioactive processes. At this point, a critical question was the charge of the electron. R. Millikan, then came up with a relatively simple approach to measure the charge of the electron while working at the University of Chicago. The experiment was initially done with water droplets but changed to oil droplets because the water evaporated too quickly. The experiments were done in 1909 and 1910 and published his best work ion this in 1913. He 1

received the Nobel Prize in Physics in 1923 for his work on determining the charge of the electron and the photoelectric effect. At this time, he had recently moved to help found the California Institute of Technology. What is the experiment? The goal of the experiment is to use a force one knows, gravity, to balance the electrical force which is the unknown. When particles (polystyrene spheres) are vaporized by an atomizer (think a perfume sprayer), some acquire extra electrons and some lose electrons due to frictional processes similar to drawing a comb through your hair on a dry day. Some particles will acquire more charge than others and when they are exposed to an electric field in the region between a pair of electrodes, they experience a force proportional to their acquired charge q and to the applied electric field E. This electrostatic force FE is given in equation (1). FE = qE

(1)

The bold type indicates a vector quantity as the force and the electric field have a direction. The electric field is oriented so that for a positive charge, F is in the same direction as the electric field. If the charge (q) is negative, then the direction of F is opposite to the electric field. We can calculate the strength of the electric field, E, if we know the potential difference (V in volts) across the plates and the separation of the plates (d in meters). The equation to determine the magnitude of the electric field is given in equation (2). E = V/d

(2)

Our goal is to balance FE against any opposing forces so that the particle does not move. What other forces are present? The obvious one is FG, the force on the particle due to gravity, which pulls the particle down while FE is pushing the particle up for our given choice of charge and direction of E. There is another force, FVD, the viscous damping force which is always opposite to the direction of motion. If we choose our coordinate system (remember that these are all vectors so the forces have a direction) so that vertically upward is positive then our force equation for the polystyrene sphere at equilibrium becomes: FE - FG - FVD = 0

(3)

FE = FG + FVD

(4)

and

Now let’s look at each force in detail. By combining equations (1) and (2), we get equation (5) FE = qV/d

(5)

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where our unknown charge q is given in terms of known quantities V and d if we know FE. The next force to consider is the force due to gravity given in equation (6). FG = mg

(6)

where g is the acceleration of gravity (9.8 m/sec2). What is the mass of our particle, a single polystyrene sphere? Do you think it would be easy to weigh a single sphere? Probably not very accurately as it is very light, so we must express the mass of a single sphere in terms of a bulk property of the material that is easier to measure. The density (ρ) of the polystyrene used is given on the bottle label, as is the diameter of the spheres (in microns, 1 micron = 1 x 10 -6 m). Given this data, the mass of a single sphere is the density (ρ) times the volume (Vol, equation (7)). m = ρ(Vol)

(7)

with Vol the volume of the sphere given in equation (8) (remember that the equation for Vol has the radius r in it). Vol = (4/3)πr3

(8)

Substituting (8) into (7) and the resulting equation into (6) gives equation (9). FG = ρ(4/3)πr3g

(9)

The last force we need to look at is the viscous damping force. Viscous drag is experienced by a body of any shape but the force is only readily calculable for a sphere. For this, we will need the equation worked out in 1845 by Sir George Stokes, which is known as Stokes’ Law. Stokes’ Law gives us the viscous damping force on a sphere moving in an ideal fluid. What is our fluid? Air! Assuming that air is an ideal fluid does not affect our experimental error significantly (Why not?). The Stokes equation equivalent for viscous drag on a sphere is given by equation (10). FVD = 6πηrvT

(10)

where η is the viscosity of the fluid (for dry air at 760 mm of mercury η = 1.81x10 -5 N sec/m2), r is the radius of the sphere and vT is the terminal velocity of the particle which we will measure. Note that vT is our vector quantity. Substituting equations (5), (9), and (10) into our force equation (4) gives equation (11), where we now only use the magnitudes of the forces. qV/d = 6πηrvT + ρ(4/3)πr3g

(11)

Solving for the charge, q, gives equation (12). q = (6πηrvT + ρ(4/3)πr3g) d/V

(12)

In the course of the experiment we will measure the needed unknown, the terminal velocity, v T, of the particles and the experimental variable, the voltage across the electrode plates V. The other 3

quantities are known. Using equation (12), it is possible to calculate the charge of a single electron, which also illustrates the quantized nature of charge. Why is this latter idea important? Experiment: Basic idea: The basic apparatus is shown in Figure 1. A small puff of opaque polystyrene spheres of known size distribution is delivered to the electrode assembly by the atomizer. When the spheres enter the space between the electrodes, the incident light is scattered by the spheres and some of this light is redirected toward the microscope. Because the spheres are on the order of one micron in diameter, they are too small to readily measure their size with the fixed magnification of this microscope. However, each sphere or small cluster will be easily visible as a bright point of light that will drift slowly downward under the influence of gravity. At this point, after a few short quick pumps of the atomizer bulb, the view through the microscope should look like a dark sky with many stars slowly moving downward. The microscope in this optical system is fitted with a reticle or eyepiece micrometer which can be used with or without calibration to observe the behavior of neutral and charged spheres in the presence or absence of a constant electric field between the electrode plates. The polarity of the electrodes can be changed by using the three position switch on the device. The particle response will be rapid motion toward the plate with the charge opposite that of the particle. Quick reversal of the electrode polarity (inversion) can be used to trap individual spheres for use in repeated timing of the path velocity for a single sphere. This allows the user to make repeated measurements on the same sphere, thus, allowing statistically valid data to be collected for measuring the charge on the particle.

Atomizer Voltage display Microscope Light block

Main chamber Voltage knob

Figure 1. Millikan Apparatus

Polarity switch

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Safety Instructions: 

This apparatus uses high voltage. Do not touch any exposed metal surfaces in the experiment.



Do not put anything metal into the hole in the left side of the main chamber when the voltage is on (the voltage knob is not turned to its counter-clockwise limit).



Do not remove your safety glasses when performing this lab. You may lift them up when you are looking through the microscope, but they need to remain on your face. As soon as you are done looking through microscope, the glasses need to be back over your eyes.

Equiment:   

Millikan apparatus Microscope Atomizer

  

Bottle of polystyrene spheres in liquid suspension Plastic machine screw Stopwatch

Procedure Step A: Apparatus Set Up and Initial Results 1) Carefully set up the Millikan Apparatus (figure 1) by following steps 2-6. 2) Begin by plugging in the Millikan Apparatus into an electrical outlet. Make sure that the voltage knob is turned off (to the counter-clockwise limit) and the polarity switch is in its central (neutral) position before plugging it in. Do not force the voltage knob as it will stop turning at this limit. Press the power button.

Figure 2. Main chamber

Figure 3. Atomizer

3) To assemble the microscope, pull back on the black focusing knob, retracting the rubber roller. Slide the microscope tube into the focusing block and release the knob to trap the tube (Figure 2).

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4) Initial focus may be achieved by inserting the plastic machine screw into the hole on the left side of the main chamber (Figure 2). Moving the eyepiece by hand while the knob is retracted provides coarse adjustment. Turn the engaged knob for fine focus. Once a good focus has been achieved, remove the machine screw. 5) Unscrew the cap and fill the atomizer with a sufficient volume of the latex particles to cover the bottom of the large vertical atomizer barrel (Figure 3). Do not exceed the max fill level as the air mix port must not be obstructed. Replace the cap. 6) Place the atomizer into the hole in the main chamber. Insert the delivery tube into the hole on the left side of the chamber (figure 2). The delivery tube will only go in about 1 ½ cm. Do not force the delivery tube past this point. Look through the microscope and make sure that you cannot see the tube. If you can see it, pull back on the delivery tube until you cannot see it. 7) At this point, your set up should look like Figure 1. If it does not, ask your TA for help before proceeding with the experiment. 8) Squeeze the atomizer bulb quickly two times. Look through the microscope and note the spheres which are visible as tiny points of light. If necessary, rotate the microscope tube so that the reticle is right side up. Sharpen the focus for the individual viewing. Slide the knobs on the top and back of the light block to adjust the amount of light entering the electrode chamber (Figure 1). 9) To observe the polystyrene sphere behavior in the applied electric field, turn the voltage adjust knob clockwise for a ½ turn. While looking through the microscope, move the polarity switch from the center (neutral) position to one side (charged). 10) Squeeze the atomizer bulb 2 times quickly. Turn the voltage knob clockwise as far as it can go. While looking through the microscope, move the polarity switch to charged. Answer Procedure A Question 1. 11) Squeeze the atomizer bulb 2 times quickly. Turn the voltage knob counter clockwise to the beginning of the white semi-circle. While looking through the microscope, move the polarity switch to one side (charged). Answer Procedure A Question 2. 12) Wait 5 minutes. Look through the microscope and answer Procedure A Questions 3 - 4. 13) Turn the voltage off and the polarity switch to neutral. Squeeze the atomizer bulb 2 times. Look through microscope. Answer Procedure Step A Question 5.

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Questions: Procedure Step A 1) What do you see? Describe the speed and direction of the particles. Are all of the particles moving in the same direction with the same speed? If not, explain why.

2) What do you see? What happened to the magnitude of the electric field and how does this affect the force on the particle? Use the equations given above to answer this question.

3) What happens to the particles if you do not pump the atomizer before you look into the microscope? Are the particles gone?

4) Why are we only interested in the particles moving upward?

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5) What happens to the particles when there is no applied electric field? Are they accelerating downward or floating downward at a constant speed?

6) Draw a force diagram for a particle moving upward under the influence of an electric field.

Procedure Step B: Calibration and Data Collection

1) We will need to calibrate the reticle scale to determine the actual speed of the particles as we view them through the microscope. The included machine screw used for initial focusing will be used for this.

2) Turn the eyepiece on the microscope so that its scale runs sideways. Remove the atomizer delivery tube and insert the plastic machine screw into the hole on the left side of the main chamber. Use the reticle scale to determine the ratio of threads to reticle divisions.

3) The screw has 40 threads/inch or 6.4x10-4 m/thread. Multiply this value by your determined threads/division to determine your calibration factor in m/division. Have each member of the lab group perform this calculation and average the results. Record this value on the next page for future calculations.

4) When you are finished calibrating the reticle scale, remove the machine screw and reinsert the atomizer delivery tube into the electrode chamber. 9

5) With the apparatus turned on, adjust the voltage so the meter reads approximately 200 volts. Record this voltage. NOTE: You will have to turn the polarity switch to one side (charged) to see the voltage, and then turn the polarity switch back to neutral.

6) In the next part, you will use the stopwatch provided to record the time is takes for a latex particle to pass one scale division. By timing the motion of a particle as it crosses scale divisions, you will be able to determine its actual speed in meters per second.

7) Pump the atomizer bulb 2 times to inject a cloud of particles into the electrode chamber. Allow the faster moving particles to clear, and then pick a particle that is slowly moving upward. Wait for it to cross a scale division, and then begin timing using your stopwatch. Once the particle reaches the next scale division stop timing. Record the time in one of the blanks on the next page.

8) Repeat this procedure for a total of 100 particles. You should be able to time multiple particles every time you pump the atomizer. When all the particles have dissipated, pump the atomizer bulb again.

9) Try to time a variety of particle speeds but concentrate on those moving at the slowest speeds. Have one student observe the particles motion and run the stopwatch while the other records the time. Answer Procedure B Question 1.

10)

Each person in the lab group should make observations and time the particle’s motion for 50 particles.

Clean-up: 1) Do not use organic solvents in cleaning parts of the apparatus. 2) Empty the atomizer chamber by pouring the latex particles into a supplied clean container. Do not pour the used suspension into the original bottle as it may contaminate the remainder of the bulk solution.

3) Clean the atomizer assembly several times with clean water, repetitively squeezing the bulb to force water through the assembly.

4) The electrode chamber should be wiped out prior to storage, using care to avoid stripping the chamber threads with the cover screws or scratching the electrodes. TO BE DONE BY TA

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Record the speed of 100 slowly moving particles in the spaces below.

Calibration factor ________________________

Plate voltage ______________

Terminal velocity _________________________

# of divisions crossed __________

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Data Analysis: 1. Enter the collected data (100 speeds) into an Excel spreadsheet. Sort the speeds from low to high. Answer Procedure B Questions 2 - 3. 2. Use Excel to calculate the terminal velocity (m/sec) of each time by dividing the number of divisions crossed divided by the elapsed time and then multiplying by the calibration factor. 3. Plot a graph of the # of divisions (x-axis) vs. terminal velocity (y-axis). See figure 4 as an example. 4. On your graph, draw horizontal lines through the center of each distinct group of velocities and record the velocity you read on the axis of the graph. 5. Use your spreadsheet to group particles into the steps you observe in the graph and determine the average velocity for each group. Answer Procedure B Question 4. 6. Calculate the difference in velocity between adjacent groups. 7. Calculate the average of these differences. This difference is your terminal velocity (the average of each step in the graph) is the increase in velocity due to the addition of a single electron.

Figure 4. Plot example

8. Use equation (12 )to calculate the charge of a single electron. Answer Procedure B Questions 5 – 7. In the course of the experiment you should have measured the following experimental parameter: V = plate voltage in volts (recorded on page 8) and the following variable vT = terminal velocity in m/s (the average step in velocity recorded on page 8) The remaining experimental parameters are given: ρ = density of spheres in kg/m3 (found on the latex sphere bottle) d = diameter of the spheres in meters (found on the latex sphere bottle). Remember you need the radis r. g = gravitational acceleration (9.8 m/s2) η = viscosity of air (1.73x10-5 N sec/m2) d = plate separation in meters (found on the back of the Millikan apparatus) 12

Attach your spreadsheet and graph. Give your graph a title, label your axes, and include units. Questions: Procedure B 1) Why did we concentrate on the particles moving at the slowest speeds?

2) What can you tell from the plot? Do you see a uniform distribution of terminal velocities or are they “clumped up” forming several steps? If there are steps in your plot, what does this imply? Do the steps occur at high or low velocities? What does this mean?

3) If you ran this experiment with a higher voltage, how would the graph of the data points change? Think about this in terms of the particle’s speed.

4) Are these lines you’ve drawn on the graph equally spaced? What is the average spacing between these lines? Did the average velocities you calculated for each group match the line you drew for each group?

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5) Calculate the charge of an electron. Show your work.

6) The accepted value for the electron charge is 1.602x10-19 coulombs. Calculate the percent error of your result. Show your work.

7) Is this a reasonable error? Can it be accounted for? What are the most likely causes for this error?

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