Name:    Date:

Measurement of Elementary Charge

or

MILLIKAN OIL DROP EXPERIMENT

R.A. Millikan performed his famous experiment about 1910. It was fundamental in the process of describing the structure of the atom. J.J. Thomson had recently measured the ratio of charge to mass. This particular result allowed us then to know both the charge (from this experiment) and the mass by combining this result with Thomson's.

The experiment is quite simple. The apparatus is located in a darkened room so as to avoid external light scattering. A container with a substance of known dimensions is atomized much like a spray of perfume. As the droplets of latex in this case are forced up a rubber tube they are ionized, either gaining electrons or losing some by friction with the rubber tube. They then enter an area between two plates. Gravity tends to pull them down. The electrical charges on the plates can balance this. We can calculate the force needed to balance this. There are a few complications. These are described in the procedure.

OBJECTIVES:

APPARATUS:

PROCEDURE:

  1. Read about the Millikan Oil Drop Experiment. A description will be found in your text.

    2.  
  2. The apparatus is connected and in working order. Your instructor has already put latex spheres in the atomizer.

    3.  
  3. Turn on the apparatus. The light will shine between the plates. Focus the microscope with the small knurled knob on the right hand side of the scope. You should see some lines for reference. Get the image of the plates as clear as possible. When you make measurements the droplets will be very difficult to see, so focus is important.

    4.  
  4. The latex spheres have a mean density of 1.05 g/cm3. The mean diameter of the spheres is 1101 x 10-9 m. Find the mass of each sphere. There is a standard deviation of 5.5 x 10-9 m in the size of each sphere. This will give you a range of uncertainty. Be careful not to mix your units. If you need help, ask your instructor.

    5.  
  5. On the right side of the apparatus is a three position switch. Initially it should be in the center position. When you use the apparatus, you can alternately switch the polarity of the voltage on the plates.

    6.  
  6. Squeeze the atomizer two or three times until you see some particles drift into view. These will be very difficult to see as they are very small. You do not have to measure their size since you already calculated it from known information. The light shines on them so they appear as tiny white dots on a black background. It will probably take some getting used to the apparatus.

    7.  
  7. You should note that the droplets are falling upward. This is because the image is inverted in the microscope. This should create no problem. You will now balance the gravitational force with the electric force from the field created by the potential difference on the two plates.
    8. mg = Eq (1)

    but the mass is from the density and volume:
     
    m = r  Vol = (4/3 p r3) (2)

    and the Electric Field:
     
    E = V d (3)

    where d is the distance between the plates. You will need to measure this value.

    Thus we can determine the charge directly:
     
    q = mg / E = mg d / V = (4/3pr3r) g d/V (4)

    where
    g = the acceleration due to gravity
    V = potential between the plates in volts
    r = density of the spheres
    r = mean radius of the spheres
    d = distance between the plates


    Be sure to keep the units consistent.
     

  8. Historically (you could do this if you wished) the drop radius r, which is small (10-4 cm) can be estimated by cutting off the E field and letting the drop fall through a distance d defined by the reference lines in the ocular of the viewing scope. Terminal velocity occurs when the weight (mg) equals the viscous force f on the sphere. By Stoke's Law, f in a sphere of radius r, moving with a velocity v through a fluid viscosity is:
    9. f = 6ph rv = mg (5)
    therefore 4/3 pr3rg = 6ph rv (6)
    r = 3  [vh /(2 rg)]1/2 (7)
    Thus we could write:
    q = 36p g d r /V (h v / 2 rg)3/2 (8)

     
  9. The charge on a particular particle can then be determined by:
    10. q = (mgd)/V (9)
    When you turn on the voltage to the plates you will need to balance the forces on the particles by adjusting the voltages.
     
  10. There are some precautions to be aware of:
    1. Sometimes a clump of particles move together as one particle. Do not measure these as the mass is unknown.
    2. Some particles move faster up and down. This is because they have differing amounts of charge. Some will have lost one, two or three electrons, or gained them.
    3. Some particles move up rather than down and vice versa.

     
  11. It is not worth taking measurements below 50 volts. Only highly charged particles can be balanced in these small fields and we are interested in gaining the smallest charge possible.

    12.  
  12. Initially use values about 75 volts. Reverse the field so the swiftly moving particles are swept away.

    13.  
  13. Once you have isolated a particle with a low charge, adjust the voltage so it hangs motionless. Remember that even air molecules can disturb these particles.

    14.  
  14. Record the voltage.

    15.  
  15. Repeat for about a dozen particles.

    16.  
  16. The more data you have, the better. You may wish to pool your results with others in the class.

    17.  
  17. Arrange the values of V in a vertical column of increasing magnitude. Do the numbers seem to group together or spread out smoothly for low to high? Why?

    18.  
  18. Calculate charges on the particles.

    19.  
  19. Construct a histogram using data from the rest of the class as well as your own. Remember, it is the discrimination between levels that is important, not the actual charges on the particles. The difference in charge is caused by the charge on one electron! This is the smallest discrete charge, or the quanta of charge.

    20.  
  20. What is the quantum of charge? Report this with the appropriate uncertainty as determined from your data.

    21.  
  21. The value of q/m as measured earlier is 1.76 x 1011. Determine the mass of an electron. All calculations should include the effects of uncertainties.

    22.  
  22. If your results are within a factor of ten this is certainly an intellectual triumph!

    23.  
  23. Summarize.

    24.  
  24. Conclusions and Recommendations.

    25.  
  25. Write one page evaluating the journal article, Physics Today, June 1982,  by Harvey Fletcher regarding the Millikan Oil-Drop experiment. Specifically tell what you think and why. Address ethical and/or moral implications. This will be counted as a separate lab grade. Your instructor will discuss this briefly..
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