1/11/06clc

 

 

Millikan Oil Drop Experiment

 

This is the classic experiment which Millikan used to measure the charge on the electron.  He did this by measuring the charge on small oil droplets and by noticing that this charge always seemed to be a multiple of some quantized charge unit.  A thorough description of the technique is given in the accompanying reprint, and Melissinos, p. 2.  Your apparatus includes:

·        Millikan oil drop apparatus, including plates and reversing switch

·        Telescope with scale

·        Leybold lamp and transformer (use 4V to extend bulb life)

·        Regulated power supply

·        Oil atomizer

·        Voltmeter

Be careful with the power supply--it will deliver up to 300 V at several hundred ma.  Your only reliable protection against shock is your own carefulness.

You will want to use small, low-charge drops.  These are ones which move slowly with and without field.  It is worthwhile to do a preliminary calculation of the charge on your drops early in the game in order to gain some idea of how many electronic charges you are dealing with.  Your best evidence for a quantized charge will probably come from seeing a single drop change its charge.  This can be made probable with the help of a 57Co source. Ask your instructor. This is an important part of the experiment and should not be overlooked.  Q: Why should it be easier to see a quantization effect if your drops have low charge?

MILLIKAN OIL DROP:  EXPERIMENT I.1

 

By observing the motion of oil drops in a uniform electric field it can be established that the drops are electrically charged and this charge can be determined.  With no electric field the drops drift down in the earth’s gravitational field with some velocity Vd.  If the uniform electric field is turned on and in a particular direction the drop can be speeded up to some velocity .  By reversing the field it can be slowed down or in fact reversed in direction with velocity Vu. 

The amount of charge on the oil drop can be determined by examining the equations of motion of the drop.  For example, in free fall the drop of mass, m, and the velocity, Vd, follows the equation (sign conventions: all Vi  in these equations are positive for normal rising and falling drops)

 

-mg = -kVd                                                                  (1)

 

whereas with the electric field (E) in opposite direction to the gravitational field the drop rises according to the equation

 

                                                          (2)

 

With both forces in the same direction the equation is

 

                                                    (3)

 

From these equations we can deduce two determinations of the charge on the drop

 

                                 (4)

 

These two values should be the same as long as the charge on the drop remains the same.  In order to determine this charge “e” it is necessary to measure the velocities Vd,  and Vu and to determine the mass of the drop  from the density (s) and the radius (a). 

The radius a can be found from the free fall terminal velocity from Stokes’ Law:

 

                                    F=6pah Vd                                                                                                                        (5)

 

This relates a to Vd . Unfortunately, a corrected version of this law must be used for small a.

After subsituting mg for F, the result is 

                                                                     (6)

 

In these equations h is the viscosity of air, p is the atmospheric pressure, g the acceleration due to gravity, and b is a constant (explain this result when you write up your experiment). This is solved for a below.

The experiment to measure the charges on several oil drops therefore requires a high voltage source, a telescope and light to track the drops, oil and atomizer, stop watch, a good set of eyes and a little persistence.  Measure the density of the oil, barometric pressure, temperature and look up the viscosity of air.

Make several sets of measurements and compute the charge.  If a single electron charge is on the drop then you have measured the electron charge.  Of course you cannot be sure of this.  By placing a radioactive source near the oil drop it is possible to induce charges on the drop.  By making measurements of drops of several different charges you should be able to deduce a basic unit of charge involved in your experiments.  Good luck and have fun. 

 

Before taking final data, it is a good idea to set up a program (for example, using a spreadsheet such as Excel) to evaluate your results as you take them. In such a spreadsheet you could enter the relevant constants and the times, and calculate the charges from

,  and .

 

where  the coefficient  , a is the drop radius, d is the distance between the plates, and V is the voltage across the plates.

 

The values of some constants are infernal because most text books deal in cgs units. In MKS units ,

h = 1.825 x 10-5     kg/m-s

            s = 867 kg/m3

b = 6.17 x 10-6 if p is in cm of Mercury (a non MKS unit, but such is life..) and a is in m.

 

Note:  You must assume that you do not know the value of e so you will need to develop a technique of finding the largest possible charge such that the charges on your oil drops are integral multiples of this charge.

 

 

 

Spreadsheets: cgs, mks

 

Tips: Use drops with the smallest charge and lightest mass possible. That is, use those which react, but only weakly, to the field, and which drift slowly. These have fewer quanta of charge.