OVERVIEW
At the turn of the century, Robert Millikan made an important refinement upon a method to measure the charge of a single electron. The method is simple in concept but challenging in practice. Oil droplets are introduced into a chamber between two parallel conducting plates. The oil droplets are created with an atomizer and are so small that they must be viewed through a microscope. The miniscule size also means that they reach terminal velocity very quickly as they fall through the air. Terminal velocity is only a few millimeters per second and its value can be easily measured. This value will allow the mass of the droplet to be determined.
The process of atomizing the oil usually places an electrostatic charge (resulting from just a few electrons) on the droplets. If a positive potential is applied to the upper plate, those droplets will quickly move upward towards the upper plate due to the electric force on the electrons. Note that some droplets will be stripped of electrons during atomization creating a net positive charge. These droplets will move to the lower plate. We will focus on the former cases in which an excess of electrons reside on the droplets.
THE PROCEDURE
You will be provided with a detailed explanation of the lab procedure and equipment later. This summary is designed to give you a solid understanding of general concepts.
The atomizer is squirted into a small entrance hole near the top of the chamber. Through the microscope, you will be able to see many droplets falling at different rates. Adjust the focus and notice that some droplets come into view while others disappear as the focal plane is changed. If you toggle the high voltage switch to the plates, you will see some droplets move upward while others drop with increased speed.
Focus your attention on one droplet that is falling slow enough to remain in view for about 10 seconds. Toggle the plate voltage switch to make sure the droplet has a net negative charge. That is, it heads upward when the voltage is applied.
The terminal velocity for your chosen droplet is measured by recording the time required for the droplet to fall between two marks etched on the chamber's glass viewing window (fall time). These marks are well within the field of view. BEFORE the droplet drops out of sight, apply the voltage to the plates and record the time the droplet takes to travel between the etched marks on its upward journey (rise time). Repeat this procedure until you lose the droplet. Often the upward travel time will change as the droplet loses electrons. Eventually the droplet will lose all of its charge and it will drop out of sight. If you are lucky, you will get many different rise times from one droplet. If not, go find another one.
THE CALCULATIONS
Whether rising or falling, the droplet achieves terminal velocity very quickly. We will use Stokes's Law for the viscous drag of the air on the droplet. At terminal velocity, the net force on the droplet is zero, so we have,
| Ftotal = Fdrag - mg = 6(pi)£rv1 - mg | (falling) |
| Ftotal = -Fdrag - mg + qE = -6(pi)£rv2 - mg +Ed | (rising) |
Note that £ is the viscosity of air. The electric field (E) can be found from the voltage across the plates and plate separation, E = V/d. The radius of the droplet cannot be easily measured directly, so we use Stokes's Law again for a drop at terminal velocity to obtain,
where D is the density of oil and D' is the density of air. From this, the radius is
The charge on any droplet is Q = nqe where n = the number of electrons on the droplet during any particular "run".
You will find v1 (falling velocity) for the droplet and then start collecting data for the value(s) of v2 (rising velocity). Examining the values of Q for all the droplets, you will look for the smallest common integer multiple of all the values. For example, suppose the values of Q (in units of 10-19 C) are 4.8, 8.0, and 9.6. A little calulator work will show that these numbers are in the ratio of 3:5:6. So the value corresponding to one unit of charge will be 4.8/3 = 1.6.
Greater detail concerning the procedure and operation of the Millikan Oil Drop apparatuses will be provided in the lab. You will spend several hours in the dark looking through a microscope. So get a good night's rest!