Oil Drop Experiment

The Oil Drop Experiment was performed by the American physicist Robert A Millikan in 1909 to measure the electric charge carried by an electron. Their original experiment or any modifications thereof to reach the same goal, are termed as oil drop experiments, in general.

Oil Drop Experiment
Oil Drop Experiment

Millikan’s Oil Drop Experiment


In the original version, Millikan and one of his graduate students, Harvey Fletcher, took a pair of parallel horizontal metallic plates. A uniform electric field was created in the intermediate space by applying a potential difference between them. The plates were held apart by a ring of insulating material. The said ring had four holes, three for allowing the setup to be illuminated by a bright source of light and the fourth one was to allow a microscope for viewing. A closed chamber with transparent walls was fitted above the plates.

At the beginning of the experiment, a fine mist of oil droplets were sprayed into the chamber. In modern setups, an atomizer can be used to achieve the end. The oil was so chosen such that it had a very low vapor pressure and of the type used in vacuum apparatus. Some of the oil drops became electrically charged by friction as they forced their way out of the nozzle. Alternatively, charging could also be induced by incorporating a source of ionizing radiation, such as an X-Ray tube, in the apparatus. The droplets thus entered the space between the plates and could be made to rise or fall according to the requirement by varying the plate voltage.

Millikan Oil Drop Experiment
Millikan Oil Drop Experiment

Method Summary

In terms of a simulated present-day arrangement, when the electric field is turned off, the oil drops fall between the plates under the action of gravity only. The friction with the oil molecules in the chamber makes them reach their terminal velocity fast. The terminal velocity is the velocity of a body in the absence of any electric field. Once the field is turned on, the charged ones start to rise. This happens since the electric force directed upwards is stronger than the gravitational force acting downwards. One such drop is selected and kept at the center of the field of view of the microscope after allowing all other drops to fall by alternately switching off the voltage source. The experiment is conducted with this drop.

Theory and Calculations

First, the oil drop is allowed to fall in the absence of an electric field and its terminal velocity, say v1, is found out. Using Stokes’ law, the drag force acting on the drop is calculated using the following formula.

F_{d}=6pi reta v_{{1}}

Here r is the radius of the drop and ɳ, the viscosity of air.

The weight of the drop, w’, which is the product of its mass multiplied by the acceleration due to gravity g, is given by the equation,

  w^{'}=frac{4}{3}pi r^{3}rho g 

where ρ is the density of the oil.

However, what we need here is the apparent weight w of the drop in air given by the difference of the true weight and the upthrust of the air. We can express w  by the following formula.

 w =frac{4}{3}pi r^{3}(rho-rho_{air}) g                     ——-(i)

Here ρair denotes the density of air.

When the drop attains terminal velocity, then it has no acceleration. Hence, the total force acting on it must be zero. That means,


or, 6pi reta v_{1}=frac{4}{3}pi r^{3}(rho-rho_{air}) g

or,  r^{2}=frac{9eta v_{1}}{2g(rho-rho_{air})}

The above equation can be used to find out the value of r. Once r is calculated the value of w can easily be found out from equation (i) marked above.

Oil Drop Experiment Free Body Diagram
Oil Drop Experiment Free Body Diagram

Now on turning on the electric field between the plates, the electric force FE acting on the drop is,


Where E is the electric field and q the charge on the drop. For parallel plates, the formula for E is,


Here V is the potential difference and d the distance between the plates. That implies,


Now if we adjust V to make the oil drop remain steady at a point, then


or, qfrac{V}{d}=frac{4}{3}pi r^{3}(rho-rho_{air})g

or, q=frac{4}{3}pi r^{3}frac{d}{V}(rho-rho_{air})g
Thus, the value of q can be calculated.  By repeatedly applying this method to multiple oil droplets, the electric charge values on individual drops were always found to be integer multiples of the smallest value. This lowest charge could be nothing but the charge on the elementary particle, electron. By this method, the electronic charge was calculated to be approximately, 1.5924×10−19 C, making an error of 1% of the currently accepted value, 1.602176487×10−19 C. All subsequent researches pointed to the same value of charge on the fundamental particle.

Millikan’s Oil Drop Experiment Conclusion

The experimental results confirm that charge is quantized in nature. The value of the fundamental unit of charge, or the charge on a single electron could also be calculated from it.

Robert Millikan’s Oil Drop Experiment Animation

Millikan’s Oil Drop Experiment and the Atomic Theory

Until the time of the Oil Drop Experiment, the world had little or no knowledge of what is present inside an atom. Earlier experiments by the English Physicist J.J. Thomson had shown that atoms contain some negative charged particles of masses significantly smaller than that of the hydrogen atom. Nevertheless, the exact value of the charge carried by these subatomic particles remained in the dark. In fact, the very existence of these particles was not accepted by many due to lack of concrete evidence. Thus, the atomic model was shrouded in mystery. In this scenario, with Millikan’s groundbreaking effort to quantify the charge on an electron, the atomic theory came of age in the early years of the twentieth century.

Controversy about the Oil Drop Experiment and Discovery

The famous scientist, Millikan was the sole recipient of the Nobel Prize in Physics in the year 1923 for both his work in the classic experiment discussed as well as contributions to the research in photoelectric effect. Fletcher’s work on the oil drop project, however, was not recognized. Many years later, the writings of Fletcher revealed that Millikan wished to take the sole credit for the discovery in exchange of granting him a Ph.D. and helping him secure a job after his graduation.

The beauty of the oil drop experiment lies in its simple and elegant demonstration of the quantization of charge along with measuring the elementary charge on an electron that finds widespread applications to this day. With the progress of time, considerable modifications have been made to the original setup resulting in obvious perfection in the results. Still, no substantial deviation from the results of the classical experiment could yet be found.







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