This material is protected under all copyright laws, as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the author.

⧉ Millikan's Oil Drop Experiment

In 1909, Robert Millikan and Harvey Fletcher conducted the oil drop experiment to determine the charge of an electron. Before this experiment, existence of subatomic particles was not universally accepted. Electron is a subatomic particle having a negative charge and orbiting the nucleus; the flow of electrons in a conductor constitutes electricity.

They suspended tiny charged droplets of oil between two metal electrodes by balancing downward gravitational force with upward drag and electric forces. The density of the oil was known, so Millikan and Fletcher could determine the droplets' masses from their observed radii (since from the radii they could calculate the volume and thus, the mass). Using the known electric field and the values of gravity and mass, Millikan and Fletcher determined the charge on oil droplets in mechanical equilibrium. By repeating the experiment, they confirmed that the charges were all multiples of some fundamental value. They calculated this value to be 1.5924 × 10−19 Coulombs (C), which is within 1% of the currently accepted value of 1.602176487 × 10−19 C.

∘ Therefore they proposed it was the charge of a single electron ∘ Experimental setup and Theory - An experimental setup of Millikan’s experiment to determine the change in oil drop is shown in figure. The apparatus incorporated a pair of metal plates and a specific type of oil. Millikan and Fletcher discovered it was best to use an oil with an extremely low vapor pressure, such as one designed for use in a vacuum apparatus. Ordinary oil would evaporate under the heat of the light source, causing the mass of the oil drop to change over the course of the experiment.

Picture 1 - Simplified scheme of Millikan’s Oil Drop Experiment

This material is protected under all copyright laws, as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the author.

Picture 2 - Simplified scheme of Millikan’s Oil Drop Experiment

At first, clock oil which is non volatile is allowed to fall drop wise from the opening of upper plate with the help of atomizer. A fine mist of oil droplets was sprayed into a chamber above the plates. The oil drops become electrically charged through friction with the nozzle as they are sprayed. Alternatively, charge can be induced by including an ionizing radiation source (such as an X-ray tube). The whole apparatus is kept inside double walled chamber inside which water is circulated for cooling purpose. The chamber consists of 2 windows. Window W1 allows visible light to pass and window W2 allows X-ray (to ionize the oil drop) to pass. The upper plate is connected with positive terminal of battery and lower plate is earthed i.e. kept at negative potential. The droplets enter the space between the plates and, because they are charged, they can be controlled by changing the voltage across the plates.

Initially, the oil drops are allowed to fall between the plates with the electric field turned off. They quickly reach terminal velocity 𝑣𝑇 = 𝑣1 due to friction with the air in the chamber.

At this condition, at equilibrium, the drop experiences following forces,

Weight 𝑚𝑔 of an oil drop is downward. If the density of oil is 𝜌 and radius of an oil drop is 𝑟 then its

volume is 43

𝜋𝑟3𝜌; so we have 𝑊 = 𝑚𝑔 = 43

𝜋𝑟3𝜌𝑔; Now up thrust of air 𝑈 = 43

𝜋𝑟3𝜎 is upward where 𝜎 is

the density of air. Again we have upward viscous force or drag force 𝐹1 = 6𝜋𝜂𝑟𝑣1. Therefore we can write

𝐹1 + 𝑈 = 𝑊 or 6𝜋𝜂𝑟𝑣1 +

43

𝜋𝑟3𝜎𝑔 = 43

𝜋𝑟3𝜌𝑔

or 𝑟 = � 9𝜂𝑣1 2(𝜌−𝜎)𝑔

------------------ (i)

From this equation we get the radius of the oil drop. Now the second step comes into picture. Electric field will be applied between the two plates. The charged oil drop will attain terminal velocity 𝑣2. The field is turned on and if it is large enough then some of the drops (the charged ones) will start to rise. This is because that the upwards electric force 𝐹𝐸 is greater than the downward gravitational force 𝑚𝑔. We have upward viscous force or drag force 𝐹2 = 6𝜋𝜂𝑟𝑣2. We can write

𝐹𝐸 + 𝑈 = 𝑊 + 𝐹2

or 𝑞𝐸+ 43

𝜋𝑟3𝜎𝑔 = 43

𝜋𝑟3𝜌𝑔 + 6𝜋𝜂𝑟𝑣2------------------ (ii)

This material is protected under all copyright laws, as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the author.

From this equation (ii) putting the value of 𝑟 we can find out the value of charge 𝑞. Different observations on different oil drops of different sizes verify that charge is integral multiple of 𝑒 i.e. 𝑞 = ±𝑛𝑒 where 𝑛 is an integer.

∘ So charge is quantized in nature ∘