MILLIKAN'S OIL DROP EXPERIMENT

1. Quantization of charge

In 1910, Robert Millikan of the University of Chicago published the details of an experiment that proved beyond doubt that charge was carried by DISCRETE positive and negative entities each of which had an equal magnitude.

He was also able to measure the unitary charge (which we now recognise to be the ELECTRON) accurately. This experiment is considered to be one of the most significant ever carried out, and Millikan received the Nobel Prize in 1923.

(See the background to the experiment).

2. The oil drop experiment

Millikan began by repeating the experiments of the Cavendish laboratory and ultimately, with penetrating experimental insight, built the apparatus below in 1909:

The atomizer produced a fine spray of oil droplets with a radius of about 1 Ám. Many of the droplets were charged. Occasionally a droplet fell through the pinhole. If the droplet was charged, it could be brought to a halt and held stationary by applying a voltage across the metal plates.

When the droplet was stationary, the force exerted by the electrostatic field, EQ (where E is the field and Q is the charge on the droplet), was equal to the weight of the droplet, mg, where m is its mass and g the acceleration due to gravity.

E can be calculated by measuring the voltage across the plates.

How do we measure the mass of this very tiny oil drop?

3. The electronic charge as a discrete quantity

The charge on the trapped droplet could be altered by briefly turning on the X-ray tube. When the charge changed, the forces on the droplet were no longer balanced and the droplet started to move.

The field was then altered by changing the applied voltage V, until the droplet was again motionless. This procedure was repeated many times and the voltages required to hold the droplet tabulated.

On analyzing his readings, Millikan found that the changes in the charges were always integral multiples of 1.602 x 10-19 C. Also, the total charge on the droplet was always an integral multiple of this quantity.

Since negative and positive changes in charge were always multiples of the same quantity, it was possible to conclude that the elementary carriers of both positive and negative charge had the same magnitude, namely 1.602 x 10-19 C.


Background to Millikan's oil drop experiment

At the beginning of the 20th century, there was no established model of the atom. It was generally believed that atoms were indivisible although this notion was being seriously challenged by the discovery of radioactivity.

For example, one could follow the course of the decay of radioactive elements such as radium in Wilson's "cloud chamber", where α-particles left a trail as a condensation track in saturated vater vapour.

Faraday's laws of electrolysis, which were discovered around 1840, provided strong evidence for the quantization of charge, but Faraday himself never supported the idea of an elementary charge. His idea was that charge, like mass, was an infinitely divisible quantity.

This view was strongly supported by Prof. James Clark Maxwell who had expressed the behaviour of electric and magnetic fields in mathematical form. Indeed, Maxwell had written in 1873:

"It is strongly improbable that when we come to understand the true nature of electrolysis we shall retain in any form the theory of molecular charges, for then we shall have obtained a secure basis on which to form a true theory of electric currents and so become independent of these provisional hypotheses."

This was an expression of the prevailing view from 1840 to 1900 that charge was a manifestation of "strain in the ether".

However, the laws of electrolysis could not be satisfactorily reconciled with this view, and by 1891, Prof. G Johnstone Stoney was actively promoting the idea of indivisible units of charge and had introduced the word ELECTRON to describe these charges. By 1890 Sir Joseph Thompson and his pupils at the Cavendish Laboratory in Cambridge were well advanced with their studies of cathode rays and conduction in gases. They had developed a model of light negative "corpuscles" being detached from atoms, leaving positively charged ions which were responsible for electrical conductivity in gases.

Their efforts to prove that there was a fundamental unit of charge had been frustrated by experimental difficulties. But by 1903 they had devised several methods for measuring charge that were similar to that ultimately used successfully by Millikan.


Faraday's laws of electrolysis

Faraday's first law may be stated as follows:

Faraday's First Law of Electrolysis
"The amount of any substance deposited, evolved, or dissolved at an electrode is directly proportional to the amount of electrical charge passing through the circuit."

Faraday's second law may be stated as follows:

Faraday's Second Law of Electrolysis
"The mass of different substances produced by the same quantity of electricity are directly proportional to the molar masses of the substances concerned, and inversely proportional to the number of electrons in the relevant half-reaction."


How do we measure the mass of the oil drop?

We have seen that the charge, Q, on the oil drop is equal to dmg, where d is the distance between the plates, m the mass of the oil drop, and g the acceleration due to gravity.

From this equation it can be seen that the charge can be determined if the mass is known. The problem is to determine accurately the mass of this microscopic oil drop!

Consider an oil droplet moving through air. When it is subject to a nett force, it accelerates. As it accelerates through the air, it encounters frictional forces with air molecules.

These forces are proportional to the velocity. Soon the frictional forces become equal to the accelerating force, so that the droplet experiences no nett force and it moves with a constant TERMINAL VELOCITY.


When the electric field holding the droplet stationary was turned off, only the gravitational force acted on the droplet (see diagram on the right).

Thus, the droplet accelerated under gravity, and reached its terminal velocity. This happened when all the frictional forces were equal to the gravitational forces (see diagram on the right):

In this way, by measuring the terminal velocity, Millikan could determine the value of the mass m from the relationship m = kv/g.