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At the same time it was generally believed that electric charge, like mass, was infinitely divisible.
To explain the connection between electricity and matter, some scientists in the late 19th century argued that there had to be a fundamental unit of electricity. In 1891 the Irish physicist, George Stoney, introduced the term “electron” to describe this smallest unit of negative charge.
In 1897 J. J. Thomson, an English physicist, conducted a series of experiments on cathode rays and after observing that the beam of light in the cathode ray tube is attracted to a positive charge and repelled by a negative charge he concluded that the rays consist of a stream of small, electrically negatively charged particles which have a mass over a thousand times less than that of a hydrogen atom. Thomson has discovered the electron. From this point onward, it becomes increasingly clear that atoms are not fundamental particles, but in fact are made up of smaller particles.
As a result of his experiments, Thomson was able to measure the charge to mass ratio of the electron; he could not however, measure accurately the charge or mass independently.
The measurement of the electron's charge independently was achieved by Millikan by his famous experiment from 1909 and with Thomson's results also a value for the electron mass was obtained.
This experiment is called the "oil-drop experiment" and it was the first successful scientific attempt to detect and measure the effect of an individual subatomic particle.
For this and his work on the photoelectric effect Robert Millikan won the 1923 Nobel Prize in physics.
The scheme of the experiment is as follows: An atomizer sprayed a fine mist of oil droplets into the upper chamber. Some of these tiny droplets fell through a hole in the upper floor into the lower chamber of the apparatus. Millikan first let them fall until they reached terminal velocity due to air resistance. Using the microscope, he measured their terminal velocity, and by use of a formula, calculated the mass of each oil drop.
Next, Millikan applied a charge to the falling drops by irradiating the bottom chamber with x-rays. This caused the air to become ionized, which basically means that the air particles lost electrons. A part of the oil droplets captured one or more of those extra electrons and became negatively charged.
By attaching a battery to the plates of the lower chamber he created an electric field between the plates that would act on the charged oil drops; he adjusted the voltage till the electric field force would just balance the force of gravity on a drop, and the drop would hang suspended in mid-air. Some drops have captured more electrons than others, so they will require a higher electrical field to stop.
Particles that did not capture any of that extra electrons were not affected by the electrical field and fell to the bottom plate due to gravity.
When a drop is suspended, its weight  m · g  is exactly equal to the electric force applied, the product of the electric field and the charge q · E.
The values of E (the applied electric field), m (the mass of a drop which was already calculated by Millikan), and g (the acceleration due to gravity), are all known values. So it is very easy to obtain the value of q, the charge on the drop, by using the simple formula:
Millikan repeated the experiment numerous times, each time varying the strength of the x-rays ionizing the air, so that differing numbers of electrons would jump onto the oil molecules each time. He obtained various values for q.
The charge q on a drop was always a multiple of 1.59 x 10-19 Coulombs. This is less than 1% lower than the value accepted today: 1.602 x 10-19 C.
Warning: This experiment should be performed under teacher or adult supervision familiar with chemical, electricity and safety procedures.
In the original experiment, Millikan ionized the air with x-rays which could be very dangerous and can harm your health. Today, in similar experiments are used instead low level alpha particles emitted from thorium-232 to ionize the air. Thorium-232 is now classified as carcinogenic and also poses hazards to the user.
Our sound advice is to use an established laboratory facility in order to perform safely this experiment.
This experiment requires some mechanics, physics, and electricity skills, and it is rather expensive and difficult to do properly, but not too much to deter a determined student.
Read carefully the experiment links and ensure that you understand the basic principles. Brows further the web and consult your local library. Consider to buy an oil-drop experiment kit for your experiment - scientific supplies links are provided in the link section.
Consult your teachers and other knowledgeable adults and experts before you begin.
The Oil-Drop Experiment
Millikan's Oil-Drop Experiment - Bill Willis
Millikan Oil-Drop Experiment - Catharine H. Colwell - PhysicsLab
Determination of the Charge on an Electron - John L. Park
Millikan Oil-Drop Apparatus - PASCO
Robert Andrews Millikan 1868-1953 - AIP
Millikan's Oil-Drop Experiment - University of Dresden
The Millikan Oil-Drop Experiment - University of Toronto
In Defense of Robert Andrews Millikan - California Institute of Technology
Millikan's Experiment - Thinkquest
Millikan's Oil-Drop Experiment - G R Delpierre, B T Sewell, Physichem
Oil-Drop Experiment - Wikipedia
Millikan Oil-Drop Experiment - Mike Lee and Lee Burnett, Davidson College
Measuring e: Using the Millikan Apparatus
Oil-Drop Experiment Simulations
Millikan's Oil-Drop Experiment Simulation - Magnus Karlsson
Buy an Oil-Drop Experiment Kit
Millikan Oil Drop Apparatus - PASCO
Robert Millikan Biographies
Robert Andrews Millikan- The Nobel Foundation
Robert Andrews Millikan (1868-1953) - AIP
Robert Andrews Millikan - Corrosion Doctors
J.J. Thomson and the Discovery of the Electron
The Discovery of the Electron - AIP
Electrons in Atoms - Science Museum
A Breief History Of The Electron - Peter Richards
Atomic Structure: Development of the Atom - Thinkquest
The Discovery of the Electron - John L. Pollock, University of Arizona
The Electrons - Paul Charlesworth, Michigan Tech
J. J. Thomson: Cathode Rays - Carmen Giunta, Le Moyne College