The Millikan Oil Drop Experiment: Measuring the Charge of a Single Electron

Historical Context and the Apparatus

By the early twentieth century, physicists suspected that electric charge might come in discrete units carried by electrons, but no one had directly measured how large that unit was. Robert Millikan and his student Harvey Fletcher set out to settle the question experimentally. Their apparatus, built between 1909 and 1913, was remarkably simple in concept. A fine atomizer sprayed a mist of tiny oil droplets into a chamber above two flat, horizontal metal plates. The friction of being forced through the atomizer's nozzle left many droplets with a small electric charge, a handful of electrons either stripped away or added. A few droplets would drift down through a small hole into the space between the plates, where an observer watched them through a horizontal microscope. To vary and control the charge on the droplets further, Millikan often used a source of X-rays or radioactive material to ionize the surrounding air, which let charged ions attach to or detach from a droplet mid-experiment. The two plates could be connected to a battery, creating a strong, adjustable vertical electric field inside the chamber. This combination of a viewing microscope, a controllable electric field, and a supply of individually charged oil droplets gave Millikan everything he needed to isolate and study one droplet at a time under carefully controlled conditions.

Balancing Forces and Using Stokes' Law

The heart of Millikan's method was a careful balance of forces acting on a single oil droplet. With the electric field switched off, a charged droplet would fall slowly through the air under gravity, quickly reaching a constant terminal velocity where the downward pull of gravity, reduced slightly by the buoyant force of the air pushing up on it, exactly matched the upward drag of air resistance. Because the droplets were so small, this drag followed Stokes' law, which relates the viscous drag force on a tiny sphere to its radius, its velocity, and the viscosity of the surrounding air. By timing how long a droplet took to fall a measured distance, Millikan could calculate its terminal velocity and, from Stokes' law, work backward to find the droplet's radius, and from that its mass, since oil's density was already known. Next, Millikan switched on the electric field between the plates and adjusted its strength until the upward electric force on the droplet's charge exactly balanced the net downward force of gravity minus buoyancy, causing the droplet to hang perfectly suspended, motionless, in the microscope's field of view. Sometimes he instead adjusted the field so the droplet rose or fell at a slow, measurable terminal velocity, which gave an equivalent but independently checkable calculation. Because he already knew the droplet's mass from the free-fall measurement, and he could read off the strength of the electric field from the voltage and plate separation, the balance equation let him solve directly for the electric charge sitting on that one droplet.

The Key Discovery: Charge Is Quantized

Millikan and Fletcher repeated this force-balancing measurement on droplet after droplet, sometimes changing a droplet's charge mid-run by exposing it to ionizing radiation and watching it jump to a new equilibrium. Across hundreds of careful trials, a striking pattern emerged. No matter which droplet was measured or how many times its charge was altered, the resulting charge value was never arbitrary. Instead, every single measurement came out extremely close to a whole-number multiple of one particular smallest value. That smallest value, the elementary charge, worked out to approximately 1.6 times 10 to the negative 19 power coulombs. A droplet might carry one, two, three, or any other whole number of these units, but it was never observed carrying one and a half units, or two point seven units, or any other fractional amount. This was the first direct experimental proof that electric charge does not vary smoothly like a continuous fluid, but instead comes packaged in fixed, indivisible portions, each equal to the charge of a single electron.

Why Quantization Mattered for Atomic Physics

The discovery that charge is quantized, meaning it exists only in discrete, indivisible units rather than being continuously divisible, was far more than a technical curiosity. It gave physicists their first solid numerical anchor for describing the electron itself, and by extension, the structure of the atom. Once the elementary charge was known precisely, it could be combined with other measured quantities, such as the charge to mass ratio of the electron that J. J. Thomson had already measured in his cathode ray experiments, to calculate the electron's actual mass for the first time. This result also reinforced the emerging picture of matter as built from discrete particles rather than continuous substances, a theme that would soon become central to quantum mechanics. If charge came in fixed indivisible units, it suggested that the underlying particles carrying that charge were themselves fundamental and countable, not arbitrarily divisible. Millikan's measurement of the elementary charge became one of the fundamental constants of physics, used ever since in calculations spanning chemistry, electronics, and particle physics, and it remains a standard experiment that physics students still recreate today to appreciate how such a small, invisible quantity was first pinned down through careful, patient observation.

A Worked Numeric Example

Imagine Millikan recorded the charge on five different oil droplets during a single session, expressed here in coulombs to illustrate the pattern he observed. The first droplet showed a charge of about 3.2 times 10 to the negative 19 power coulombs. The second showed about 4.8 times 10 to the negative 19 power coulombs. The third showed about 1.6 times 10 to the negative 19 power coulombs. The fourth showed about 8.0 times 10 to the negative 19 power coulombs, and the fifth showed about 6.4 times 10 to the negative 19 power coulombs. Dividing each of these values by the elementary charge of approximately 1.6 times 10 to the negative 19 power coulombs reveals the underlying pattern immediately. The first droplet carried exactly 2 units of charge, the second carried 3 units, the third carried just 1 unit, the fourth carried 5 units, and the fifth carried 4 units. Every single droplet, regardless of its size or how it was charged, landed precisely on a small whole-number multiple of the same base value. It was exactly this kind of clean, repeatable arithmetic, appearing again and again across hundreds of droplets, that convinced Millikan he had found the true, indivisible unit of electric charge.

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