The Charge on the Electron Was Calculated By Millikan: Interactive Calculator
The charge on the electron was famously calculated by Robert A. Millikan through the oil drop experiment. Use the calculator below to estimate the elementary charge by dividing a measured total charge by the number of excess electrons. You can also compare your result against the accepted SI value.
Formula used: elementary charge magnitude e = |Q| / n, where Q is the measured total charge in coulombs and n is the number of excess electrons. Accepted value of e is 1.602176634 × 10^-19 C.
The Charge on the Electron Was Calculated By Robert A. Millikan
If you are asking, “the charge on the electron was calculated by whom?”, the accepted historical answer is Robert Andrews Millikan, whose celebrated oil drop experiment produced the first convincing and precise measurement of the elementary electric charge. His work showed that electric charge is quantized, meaning it occurs in discrete packets rather than any arbitrary amount. That packet is the elementary charge, now denoted by e, with the exact SI value of 1.602176634 × 10^-19 coulomb.
Millikan’s experiment is one of the great landmarks in modern physics because it connected abstract electromagnetic theory with direct laboratory evidence. Before his work, scientists had good reason to suspect that atoms and subatomic particles carried definite charges, but they lacked a clean, persuasive way to measure that fundamental unit. By observing charged oil droplets suspended between electric plates, Millikan was able to infer that each droplet’s charge was always a whole-number multiple of the same tiny value. That repeated value was the charge of the electron in magnitude.
Why Millikan’s Result Mattered So Much
The importance of this discovery goes far beyond one number in a textbook. Measuring the electron’s charge helped establish the particle picture of matter, supported the developing atomic model, and allowed later physicists to calculate other constants. Once the elementary charge was known, researchers could combine it with measurements of charge-to-mass ratio from J.J. Thomson’s cathode ray studies to estimate the electron’s mass. In other words, Millikan’s work did not stand alone; it unlocked additional pieces of the subatomic puzzle.
This was also a major victory for experimental technique. Measuring a quantity as tiny as 10^-19 coulomb in the early 20th century required extraordinary care. Millikan’s setup accounted for gravity, electric force, drag, and droplet motion. His experimental design showed that precision science is often about reducing noise, controlling variables, and repeating measurements until a pattern becomes undeniable.
How the Oil Drop Experiment Worked
In the oil drop experiment, very small droplets of oil were sprayed into a chamber between two electrically charged plates. Some of these droplets picked up electric charge, often due to friction or ionization. Under normal conditions, a droplet falls because of gravity. But by applying an electric field between the plates, Millikan could create an upward electric force that opposed the droplet’s weight. By adjusting the voltage carefully, he could make a droplet slow down, rise, or even remain suspended nearly motionless.
The basic physics is elegant. A charged droplet in an electric field experiences an electric force given by:
F = qE
Here, q is the droplet’s charge and E is the electric field strength. Gravity pulls the droplet downward with force:
F = mg
By balancing these forces, Millikan could solve for the droplet’s charge. Once he repeated the process for many droplets, he found that the values were not random. They clustered around multiples of a smallest common amount. That smallest amount corresponded to the electron’s charge magnitude.
Key steps in the method
- Generate tiny oil droplets inside a viewing chamber.
- Allow droplets to become electrically charged.
- Observe their motion through a microscope.
- Apply a known voltage across two plates to create an electric field.
- Adjust the field until a droplet is stationary or moves at a known speed.
- Calculate the droplet’s charge from the balance of forces.
- Compare many droplets and identify a smallest repeating charge value.
What the Calculator on This Page Does
The calculator above is a simplified educational model inspired by Millikan’s result. Instead of asking you to derive the droplet charge from electric field and force balance, it lets you input a measured total charge and the number of excess electrons associated with that charge. It then computes:
e = |Q| / n
In this formula, Q is the total measured charge in coulombs and n is the number of electrons. The result is your estimate of the elementary charge. The calculator then compares your estimate to the modern accepted SI value and displays the percentage error. This is useful for classroom demonstrations, lab summaries, and conceptual understanding of charge quantization.
- Total charge: the overall charge measured on an object or droplet.
- Number of excess electrons: the whole-number count of electrons responsible for the charge.
- Accepted value: 1.602176634 × 10^-19 C.
- Percent error: how far your estimate differs from the accepted value.
Millikan vs Thomson: Who Did What?
Students often confuse the roles of J.J. Thomson and Robert Millikan. Thomson discovered the electron through cathode ray experiments and measured its charge-to-mass ratio, commonly written as e/m. Millikan, by contrast, measured the charge e itself. Once those two pieces were known, the mass m of the electron could be calculated.
| Scientist | Major Contribution | Approximate Year | Why It Was Important |
|---|---|---|---|
| J.J. Thomson | Measured electron charge-to-mass ratio and identified the electron | 1897 | Showed cathode rays were made of negatively charged particles smaller than atoms |
| Robert A. Millikan | Measured the elementary charge using oil drops | 1909 to 1913 | Demonstrated charge quantization and enabled calculation of electron mass |
| Modern SI | Defined elementary charge exactly | 2019 | Made e an exact defining constant for the ampere and SI electrical metrology |
This distinction is critical. If a test question asks, “The charge on the electron was calculated by whom?” the standard answer is Millikan. If it asks, “Who discovered the electron?” the answer is J.J. Thomson. If it asks, “Who determined e/m?” that is also Thomson.
Accepted Value and Real Statistics
Today, the elementary charge is not just measured approximately; it is built into the structure of modern units. Since the 2019 SI redefinition, the elementary charge has an exact value:
e = 1.602176634 × 10^-19 C exactly
Historically, however, the measured value improved over time as laboratory methods became more refined. Early 20th-century experiments produced values very close to the modern one, but instrumentation limits, air viscosity corrections, droplet behavior, and statistical treatment all affected precision.
| Quantity | Value | Unit | Use in Physics |
|---|---|---|---|
| Elementary charge, e | 1.602176634 × 10^-19 | C | Fundamental unit of electric charge |
| Electron mass, me | 9.1093837015 × 10^-31 | kg | Mass of the electron |
| Electron charge-to-mass ratio, e/m | 1.75882001076 × 10^11 | C/kg | Links charge and mass in particle dynamics |
| Faraday constant, F | 96485.33212 | C/mol | Total charge per mole of electrons |
| Avogadro constant, NA | 6.02214076 × 10^23 | mol^-1 | Number of entities in a mole |
These values are tightly connected. For example, the Faraday constant can be interpreted as the charge carried by one mole of electrons, and it is directly related to the elementary charge through Avogadro’s constant. This is one reason Millikan’s work had effects far beyond atomic physics; it also influenced chemistry, electrochemistry, and precision metrology.
Why Charge Quantization Was a Breakthrough
One of Millikan’s deepest insights was not merely a numerical value but a pattern: charges appeared in integer multiples of a basic unit. If one droplet had charge q and another had 2q, 3q, or 4q, then electric charge behaved like a countable quantity. This quantization strongly supported the existence of a fundamental charge carrier.
In modern physics, this idea is foundational. Electrons, protons, ions, and many particle interactions are described using discrete charge units. Even though macroscopic objects can have a broad range of total charges, those total charges are built from combinations of elementary charged particles. Millikan’s experiment gave direct laboratory evidence of that principle.
Why students still study this experiment
- It demonstrates the balance of gravitational and electric forces.
- It shows how indirect measurement can reveal fundamental constants.
- It provides one of the clearest examples of quantization in introductory physics.
- It connects experimental observation to particle theory.
- It illustrates how repeated data points can uncover a hidden rule.
Common Misconceptions
1. Millikan discovered the electron
This is incorrect. J.J. Thomson discovered the electron. Millikan measured its charge.
2. The charge of an electron is positive
The electron carries a negative charge. When physicists quote the elementary charge e, they often mean the positive magnitude. The electron’s actual charge is -e.
3. The oil drop experiment directly counted electrons one by one
Not exactly. Millikan inferred the elementary charge by measuring droplet charges and noticing they appeared as whole-number multiples of a smallest value.
4. Any measured charge is acceptable
In the context of quantization, physically meaningful isolated charges should typically correspond to integer multiples of the elementary charge. If your measured value does not do so closely, it usually indicates experimental uncertainty or a modeling issue.
How to Use This Topic in Exams and Academic Writing
If you encounter the phrase “the charge on the electron was calculated by,” the safest concise answer in exams is:
For longer answers, mention that Thomson had already determined the electron’s charge-to-mass ratio, while Millikan’s contribution was the direct measurement of charge. In university-level writing, it is also good practice to mention the significance of charge quantization and the fact that the modern SI now fixes the value of the elementary charge exactly.
Authoritative Sources for Further Reading
- NIST: Value of the elementary charge
- Encyclopaedia Britannica: Robert A. Millikan biography
- The Physics Classroom: Charge and Charge Carriers
- Rice University: Thomson and e/m historical notes
- Nobel Prize: Facts on Robert A. Millikan
For strict .gov or .edu references, the most useful links are the NIST elementary charge page and the Rice University educational materials. Those sources are especially suitable when you need academically credible citations.