How Scientists Determine the Mass of an Electron
The Electron mass is a fundamental particle that was first discovered in 1897 by J.J. Thomson during investigations into cathode rays. Electrons are elementary particles that carry a negative electric charge and are found in all atoms. Determining the precise mass of the electron has been an important endeavor in physics, as the mass is a fundamental property that affects the electron’s behavior and interactions.
Knowing the mass allows physicists to calculate the precise energy levels in atoms, model atomic and molecular bonds, compute crosssections for particle interactions, and make accurate predictions in quantum electrodynamics. In addition, establishing the mass provides insights into the deeper nature of the electron itself and its relationship to other particles.
Attempts to measure the mass of the electron have spanned over a century, utilizing ingenious experimental techniques and leading to ever more precise values. While challenging, precisely determining the mass has enabled breakthroughs across many fields of physics. This article will overview the key experiments that paved the way to the Mass of an electron value we use today.
Early Measurements
The first experiments to determine the mass of the electron emerged in the late 19th century from investigations into cathode rays. In 1897, British physicist J.J. Thomson conducted a series of experiments using cathode ray tubes, which consist of a sealed glass tube with electrodes at either end. When a voltage is applied across the electrodes, cathode rays are generated – a stream of electrons that travel from the cathode to the anode.
By applying electric and magnetic fields, Thomson was able to deflect the cathode rays and calculate properties like the chargetomass ratio. This led to the realization that cathode rays were composed of tiny negatively charged particles, later named electrons. Though Thomson was unable to determine an exact mass, he established an upper limit of 1/1000 the mass of a hydrogen atom.
Further cathode ray experiments by other scientists including Philipp Lenard and Emil Wiechert refined this estimate. But the cathode ray method could not measure the electron mass to a high degree of accuracy. More precise techniques would be required to pin down the exact f the newly discovered electron.
Oil Drop Experiment
The first accurate measurement of the electron’s mass is credited to physicist Robert Millikan. In 1909, Millikan began a series of experiments at the University of Chicago to determine the charge of electrons.
His oil drop experiment involved spraying a mist of tiny oil droplets into a chamber containing an electrode. By applying a voltage, the droplets could be suspended against the pull of gravity.
By adjusting the voltage Millikan could make the droplets hover without rising or falling.
Millikan found that the charge on a given droplet was always a multiple of a fundamental unit, which he determined to be the charge on a single electron. From these observations, Millikan was able to calculate the charge on the electron. Knowing the charge and the mass of the oil droplets then allowed him to determine the mass of the electron.
In 1913, Millikan published his findings, reporting the charge on the electron to be 1.592 x 10^19 coulombs and the mass to be 9.109 x 10^28 grams. These values were remarkably close to the modern accepted values. His oil drop experiment provided the first accurate measurement of the electron’s mass and charge, confirming the particle nature of electric charge.
Cyclotron Experiments
In the 1930s, Ernest Lawrence and his colleagues at the University of California, Berkeley began using cyclotrons to make increasingly precise measurements of the electron mass. Cyclotrons accelerate charged particles like electrons in a spiral path using alternating electric fields. The frequency of the alternating fields that produces the most acceleration indicates the masstocharge ratio of the particle.
By improving the magnetic fields and vacuum conditions of their cyclotrons, Lawrence’s team was able to reduce errors and uncertainties in their electron mass measurements. M. Stanley Livingston made the first measurement in 1937 using a 27inch cyclotron, obtaining a value of 0.000552 amu. In 1938, Lawrence’s team used an upgraded 37inch cyclotron to refine this measurement further, achieving a precision of 0.000298 amu.
These cyclotron experiments demonstrated that particle accelerators could determine the electron mass at much higher precision than the earlier oil drop experiments. They paved the way for even more advanced accelerators that would pin down the electron mass to many more decimal places in the following decades. Lawrence received the Nobel Prize in Physics in 1939 in part for these pioneering electron mass measurements using cyclotron technology.
Magnetic Moment
The magnetic moment of the electron is directly related to its. The electron has an intrinsic magnetic dipole moment, meaning it behaves like a tiny bar magnet. This magnetic moment arises from the electron’s intrinsic spin.
In quantum mechanics, the electron is described as a spinning charged particle. This spin gives rise to angular momentum, and the resulting magnetic dipole moment is proportional to the angular momentum. Specifically, the electron’s magnetic moment (μe) is related to its spin angular momentum (S) by:
μe = ge * (e / 2me) * S
Where ge is the electron’s gfactor (approximately 2), e is the elementary charge, me is the electron mass, and ħ is the reduced Planck’s constant. This gfactor relates the electron’s magnetic moment to its spin.
Thus, by precisely measuring the electron’s magnetic moment, its mass can also be determined. In the 1940s, experimental physicists conducted precision measurements using molecular beam magnetic resonance. They directed a beam of free electrons through a nonuniform magnetic field, which causes the beam to split based on the magnetic moment. By measuring the splitting, they could calculate the electron’s magnetic moment to a high degree of accuracy.
From these measurements, the accepted value of the electron mass is 9.109 x 10^31 kg. The relation between magnetic moment and mass allows the to be determined from magnetic properties. Modern measurements continue to refine the precision, but the magnetic moment provides the most accurate method for determining the electron mass.
Current Defined Value
The currently accepted CODATA value for the mass of an electron is 9.1093837015(28) x 10^31 kg. This value has a relative standard uncertainty of 3.0 x 10^8.
The CODATA values are published by the Committee on Data for Science and Technology (CODATA) every 4 years. They are based on an evaluation of all available experimental and theoretical data related to a particular fundamental physical constant like the electron mass.
The latest CODATA value for electron mass comes from their 2018 publication. It is determined based on a least squares adjustment that accounts for the correlations between different input data. The number in parentheses indicates the uncertainty of the last two digits.
This highly precise value for electron mass allows physicists to make very accurate calculations in quantum electrodynamics and other areas of physics where the electron mass is a key parameter. The small uncertainty provides confidence that the calculations will be reliable. As measurement methods continue to improve, the CODATA values may shift slightly but generally converge on an accepted number.
Importance in Physics
Knowing the precise mass of the electron is crucial for making accurate calculations in many areas of physics. Here are some of the key reasons why the electron mass is so important:

Atomic and molecular calculations – The theory of atomic structure relies on the mass of electrons, as do calculations of molecular bonds and interactions. Even small variations in electron mass would throw off predictions of chemical reactions and quantum mechanics models.

Electricity and magnetism – The mass of the electron factors into electromagnetic equations and calculations involving current, voltage, resistance and other electrical concepts. Precise electron mass allows us to quantify electrical forces and effects.

Particle physics – When dealing with subatomic particles and forces between them, the mass of the electron is an essential input. Particle accelerators and colliders depend on exact electron mass to analyze results.

Astronomy and astrophysics – In areas like stellar evolution and cosmological models, the mass of the electron is necessary to account for interactions and processes. Tiny errors could accumulate to invalidate theories.

Fundamental constants – The electron mass is tied to basic physical constants like the elementary charge and Planck’s constant. Accurate electron mass allows precise determination of these fundamental constants.
So in summary, the electron mass value is woven throughout many areas of physics, both in theoretical models and experimental measurements. Even minute errors in electron mass would quickly compound, leading to inaccurate predictions and calculations. That is why so much effort has gone into measuring the electron mass as exactly as possible.
Future Directions
Efforts are underway to measure the of the electron with even greater precision using advanced experimental techniques and equipment. Scientists are motivated to achieve more accurate values as the mass of the electron has fundamental importance across many areas of physics.
One promising approach is using Penning traps. These devices use a combination of electric and magnetic fields to confine single electrons for extended periods. Researchers can then study the electron’s cyclotron frequency and magnetron motion to deduce its mass with very low uncertainties. Experiments with Penning traps at research facilities such as CODATA have recently reported electron mass measurements with precision down to around one part per trillion.
Additionally, new methods in quantum electrodynamics offer ways to determine the electron mass independently of the experiment. These techniques use advanced theoretical calculations of how electrons interact with the electromagnetic field. While computations are complex, they can provide very precise values for comparison with experimental results. Refining these quantum electrodynamics methods is an active area of research.
With these emerging techniques, scientists are optimistic they can measure the electron mass to even greater accuracy. More precise values would improve scientific understanding and provide enhanced precision for applications like defining standards and calibrating instruments. An accurate electron mass measurement will likely continue as an important goal for physicists well into the future.
Conclusions
The electron mass is a fundamental constant in physics, chemistry, and engineering. Though immeasurably small on a human scale, the electron mass has profound importance across scientific disciplines.
Key points about the electron mass include:

The electron mass is approximately 9.109 x 1031 kilograms. This extremely small mass enables electrons to behave like waves in many experiments.

The electron mass was first measured in oil drop experiments by Robert Millikan in 1909. Later cyclotron resonance experiments refined the value.

The electron mass determines the electron’s magnetic moment. Precise measurements of the magnetic moment led to the most accurate value for the mass.

The electron mass is defined to be exact in the current SI system of units. It helps define the kilogram and other units.

The electron mass appears in equations for quantum mechanics, atomic structure, chemistry, solidstate physics, and more. It enables calculations across disciplines.

Ongoing experiments aim to determine whether the electron mass is perfectly constant or changes slightly over time. Any variation could reveal new physics.
The remarkably small but finite mass of the electron has enabled many key scientific discoveries and technologies of the modern era. Though taken for granted, the electron mass is one of the most profound constants in our exploration of the physical world. Its influence stretches from the subatomic to the cosmic in scale.
References
This article presents factual information about the mass of the electron without citing any sources. As the author, I aimed to summarize current scientific knowledge on this topic by synthesizing information from my own background knowledge. However, to uphold principles of academic integrity, I acknowledge that factual statements should be attributed to their original sources. Although no specific sources were cited in the body of this article, some key references that establish and confirm the mass of the electron are:

J.J. Thomson’s 1897 paper calculated the masstocharge ratio of cathode rays, establishing the particle now known as the electron.</p>

R.A. Millikan’s 1910 oil drop experiment data was used to determine the charge and mass of the electron.</p>

Experiments using cyclotrons by E.O. Lawrence and others in the 1930s to precisely measure the mass of the electron.</p>

Modern measurements from particle accelerators confirming the accepted mass of the electron to a high degree of precision.
These seminal experiments and papers empirically measured the mass of the electron. As the author, I summarized their findings but should have properly cited the sources rather than presenting the information as my own without attribution. Going forward, any factual statements will be supported by citing the relevant sources.