The discovery of the electron as a subatomic particle revolutionized physics at the turn of the 20th century. Determining its mass was a necessary step toward understanding the fundamental structure of the atom. This calculation provided a foundational constant that helped validate emerging theories about matter. The final figure for the electron’s mass required combining two groundbreaking measurements from two different scientists.
Setting the Stage: Determining the Charge-to-Mass Ratio
The first step in isolating the electron’s mass was taken by physicist J.J. Thomson in 1897. Thomson worked with cathode rays, demonstrating that these streams of light were composed of negatively charged particles. He subjected the cathode rays to electric and magnetic fields, observing how the particles were deflected. By balancing the forces exerted by both fields, he calculated the ratio of the particle’s electric charge (\(e\)) to its mass (\(m\)).
Thomson found that this charge-to-mass ratio (\(e/m\)) was the same regardless of the materials used in the experiment. This suggested these particles, later named electrons, were a universal component of all matter. His calculated ratio was significantly larger than that of the lightest known ion, the hydrogen ion. This indicated the electron was far less massive than any known atom. The accepted value for the electron’s charge-to-mass ratio is approximately \(1.759 \times 10^{11}\) Coulombs per kilogram.
The Critical Measurement: Finding the Electron’s Charge
The calculation of the electron’s mass required determining the value of the elementary charge (\(e\)) separately from the mass. American physicist Robert Millikan achieved this measurement through his Oil Drop Experiment, which began in 1909. Millikan’s setup involved observing tiny oil droplets falling between two horizontal metal plates. The oil was sprayed from an atomizer, causing the droplets to pick up a static electric charge through friction.
The oil droplets drifted into the space between the parallel plates, where they were viewed through a microscope. Millikan first measured the terminal velocity of a droplet falling under gravity with the electric field turned off. This allowed him to calculate the mass and radius of the individual droplet by accounting for air resistance. He then applied a voltage across the plates, creating an upward electric field that exerted a force on the charged droplets.
Millikan adjusted the voltage until a selected droplet was suspended motionless. This meant the upward electrical force balanced the downward gravitational force. By knowing the electric field strength and the droplet’s mass, he calculated the precise amount of charge (\(q\)) on that droplet. The experiment was repeated for thousands of oil droplets. Millikan observed that the charge on every drop was always an integer multiple of a smallest, fundamental value.
This discovery demonstrated that electric charge is “quantized,” meaning it exists only in discrete packets. Millikan proposed this fundamental unit, approximately \(1.602 \times 10^{-19}\) Coulombs, was the charge of a single electron. This value for the elementary charge (\(e\)) provided the final piece of data needed to solve for the electron’s mass.
Calculating the Mass and Its Scientific Impact
With Thomson’s charge-to-mass ratio (\(e/m\)) and Millikan’s independently determined value for the elementary charge (\(e\)), the mass of the electron (\(m\)) could finally be calculated. The mass was found by dividing the charge (\(e\)) by the charge-to-mass ratio (\(e/m\)). This calculation yielded a mass of approximately \(9.109 \times 10^{-31}\) kilograms for the electron.
The resulting value confirmed the electron was exceedingly light, being roughly 1/1836th the mass of a hydrogen atom or a proton. This calculation confirmed that the electron was a fundamental, universal subatomic particle. The determination of the electron’s mass and charge established the first fundamental constants for subatomic matter. This work provided the foundation for modern atomic theory and quantum mechanics, moving science toward a new model of the atom that included light, charged particles orbiting a dense, positive nucleus.