Who Found The Mass Of An Electron

The quest to determine the mass of an electron is a fascinating journey that intertwines experimental ingenuity with theoretical breakthroughs. The electron, a fundamental particle carrying a negative electric charge, plays a pivotal role in shaping the structure and behavior of atoms, molecules, and matter itself. However, measuring the mass of such a tiny entity presented immense challenges. While it is not possible to credit a single individual with definitively "finding" the mass of an electron, the story involves a series of scientists and experiments that incrementally refined our understanding. The most significant contribution came from J.J. Thomson, whose experiments in the late 19th century provided the first reliable determination of the charge-to-mass ratio of the electron. Subsequent work by Robert Millikan, who precisely measured the charge of a single electron, allowed scientists to calculate the mass of the electron with remarkable accuracy.

Early Investigations and the Nature of Cathode Rays

The story begins with the investigation of cathode rays, mysterious emanations observed when a high voltage is applied across electrodes within a vacuum tube. In the mid-19th century, physicists such as Julius Plücker, Johann Wilhelm Hittorf, and William Crookes studied these rays and discovered that they could be deflected by magnetic fields. These observations hinted at the charged nature of cathode rays.

Julius Plücker (1858): Observed that cathode rays could be deflected by a magnetic field.
Johann Wilhelm Hittorf (1869): Noted that objects placed in the path of cathode rays cast shadows, indicating that the rays traveled in straight lines.
William Crookes (1870s): Conducted extensive experiments with cathode rays, suggesting that they were composed of negatively charged particles. He developed the Crookes tube, which allowed for more controlled study of the rays.

These early experiments laid the groundwork for understanding the fundamental properties of cathode rays, but they did not reveal the nature of the particles themselves. Were they waves, or were they streams of charged particles?

J.J. Thomson and the Discovery of the Electron

The pivotal breakthrough came with the work of J.J. Thomson, a British physicist at the Cavendish Laboratory in Cambridge. In 1897, Thomson conducted a series of experiments that not only confirmed the particle nature of cathode rays but also provided the first reliable measurement of their charge-to-mass ratio (e/m).

Thomson's experiments involved using a cathode ray tube with a better vacuum than previously achieved. This allowed him to apply electric and magnetic fields to the cathode rays and observe their deflection. His apparatus consisted of a glass tube from which most of the air had been evacuated. At one end was a cathode, and at the other end was an anode with a small slit in it. The cathode rays passed through the slit, forming a narrow beam that struck a fluorescent screen at the end of the tube, producing a visible spot of light.

Thomson applied an electric field perpendicular to the path of the cathode rays using two parallel plates. He observed that the electric field deflected the rays toward the positive plate, confirming that they were negatively charged. He then applied a magnetic field perpendicular to both the electric field and the path of the rays. By carefully adjusting the strengths of the electric and magnetic fields, Thomson was able to balance the forces on the cathode rays so that they passed through undeflected.

From the balance of forces, Thomson could derive an expression for the velocity (v) of the cathode rays:

v = E/B

where E is the electric field strength and B is the magnetic field strength.

Thomson also measured the deflection of the cathode rays when only the magnetic field was applied. The magnetic force on a charged particle moving in a magnetic field causes it to move in a circular path. The radius of curvature (r) of this path is related to the charge (e), mass (m), velocity (v), and magnetic field strength (B) by the equation:

r = mv / eB

Rearranging this equation, Thomson obtained an expression for the charge-to-mass ratio:

e/m = v / rB

Substituting v = E/B into this equation, he got:

e/m = E / B^2 r

By measuring E, B, and r, Thomson was able to determine the charge-to-mass ratio (e/m) of the cathode rays. He found that the charge-to-mass ratio was constant, regardless of the gas used in the cathode ray tube or the material of the electrodes. This suggested that the particles were a universal constituent of matter.

Thomson's experiments led him to several revolutionary conclusions:

Cathode rays were composed of negatively charged particles, which he initially called "corpuscles" but were later named electrons.
These particles were much smaller and lighter than atoms.
The electron was a fundamental constituent of all matter.

Thomson's work marked a paradigm shift in physics, as it challenged the long-held belief that atoms were the smallest and indivisible units of matter. His discovery of the electron opened up a new era of atomic physics and paved the way for the development of modern electronics.

While Thomson determined the charge-to-mass ratio, he did not measure the charge or the mass of the electron independently. This was the next crucial step in understanding the electron's properties.

Robert Millikan and the Oil Drop Experiment

The determination of the electron's charge was achieved by Robert Millikan and his student Harvey Fletcher between 1909 and 1913 at the University of Chicago. Millikan's oil drop experiment is a classic example of experimental physics and provided the first accurate measurement of the elementary electric charge (e).

In Millikan's experiment, tiny oil droplets were sprayed into a chamber between two parallel metal plates. The droplets were allowed to fall under the influence of gravity. As they fell, some of the droplets acquired an electric charge, either through friction with the air or by being bombarded with ionizing radiation (such as X-rays).

Millikan observed the motion of these charged oil droplets through a telescope. By applying an electric field between the plates, he could exert an upward electric force on the charged droplets, counteracting the downward force of gravity. By carefully adjusting the electric field, Millikan could suspend a droplet in mid-air or cause it to move upward or downward at a controlled rate.

The forces acting on the oil droplet are:

Gravitational Force (Fg): The force due to gravity, given by Fg = mg, where m is the mass of the droplet and g is the acceleration due to gravity.
Electric Force (Fe): The force due to the electric field, given by Fe = qE, where q is the charge on the droplet and E is the electric field strength.
Viscous Drag Force (Fv): The force due to air resistance, which opposes the motion of the droplet. According to Stokes' law, Fv = 6πηrv, where η is the viscosity of air, r is the radius of the droplet, and v is the velocity of the droplet.

When the droplet is falling at its terminal velocity (v1) in the absence of an electric field, the gravitational force is balanced by the viscous drag force:

mg = 6πηrv1

When the droplet is suspended or moving at a constant velocity (v2) in the presence of an electric field, the electric force balances the net force due to gravity and viscous drag:

qE = mg - 6πηrv2

Substituting mg = 6πηrv1 into this equation, we get:

qE = 6πηr(v1 - v2)

From this equation, Millikan could determine the charge q on the oil droplet.

Millikan made a crucial observation: the charge on the oil droplets was always a multiple of a fundamental unit of charge, which he identified as the elementary electric charge (e). In other words, the charge on any oil droplet was always ne, where n is an integer.

q = ne

where e is the elementary charge.

By analyzing a large number of oil droplets and determining their charges, Millikan was able to determine the value of the elementary charge with high precision. His value was very close to the modern accepted value.

Millikan's oil drop experiment provided compelling evidence for the quantization of electric charge, meaning that electric charge exists only in discrete units. This was a fundamental discovery that had profound implications for our understanding of the nature of electricity and matter.

Calculating the Mass of the Electron

With Thomson's determination of the charge-to-mass ratio (e/m) and Millikan's measurement of the elementary charge (e), it became possible to calculate the mass of the electron (m).

From Thomson's experiment:

e/m = 1.758820 × 10^11 C/kg

From Millikan's experiment:

e = 1.602176634 × 10^-19 C

Therefore, the mass of the electron can be calculated as:

m = e / (e/m)

m = (1.602176634 × 10^-19 C) / (1.758820 × 10^11 C/kg)

m ≈ 9.1093837015 × 10^-31 kg

This value is very close to the currently accepted value of the electron mass.

Significance and Impact

The determination of the mass of the electron was a monumental achievement in physics. It not only confirmed the existence of the electron as a fundamental particle but also provided a crucial piece of the puzzle in understanding the structure of atoms and the nature of matter.

Atomic Structure: The mass of the electron, along with its charge, is essential for understanding the electronic structure of atoms and molecules. It plays a crucial role in determining the energy levels of electrons in atoms and the chemical properties of elements.
Quantum Mechanics: The electron's properties are central to quantum mechanics, the theory that governs the behavior of matter at the atomic and subatomic levels. The electron's mass is a fundamental parameter in quantum mechanical calculations.
Electronics and Technology: The discovery and characterization of the electron paved the way for the development of modern electronics. The electron's charge and mass are critical parameters in the design and operation of electronic devices such as transistors, diodes, and integrated circuits.
Cosmology and Astrophysics: The electron is a fundamental component of matter in the universe. Its mass and charge are important parameters in astrophysical models and cosmological calculations.

Later Refinements and Modern Measurements

While Thomson and Millikan's experiments provided the first reliable measurements of the electron's charge-to-mass ratio and charge, respectively, subsequent experiments and theoretical advancements have refined our understanding and improved the precision of these measurements.

Spectroscopy: High-resolution spectroscopy of atoms and ions has allowed for very precise measurements of the energy levels of electrons. These measurements can be used to determine the electron's mass with high accuracy.
Penning Trap Experiments: Penning traps use strong magnetic and electric fields to confine charged particles, such as electrons, for extended periods. By precisely measuring the cyclotron frequency of the electrons in the trap, physicists can determine their mass with extremely high precision.
Quantum Electrodynamics (QED): QED is the quantum field theory that describes the interactions of light and matter. It provides extremely accurate predictions for the properties of the electron, including its mass and magnetic moment.

Modern measurements using these techniques have yielded the following value for the electron mass:

mₑ = 9.1093837015(28) × 10⁻³¹ kg

This value is known with a relative uncertainty of only a few parts per billion, making it one of the most precisely known fundamental constants in physics.

The Men Behind the Measurements

While J.J. Thomson and Robert Millikan are the most prominently credited figures in the determination of the electron's mass, it's important to recognize the contributions of other scientists and researchers who played a role in this endeavor:

Early Investigators of Cathode Rays: Scientists like Julius Plücker, Johann Wilhelm Hittorf, and William Crookes laid the foundation for Thomson's work by studying the properties of cathode rays.
Harvey Fletcher: Millikan's student, Harvey Fletcher, made significant contributions to the oil drop experiment. He performed many of the painstaking measurements and calculations.
Later Experimentalists: Many physicists and researchers have contributed to refining the measurement of the electron's mass using advanced techniques such as spectroscopy, Penning traps, and QED calculations.

Conclusion

The determination of the mass of an electron is a remarkable story of scientific discovery, experimental ingenuity, and theoretical advancement. J.J. Thomson's experiments established the existence of the electron and provided the first measurement of its charge-to-mass ratio, while Robert Millikan's oil drop experiment determined the elementary electric charge. Combining these results allowed scientists to calculate the mass of the electron with unprecedented accuracy.

The electron's mass is a fundamental constant that plays a crucial role in many areas of physics, from atomic structure and quantum mechanics to electronics and cosmology. The quest to determine the mass of the electron has not only deepened our understanding of the nature of matter but has also paved the way for countless technological innovations that have transformed our world. It stands as a testament to the power of scientific inquiry and the enduring quest to understand the fundamental building blocks of the universe.