Electrons

SYLLABUS

Millikan’s oil drop experiment, Motion of electron beam in electric and magnetic fields, Thomson’s experiment to determine specific charge of electrons

What is This Chapter About?

At the end of the 19th century, physicists knew that electric currents involved the flow of something — but what exactly? Cathode ray experiments in evacuated glass tubes produced mysterious beams that travelled from the negative electrode (cathode) to the positive electrode (anode). Were these rays waves or particles? What were they made of? What was their charge and mass?

The answers came through a series of brilliant experiments that represent some of the finest quantitative physics ever done. Chapter 20 of NEB Grade 12 Physics tells this story — the discovery and characterisation of the electron through Millikan’s oil drop experiment and Thomson’s cathode ray experiment. Carrying 4 teaching hours, this chapter bridges classical electromagnetism and modern physics, introducing students to the fundamental particle that carries electricity and underlies all of chemistry and condensed matter physics.

Key Concepts You Will Learn

Millikan’s Oil Drop Experiment

In 1909, Robert Millikan performed one of the most elegant and precise experiments in the history of physics — determining the fundamental unit of electric charge, the charge of a single electron.

Principle and Setup: Millikan created a fine mist of oil droplets between two horizontal charged parallel plates. The droplets acquired charge by friction with the atomiser nozzle or by exposure to ionising radiation. By illuminating the droplets with a light source and observing them through a microscope, Millikan could track individual droplets as they moved under the combined influence of gravity, air resistance, and the electric field between the plates.

Forces on a Droplet: Three forces act on an oil droplet: gravitational force [latex]mg[/latex] downward, viscous drag force (from Stokes’ Law) [latex]F = 6\pi\eta rv[/latex] opposing motion, and electric force [latex]qE[/latex] whose direction depends on the sign of the charge and the direction of the field.

Method: When the electric field is adjusted so that the droplet is held stationary (neither rising nor falling), the electric force exactly balances gravity:

[latex]qE = mg[/latex]

The mass m of the droplet is found separately by switching off the electric field and measuring the terminal velocity of the droplet falling under gravity and air resistance (using Stokes’ Law). With m known, and E known from the voltage and plate separation, q can be calculated.

Key Result — Quantisation of Charge: After measuring the charges on thousands of oil droplets, Millikan found a remarkable result: all measured charges were integer multiples of a smallest unit — [latex]e = 1.6 \times 10^{-19}[/latex] C. This was direct experimental proof that electric charge is quantised — it comes in discrete units of e, the elementary charge. No droplet ever carried a non-integer multiple of e. This result confirmed that charge is carried by individual discrete particles — electrons.

Millikan received the Nobel Prize in Physics in 1923 partly for this work. The value of e he measured — [latex]1.6 \times 10^{-19}[/latex] C — remains one of the fundamental constants of nature.

Motion of Electrons in Electric and Magnetic Fields

Understanding how electron beams behave in electric and magnetic fields is essential for Thomson’s experiment and for the operation of cathode ray tubes.

In a uniform electric field E, an electron of charge e and mass m experiences force eE and accelerates accordingly — following a parabolic path if it enters perpendicular to the field, analogous to projectile motion.

In a uniform magnetic field B, an electron moving with speed v perpendicular to B experiences Lorentz force [latex]F = evB[/latex] perpendicular to both v and B — causing it to move in a circle of radius [latex]r = \frac{mv}{eB}[/latex].

When both electric and magnetic fields are present simultaneously, they can be arranged to act in opposite directions on the electron. For a specific velocity called the drift velocity or selector velocity:

[latex]v = \frac{E}{B}[/latex]

electric and magnetic forces exactly balance — the electron travels in a straight line regardless of its charge or mass. This velocity selector is a key component of Thomson’s experiment.

Thomson’s Experiment — Discovery of the Electron

In 1897, J.J. Thomson performed the experiment that definitively established the existence of the electron as a fundamental particle and measured its charge-to-mass ratio.

Setup: Thomson used a cathode ray tube — an evacuated glass tube with a heated cathode emitting rays, an anode accelerating them, and deflecting plates inside the tube. A fluorescent screen at the end showed where the beam struck.

Procedure: Thomson first applied only an electric field E perpendicular to the beam, measuring the deflection [latex]y[/latex] of the spot on the screen. Then he added a magnetic field B perpendicular to both the beam and E, and adjusted B until the deflection was zero — meaning electric and magnetic forces balanced, giving the beam velocity [latex]v = \frac{E}{B}[/latex].

With v known, he switched off the magnetic field and used the electric deflection alone to find the charge-to-mass ratio. The deflection y depends on the beam’s charge, mass, velocity, and the electric field geometry:

[latex]\frac{e}{m} = \frac{2yV}{B^2L^2d}[/latex]

where V is the accelerating voltage, L is the length of the deflecting plates, and d is their separation (specific forms vary with experimental arrangement).

Key Result: Thomson found that [latex]\frac{e}{m}[/latex] for cathode rays was always [latex]1.76 \times 10^{11}[/latex] C/kg — the same regardless of the cathode material, the gas in the tube, or any other experimental variable. This universality proved that cathode rays consist of identical particles — which Thomson called corpuscles, now called electrons — that are a fundamental constituent of all matter.

Combined with Millikan’s measurement of e, Thomson’s [latex]\frac{e}{m}[/latex] ratio gives the electron mass:

[latex]m_e = \frac{e}{e/m} = \frac{1.6 \times 10^{-19}}{1.76 \times 10^{11}} \approx 9.11 \times 10^{-31} \text{ kg}[/latex]

The electron is approximately 1836 times lighter than a proton — making it by far the lightest charged particle.

Why This Chapter Matters for NEB Exams

Electrons is examined consistently in NEB Grade 12 Physics. Millikan’s oil drop experiment — describing the setup, the forces on the droplet, the method of finding q, and the significance of quantisation of charge — is a classic long-answer question. Thomson’s experiment — explaining the velocity selector, the deflection method, and the significance of the universal [latex]\frac{e}{m}[/latex] ratio — appears regularly as both theory and numerical questions. Problems involving the motion of electrons in electric and magnetic fields — circular radius, velocity selector condition, deflection — are standard numerical questions.

Important Topics to Focus On

• Millikan’s oil drop experiment — setup, forces (gravity, drag, electric), balance condition
• Finding droplet mass using terminal velocity and Stokes’ Law
• Calculating charge: [latex]qE = mg[/latex]
• Quantisation of charge — Millikan’s key result and its significance
• Value of elementary charge: [latex]e = 1.6 \times 10^{-19}[/latex] C
• Motion of electrons in electric fields — parabolic path, force and acceleration
• Motion of electrons in magnetic fields — circular path, radius [latex]r = \frac{mv}{eB}[/latex]
• Velocity selector: [latex]v = \frac{E}{B}[/latex] — condition and principle
• Thomson’s experiment — setup, velocity selector, deflection measurement
• Thomson’s result: [latex]\frac{e}{m} = 1.76 \times 10^{11}[/latex] C/kg and its significance
• Calculation of electron mass from e and e/m
• Numerical problems on Millikan’s experiment, circular motion in B field, and velocity selector

Connection to Other Chapters

Electrons builds on Grade 11 Chapter 19 (Electric Charges) — the elementary charge e and quantisation of charge are central results of both chapters. Grade 11 Chapter 20 (Electric Field) and Chapter 22 (Capacitor) provide the uniform field between parallel plates used in both Millikan’s and Thomson’s experiments. Grade 12 Chapter 16 (Magnetic Field) provides the Lorentz force that deflects electron beams and enables the velocity selector. This chapter connects forward to Chapter 21 (Photons) — where the photoelectric equation involves the same electron charge e and connects to the quantum nature of light — and Chapter 23 (Quantization of Energy) — where electrons in atoms occupy quantised energy levels described by the Bohr model. The specific charge [latex]\frac{e}{m}[/latex] appears again in discussions of cyclotrons and mass spectrometers in Chapter 25 (Recent Trends in Physics).