Millikan's Oil Drop Experiment: Measuring the Fundamental Unit of Charge

Expert reviewed • 22 November 2024 • 5 minute read

Introduction

In 1909, Robert Millikan designed an ingenious experiment that precisely measured the charge of an electron. This groundbreaking work not only provided the first accurate measurement of this fundamental constant but also demonstrated that electric charge exists in discrete units - a property known as charge quantization.

Experimental Setup

The experiment consisted of these key components:

  • A sealed chamber containing two parallel metal plates
  • An atomizer to spray oil droplets
  • An X-ray source for ionization
  • A microscope for observation
  • A variable voltage source

The Experimental Process

Step 1: Creating Charged Droplets

  • Oil droplets were sprayed into the chamber using an atomizer
  • X-rays ionized air molecules, creating free electrons
  • These electrons attached to some oil droplets, giving them a negative charge

Step 2: Observing Forces

The oil droplets experienced four forces:

  • Gravitational Force (Fg=mgF_g = mg)
  • Electric Force (Fe=qE=qVdF_e = qE = \frac{qV}{d})
  • Buoyant Force (Fb=ρairVgF_b = \rho_{air}Vg)
  • Drag Force (Fd=6πηrvF_d = 6\pi\eta rv)

Where:

  • mm = mass of the droplet
  • gg = gravitational acceleration
  • qq = charge on the droplet
  • VV = voltage between plates
  • dd = distance between plates
  • η\eta = viscosity of air
  • rr = radius of droplet
  • vv = velocity of droplet

Step 3: The Measurement Process

  • Terminal Velocity Measurement
    • With no electric field, droplets fell at terminal velocity
    • This allowed calculation of droplet size using Stokes' Law
  • Suspension Method
    • Voltage adjusted until droplet suspended (v=0v = 0)
    • At this point: qE=mg−FbqE = mg - F_b
    • Therefore: q=mg−FbE=(mg−Fb)dVq = \frac{mg - F_b}{E} = \frac{(mg - F_b)d}{V}

Results and Significance

Millikan's key findings:

  • The charge on oil droplets was always a multiple of $1.59 \times 10^{-19}$ coulombs
  • This value was remarkably close to the modern accepted value of 1.602×10−191.602 \times 10^{-19} coulombs
  • The small discrepancy was later attributed to an incorrect value for air viscosity used in the calculations

This experiment conclusively demonstrated that:

  • Electric charge is quantized
  • The electron carries the fundamental unit of negative charge
  • Charge cannot exist in fractions of this fundamental unit

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