The Gold Foil Experiment: Unveiling the Nuclear Atom

Expert reviewed • 22 November 2024 • 6 minute read

Introduction

The Geiger-Marsden gold foil experiment, conducted in 1909, ranks among the most significant experiments in atomic physics. This elegant investigation led Ernest Rutherford to propose the nuclear model of the atom, fundamentally changing our understanding of atomic structure.

The Experimental Setup

The experiment used the following components:

A radioactive source producing alpha particles (helium nuclei)
A thin gold foil approximately 100 atoms thick
A fluorescent screen to detect scattered alpha particles
A microscope to observe scintillations on the screen

Key Observations and Findings

The experiment revealed two crucial observations:

Primary Observation: Most alpha particles passed straight through the gold foil without deflection, suggesting that atoms were mostly empty space.
Critical Discovery: A small fraction of alpha particles (approximately 1 in 8000) scattered at large angles, with some even bouncing directly backward.

The mathematical relationship describing the scattering of alpha particles is given by Rutherford's scattering formula:

\frac{dN}{d\Omega} = \left(\frac{Z_1Z_2e^2}{4\pi\epsilon_0mv^2}\right)^2\frac{1}{4\sin^4(\theta/2)}

Where:

$\frac{dN}{d\Omega}$ is the differential scattering cross-section
$Z_1$ and $Z_2$ are the atomic numbers
$e$ is the elementary charge
$\epsilon_0$ is the vacuum permittivity
$m$ is the mass of the alpha particle
$v$ is the velocity of the alpha particle
$\theta$ is the scattering angle

Rutherford's Nuclear Model

Based on these observations, Rutherford proposed a new model of the atom with these key features:

A dense, positively charged nucleus containing most of the atom's mass
Electrons orbiting the nucleus like planets around the sun
Mostly empty space between the nucleus and electrons

Discovery of the Proton

Following the gold foil experiment, Rutherford conducted further investigations that led to the discovery of the proton in 1919. When alpha particles bombarded nitrogen gas, the following nuclear reaction occurred:

^4\text{He} + ^{14}\text{N} \rightarrow ^{17}\text{O} + ^1\text{H}

Limitations of the Nuclear Model

Despite its groundbreaking nature, Rutherford's model had three significant limitations:

Orbital Stability: According to classical electromagnetic theory, orbiting electrons should emit radiation and spiral into the nucleus. The mathematical expression for the power radiated by an accelerating charge is:

P = \frac{2e^2a^2}{3c^3}

Where:

$P$ is the radiated power
$a$ is the acceleration
$c$ is the speed of light

Electron Behavior: The model couldn't explain electron energy levels or atomic spectra.
Nuclear Composition: The model couldn't fully account for atomic mass, later resolved by Chadwick's discovery of the neutron.

Millikan's Oil Drop Experiment

Up Next

The Discovery of the Neutron: Chadwick's Groundbreaking Experiment

Return to Module *: From the Universe to the Atom