Experimental Setup
Inhomogeneous Magnetic Field
Detection Screen
Classical vs Quantum
Experimental Parameters
Magnetic Field Parameters
Atomic Beam Parameters
Display Options
Quick Presets
Stern-Gerlach Equations
What is the Stern-Gerlach Experiment?
The Stern-Gerlach experiment (1922) was a landmark experiment that demonstrated the quantization of angular momentum and the existence of electron spin. By passing a beam of silver atoms through an inhomogeneous magnetic field, Stern and Gerlach observed that the beam split into two discrete paths, providing the first direct evidence of spatial quantization. This result was impossible to explain with classical physics but was perfectly explained by quantum mechanics with spin-½ particles.
Experimental Setup
Silver Atom Source: Silver atoms are vaporized in a high-temperature oven (≈1000°C) and collimated into a narrow beam.
Inhomogeneous Magnet: A specially designed magnet with a sharp edge creates a strong magnetic field gradient (dB/dz).
Magnetic Moment: Silver atoms (47Ag) have a single unpaired electron in their outer shell, giving them a magnetic moment.
Detection Screen: A glass plate collects the silver atoms, showing two distinct bands where atoms deposit.
Key Results and Discovery
Classical Expectation: According to classical physics, atomic magnetic moments are randomly oriented. A continuous distribution of deflections should create a broad smear on the detector.
Quantum Reality: The experiment showed only two sharp bands, corresponding to spin up (m_s = +½) and spin down (m_s = -½).
Spatial Quantization: This was the first direct observation that angular momentum is quantized in space, not just in magnitude.
50-50 Split: Approximately equal numbers of atoms went to each beam, showing random initial spin orientations.
The Discovery of Spin
In 1925, Uhlenbeck and Goudsmit proposed that electrons have an intrinsic angular momentum called "spin" with quantum number s = ½. This explained why silver atoms (with 46 paired electrons canceling their spins) behave like spin-½ particles. The magnetic moment is μ = g·μ_B·m_s, where g ≈ 2 for electrons, μ_B is the Bohr magneton, and m_s = ±½ are the only allowed values. The Stern-Gerlach experiment remains the clearest demonstration of quantum spin and spatial quantization.
Historical and Scientific Significance
Quantum Mechanics Validation: Provided crucial evidence for quantum theory when it was still controversial.
Space Quantization: First direct proof that angular momentum projection is quantized along any axis.
Spin Discovery: Led to the discovery of electron spin, a fundamental property of all matter.
Measurement Problem: Raises profound questions about measurement, superposition, and quantum state collapse.
Quantum Computing: Modern quantum bits (qubits) use Stern-Gerlach-like principles for state preparation and measurement.
Nobel Prize: Otto Stern received the 1943 Nobel Prize in Physics for this work and his discovery of the magnetic moment of the proton.
Modern Applications
Stern-Gerlach Magnets: Used to separate and prepare spin-polarized atomic beams in laboratories.
Magnetic Resonance: Principles of spin manipulation are used in NMR and MRI machines.
Atomic Clocks: Spin-state selection creates precision time standards.
Quantum Information: Stern-Gerlach measurements are fundamental to quantum computing and cryptography.
Particle Physics: Similar techniques measure magnetic moments of subatomic particles.
Spintronics: Electronic devices that use electron spin for information processing.