Stern-Gerlach experiment
A beam of spin-1/2 particles passes through an inhomogeneous magnetic field and splits into exactly two discrete beams — spin up and spin down. Classical physics predicted a continuous smear. Quantum mechanics predicts two spots. This was the first direct evidence of spatial quantization, performed by Otto Stern and Walther Gerlach in 1922.
In 1922, Otto Stern and Walther Gerlach sent a beam of silver atoms through an inhomogeneous magnetic field. Classical electromagnetism predicted the beam would spread into a continuous band, since the magnetic moment of each atom could point in any direction. Instead, the beam split into exactly two discrete spots.
This result was the first direct evidence of spatial quantization — the idea that angular momentum (and therefore magnetic moment) can only take discrete values. For spin-1/2 particles, the spin component along any axis is either +ℏ/2 or −ℏ/2, giving exactly two possible deflection directions.
The force on a magnetic dipole in an inhomogeneous field is Fz = μz · dB/dz. For spin-1/2 particles, μz = ±gsμB/2, where gs ≈ 2 is the electron g-factor and μB is the Bohr magneton. The two discrete forces produce two discrete deflections — the hallmark of quantum mechanics.
Toggle the "Classical overlay" to see what classical physics would predict: a continuous spread of deflections, since classically the magnetic moment could point in any direction. The quantum result — two discrete spots — was revolutionary.