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When you write ms = +1/2 or −1/2 for an electron, you are using a result that first showed up as two thin lines of silver on a glass plate. The Stern-Gerlach experiment is short to describe and hard to do. This post covers how it was done, why the beam split, and how big the effect is, with numbers you can check.
What did Stern and Gerlach set out to test?
Around 1920 the older quantum theory claimed that an atom's angular momentum could point only in certain directions in a magnetic field. This was called space quantisation (in German, Richtungsquantelung). According to a detailed history by Schmidt-Böcking and colleagues (2016), Otto Stern first thought the idea was nonsense. He also saw that he could test it with the molecular beam method he had just developed in Frankfurt, where Max Born directed the institute of theoretical physics.
Walther Gerlach, an experimental physicist, joined him. Money was short after the First World War. Born gave public lectures on relativity to raise funds, and Gerlach obtained support from Einstein's Kaiser Wilhelm Institute in Berlin. Born's own story is in our post on Max Born and probability.
How did the experiment work?
Silver was heated in a small oven. Atoms escaping through a hole passed through narrow slits to form a thin beam, then through a magnet shaped to give a strongly non-uniform field, and finally landed on a cooled plate. The 2016 history describes the trace on the plate as black silver sulfide.
The first attempt, on 4 November 1921, only showed the spot broadening when the field was switched on. In early February 1922 Stern and Gerlach met in Göttingen and decided to replace one circular hole with a slit. In the night of 7 to 8 February 1922, with Stern already gone to a post in Rostock, Gerlach ran it again. A photograph under the microscope showed two separate traces, barely 0.1 mm apart. Gerlach sent Niels Bohr a postcard with the photo the same day. They published the result in Zeitschrift für Physik in 1922.
Why did the beam split into two instead of smearing out?
Think of each silver atom as a tiny magnet. In a uniform field, a magnet feels only a torque, no net force. In a non-uniform field, the force along z is F = μz (dB/dz), where μz is the component of the magnetic moment along the field.
If atomic magnets pointed in every direction, as classical physics expects, μz would take every value between −μ and +μ, and the spot would spread into a continuous band. Instead, the Nobel Prize summary notes, "two distinct beams were observed". Only two values of μz were allowed.
At the time, people read this as support for Bohr's orbit model. The 2016 history explains that the experiment had in fact revealed the electron's spin, which was not understood until later: silver's outer electron has spin 1/2, so it has two allowed orientations.
How big is the deflection? A worked estimate
Use round, illustrative numbers rather than the original apparatus values.
Magnetic moment along z: one Bohr magneton, μB = 9.274 × 10⁻²⁴ J/T (NIST value).
Field gradient: dB/dz = 1000 T/m (10 T across 1 cm).
Silver atom mass: 107.87 u = 1.79 × 10⁻²⁵ kg.
Atom speed: 500 m/s. Magnet length: 3.5 cm.
Force. F = μB × dB/dz = 9.274 × 10⁻²⁴ × 1000 = 9.27 × 10⁻²¹ N.
Acceleration. a = F/m = 9.27 × 10⁻²¹ / 1.79 × 10⁻²⁵ ≈ 5.2 × 10⁴ m/s².
Time in the magnet. t = 0.035 / 500 = 7.0 × 10⁻⁵ s.
Sideways shift. z = ½at² = 0.5 × 5.2 × 10⁴ × (7.0 × 10⁻⁵)² ≈ 1.3 × 10⁻⁴ m, or 0.13 mm.
One beam moves 0.13 mm up and the other 0.13 mm down. A fraction of a millimetre is why the first photographs needed a microscope.
Common mistakes:
Using a uniform field. The torque formula τ = μ × B is in the JEE Main syllabus; the force needs the gradient, not B itself.
Forgetting the mass is tiny. Convert atomic mass units to kilograms before dividing.
Expecting three beams. For an orbital angular momentum of 1 you would get three. Silver's two beams come from spin 1/2.
The NTA JEE (Main) 2026 syllabus lists "electron spin and spin quantum number" in chemistry and torque on a magnetic dipole in a uniform field in physics; the force in a non-uniform field goes beyond it. See our post on quantum numbers and atomic structure for the exam side.
Who received the Nobel Prize?
Stern alone received the 1943 Nobel Prize in Physics, presented in 1944, "for his contribution to the development of the molecular ray method and his discovery of the magnetic moment of the proton". The 2016 history counts 31 nominations of Stern and Gerlach together, but Gerlach never received the prize.
What can a student take from Stern and Gerlach's way of working?
Test the idea you doubt. Stern disbelieved space quantisation and built the experiment that confirmed it.
Small design changes matter. Swapping a hole for a slit turned a blurred spot into a clear result.
Estimate before you build. A quick calculation like the one above tells you whether an effect is a millimetre or a micron.
Forces on dipoles are easier to grasp when you can move the magnet yourself. The Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read.
Try it: redo the estimate with a speed of 800 m/s and explain why faster atoms split less.
