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By Walther Gerlach and Otto Stern. Zeitschrift für Physik 9, 349–352 (1922), received 1 March. English translation by Martin Bauer, arXiv:2301.11343v1, 26 January 2023.

Cited passages: Experimental setup; Results, Figures 1–5; closing measurement caveat.

Immanuel Estermann, O. C. Simpson and Otto Stern used gravitational deflection to measure atomic speeds. Stern describes scanning a hot-wire surface ionization detector through a cesium beam and recording ion electric current.^[ref] Their 1947 paper reports potassium and cesium beams; a deficit of slow arrivals increased with oven pressure, supporting a source-slit collision explanation.^[ref]

First consider an original point-launch model, with horizontal speed $v>0$, zero initial vertical velocity, flight distance $L$, and uniform gravitational acceleration $g$. Downward displacement $y$ follows from flight time $t=L/v$:Slow particles fall farther. However, a detector scan counts arrivals per interval of height, not per interval of speed. Change of variables for probability densities supplies the Jacobian determinant:Here $g(v)$ denotes the effusive beam speed distribution; the unadorned constant $g$ in $C$ denotes gravitational acceleration. The integral of $p_y$ is one: substituting $u=b/y$ reduces it to ${\int }_0^{\infty }u{e}^{-u}du=1$. Its mode is $y=b/3$. Simply mapping the most probable arrival speed into a fall distance instead gives $2b/3$. The peaks differ because equal height bins cover unequal speed intervals.

For those chosen parameters, $b\simeq 176.54\mu \mathrm{m}$, so the detector-height probability density peaks near $58.85\mu \mathrm{m}$. A detector covering only $0<y<Y$ accepts the fractionAt $Y=0.80\mathrm{mm}$ this is about $97.9\%$, even before allowing for imperfect detection. Discarding the remainder changes the observed normalization.

Real slits transmit a range of launch heights and vertical velocities. Their geometrical response must be combined with the gravitational deflection and detector width; the point-launch formula is not an exact reduction of the historical apparatus. In the point-launch model, an initial vertical velocity $w$ would add $wL/v$ to $y$. Source collisions, detector efficiency and alignment can also distort a profile. Varying oven pressure helps distinguish such source losses from an incorrect thermal distribution; inferring a source temperature from the peak alone ignores both selection and the detector's coordinate transformation.

Awarded to Otto Stern for the molecular beam method and discovery of the proton magnetic moment. The molecular beam article develops direct measurements of particle speeds.^[ref]

Otto Stern's lecture describes two co-rotating toothed wheels: transit between them must match an advance between openings. He explicitly distinguishes this method from the first historical speed measurement.^[ref]

For an idealized example, let aligned wheels have $N$ equally spaced openings, separation $L$, and rotation rate $f$ in revolutions per second. A particle with constant longitudinal speed $v$ takes $L/v$ between them. The second wheel advances through $fL/v$ revolutions; transmission peaks when that advance is an integer number $k$ of opening pitches:With chosen $N=60$, $f=50\mathrm{Hz}$ and $L=0.080\mathrm{m}$, the first two orders select $240$ and $120\mathrm{m}{\mathrm{s}}^{-1}$. A second transmission maximum therefore need not represent a second source temperature. Finite opening widths admit speed intervals around each order, and an additional measurement is needed to distinguish orders. The ideal expression assumes negligible acceleration and constant rotation rate during a flight, with a fixed relative phase between the wheels.

In 1922, Otto Stern and Walther Gerlach used an electrically heated oven to emit neutral silver chemical atoms. Two platinum apertures, a pinhole and a slit $0.03$–$0.04\mathrm{mm}$ wide, supplied collimation. The beam passed along a $3.5\mathrm{cm}$ knife-edge pole in a nonuniform magnetic field. At its end, a glass plate collected the condensed silver. Continuous pumping maintained vacuum; the thin deposit required development even after eight hours.^[ref]

The field-off image established the undeflected slit width. A comparison put field-on and field-off deposits on the same plate. Microscopy revealed two deflected bands, no detectable central component, and broadening attributed to the velocity distribution. Alignment and distance from the knife-edge affected the pattern; precise magnetic field gradient measurements were still pending.^[ref]

The apertures act as a collimator: they constrain the initial transverse positions and velocities, so a magnetic displacement can be distinguished from an initially broad beam. Vacuum reduces collisions that would destroy this preparation. Deposition integrates arrivals over the exposure; a darkened band is not a time-resolved record of individual chemical atoms. The field-off comparison tests whether the magnet changes the spatial distribution, while alignment checks address a geometric source of apparent asymmetry. Finite sensitivity qualifies the absence of a central deposit: it is an experimental upper limit, not a proof that exactly zero atoms landed there.

A physicist.^[ref]

The Stern-Gerlach experiment, with Otto Stern, sent a neutral silver atomic beam through a nonuniform magnetic field and recorded its deposition pattern.