---
title: "Measuring the proton’s magnetism with a hydrogen beam"
description: "How could the deflection of neutral hydrogen molecules reveal a property of the proton?"
canonical_url: "https://sandboxphysics.com/stories/quantum-evidence/stern-proton-moment-molecular-hydrogen/"
language: "en"
page_type: "story"
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  zh-CN: "https://sandboxphysics.com/zh/stories/quantum-evidence/stern-proton-moment-molecular-hydrogen/"
last_modified: "2026-10-24"
---

[Quantum physics: reading the evidence](https://sandboxphysics.com/stories/quantum-evidence/)

Nobel A · Evidence and control

# Measuring the proton’s magnetism with a hydrogen beam

Sandbox Physics · 2026-10-15

How could the deflection of neutral hydrogen molecules reveal a property of the proton?

## A much smaller magnetic response

In 1933, Estermann, Frisch and Stern used a hydrogen molecular beam to investigate the proton’s magnetism. More than a decade earlier, Stern and Gerlach had split a silver beam with a magnet. This time the target response was much smaller: a weak molecular deflection had to reveal something about the nuclei.

A neutral molecule avoids the direct Lorentz bending experienced by a charged particle. Its magnetic moment can still feel a force in an uneven field. But a hydrogen molecule contains two protons and electrons, and it rotates. Extracting the proton’s contribution required an account of the other contributions to the molecule’s magnetic response.

Read the evidence: O. Stern (1946), The Method of Molecular Rays — Nobel lecture, December 12, for the 1943 prize I. Estermann, R. Frisch and O. Stern (1933), Magnetic Moment of the Proton, Nature 132, 169–170 — publication record

## Give a small force more time

An optically excited atom may decay quickly. A molecule in a stable internal state can spend much longer flying through a magnetic field. Stern emphasized this advantage in his 1946 Nobel lecture: given enough time, a small magnetic force produces a measurable displacement. The force requires a field that changes with position.

The beam contained a distribution of speeds. Slow molecules stayed in the field longer and deflected farther. The entrance aperture also gave the beam a finite width. To infer a magnetic moment, the experiment needed the field-off profile, the speed distribution and the magnetic-field gradient.

The beam therefore amplified a weak interaction through flight time. It turned a small force into a displacement, then used the distribution of many molecules to infer an invisible internal property.

Read the evidence: O. Stern (1946), The Method of Molecular Rays — Nobel lecture, December 12, for the 1943 prize

## The proton was more magnetic than expected

The natural unit for this comparison is the nuclear magneton, defined using the proton mass and the elementary charge. Stern’s lecture recalled an early result of about two and a half nuclear magnetons. A proton described as a simple Dirac point particle would have one nuclear magneton. Such a large discrepancy called for a better understanding of the proton.

The equation defines the unit and records that approximate early result. The elementary charge e is positive, the reduced Planck constant sets the quantum angular-momentum scale, and the mass is the proton mass. The historical approximation has no extra error bar invented here.

$$
\mu_{\mathrm N}=\frac{e\hbar}{2m_p},\qquad \mu_p\simeq2.5\,\mu_{\mathrm N}
$$

Read the evidence: O. Stern (1946), The Method of Molecular Rays — Nobel lecture, December 12, for the 1943 prize

## What the unexpected value left open

Express the moment in Bohr magnetons, the unit often used for electrons, and its numerical value becomes much smaller because the unit uses a different mass. The ratio between measurement and the simple prediction remains unchanged. The proton’s response required more explanation, although this beam experiment could not uniquely identify its internal constituents.

The electron also has a magnetic anomaly, but its relative departure from the simple Dirac value is small. The proton discrepancy was on the scale of several nuclear magnetons. The modern picture of a composite proton required further theoretical and experimental evidence.

Read the evidence: O. Stern (1946), The Method of Molecular Rays — Nobel lecture, December 12, for the 1943 prize X. Fan, T. G. Myers, B. A. D. Sukra and G. Gabrielse (2023), Measurement of the Electron Magnetic Moment, Phys. Rev. Lett. 130, 071801

## Later, one proton could stay in a trap

Stern received the 1943 prize and delivered his lecture in 1946. Decades later, researchers could store a single charged proton in a Penning trap and repeatedly compare its motion with its spin response. In 2012, DiSciacca and Gabrielse reported a direct measurement near 2.793 nuclear magnetons, with uncertainty of roughly a part per million.

The beam method started with the deflections of many molecules. The trapped-proton method started with frequencies of one particle. Each had its own calibration and corrections. Their development shows how a conspicuous early discrepancy became a quantity that could be compared with steadily greater precision.

Read the evidence: Otto Stern — official 1943 award facts O. Stern (1946), The Method of Molecular Rays — Nobel lecture, December 12, for the 1943 prize J. DiSciacca and G. Gabrielse (2012), Direct Measurement of the Proton Magnetic Moment — author abstract, arXiv:1201.3038v2

## Continue with the models

These teaching Labs produce simulated data, which are separate from the historical observations discussed above.

- [Sort simulated molecules by speed and infer the proton moment](https://sandboxphysics.com/labs/molecular-beam-proton-moment/)
- [Compare how a magnetic gradient separates silver-atom spin states](https://sandboxphysics.com/labs/stern-gerlach-sequence/)

## Sources and reading notes

We read Stern’s Nobel lecture of December 1946 by retrieving the PDF directly; his prize was the 1943 award. The 1933 Nature entry names Estermann, Frisch and Stern, but we could not access its full text. We quote the lecture’s approximate early result and add no error bars or detailed reanalysis of our own. The 2012 single-proton paper is used only to compare a different method.

1. [X. Fan, T. G. Myers, B. A. D. Sukra and G. Gabrielse (2023), Measurement of the Electron Magnetic Moment, Phys. Rev. Lett. 130, 071801](https://physics.aps.org/featured-article-pdf/10.1103/PhysRevLett.130.071801)
2. [O. Stern (1946), The Method of Molecular Rays — Nobel lecture, December 12, for the 1943 prize](https://www.nobelprize.org/uploads/2018/06/stern-lecture.pdf)
3. [I. Estermann, R. Frisch and O. Stern (1933), Magnetic Moment of the Proton, Nature 132, 169–170 — publication record](https://www.nature.com/articles/132169a0)
4. [J. DiSciacca and G. Gabrielse (2012), Direct Measurement of the Proton Magnetic Moment — author abstract, arXiv:1201.3038v2](https://arxiv.org/abs/1201.3038v2)
5. [Otto Stern — official 1943 award facts](https://www.nobelprize.org/prizes/physics/1943/stern/facts/)

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