Stern-Gerlach experiment

Plaque on the building of the Physical Society in Frankfurt am Main

With the help of the Stern-Gerlach experiment from 1922, the physicists Otto Stern and Walther Gerlach observed the directional quantization of angular momentum for the first time . The Stern-Gerlach experiment is a fundamental experiment in physics and is used again and again to explain this quantum mechanical phenomenon, which cannot be understood within the framework of classical physics.

description

The Stern-Gerlach experiment, schematic

A beam of (electrically neutral) silver atoms flies through the gap between the pole shoes of a magnet in a vacuum . One pole piece has the shape of a cutting edge parallel to the beam, the other a flat groove. As a result, the magnetic field is highly inhomogeneous in the direction transverse to the beam . After the beam has passed through the magnetic field, the silver atoms are deposited on a glass plate. Two separate spots are found, i.e. the magnetic field splits the beam into two separate partial beams.

Explanation

The silver atom has a magnetic dipole moment of a certain magnitude, on which a force acts in the inhomogeneous field : ${\displaystyle {\vec {\mu }}}$ ${\displaystyle {\vec {B}}}$

${\displaystyle {\vec {F}}=\nabla \left({\vec {\mu }}\cdot {\vec {B}}\right)={\begin{pmatrix}0\\0\\\mu _{z}\cdot {\frac {\partial B}{\partial z}}\end{pmatrix}}}$

(The field direction is chosen as the -axis, in the figure: the vertical direction.) Depending on the magnitude of the -component of the magnetic moment, i. H. Depending on the angle of attack to the direction of the field, the different atoms experience forces of different magnitudes parallel or antiparallel to the direction of the field. Classically, therefore, one expects a continuous widening of the beam in the -direction. ${\displaystyle z}$ ${\displaystyle z}$ ${\displaystyle \mu _{z}}$ ${\displaystyle \pm z}$

The magnetic moment arises from and is parallel to the angular momentum of the atom. The angular momentum with the quantum number ½ only has the setting options or ( is the reduced Planck constant ). In the classic picture, this corresponds to a charged sphere rotating to the left or right with the same rotation speed. According to classical mechanics, on the other hand, the angular momentum vector could form any angle with the axis. ${\displaystyle {\vec {S}}}$ ${\displaystyle z}$ ${\displaystyle -\hbar /2}$ ${\displaystyle +\hbar /2\,}$ ${\displaystyle \hbar }$

Projection of the spin of a spin ½ particle onto the axis ${\displaystyle z}$

Since is parallel to , the component of can only have a certain positive value or an equally large negative value. Therefore, depending on the orientation of the angular momentum, each atom is subjected to the same amount of force, but opposite in direction, perpendicular to the direction of flight. The beam splits into two sub-beams, resulting in the observed distribution. ${\displaystyle {\vec {\mu }}}$ ${\displaystyle {\vec {S}}}$ ${\displaystyle z}$ ${\displaystyle {\vec {\mu }}}$

Peculiarity of the silver atom

In principle, the magnetic moment of an atom is formed by the totality of the orbital angular momenta and the spins of all its electrons (see Landé factor of an atom; the contribution of the atomic nucleus is negligibly small.) In the silver atom, however, only the 5 electron contributes to the magnetic moment, because all other electrons form closed shells with zero angular momentum. The 5 -electron has the orbital angular momentum quantum number (it has no orbital angular momentum). So the total angular momentum is just the spin of that one electron, and the whole silver atom behaves like a single spin 1/2 particle. In contrast to the electron, however, it is electrically neutral, so it cannot be deflected by the Lorentz force in the magnetic field or by electrical interference fields. ${\displaystyle s}$ ${\displaystyle s}$ ${\displaystyle l=0}$

story

Directional quantization was predicted by Peter Debye and Arnold Sommerfeld in 1916 when investigating the Zeeman effect . As Gerlach remembers, as soon as he arrived in Frankfurt in the autumn of 1920 he was drawn in by Max Born and Otto Stern to the atomic beam experiments, with which Gerlach had already carried out optical experiments during his time in Tübingen (the field of experiments on atomic beams was in 1911 from Louis Dunoyer de Segonzac ). In 1921 Stern had proposed an attempt to prove directional quantization. Carrying out the experiment was difficult because of the lack of financial resources during the inflationary period. However, Max Born provided money from his lectures on the theory of relativity, and Fritz Haber encouraged the experimenters and supported them with funds from the Hoshi Foundation. Money came through Albert Einstein, whom Born had informed, to procure the strong magnet.

The question of whether a quantum mechanical effect could be observed at all with the experiment was controversial and discussed many times, also because of the technical difficulty. Born and Niels Bohr believed in it; Debye didn't believe it; Sommerfeld believed only a semi-classical effect would be observable. Gerlach and Stern themselves were open about the result of the experiment. However , as Gerlach reports , Stern expected more of a classic effect.

The experiment was carried out by Gerlach in February 1922 in the building of the Physical Society in Frankfurt am Main on Robert-Mayer-Strasse, according to Horst Schmidt-Böcking (according to received weather descriptions from the day of the experiment) in the night from 7 to 8 August. February. The result was surprising, because the particle spin and the existence of "half-integer" angular momenta were not yet known. The experimenters had chosen silver for practical reasons because it was easy to detect (precipitation on a glass plate). They had already shown that the silver atom has a non-zero magnetic moment in its ground state. Their accurate measurement of this magnetic moment, made shortly thereafter, gave the expected amount, 1 Bohr magneton . In terms of the Bohr-Sommerfeld atomic model, they traced the magnetic moment back to an orbital angular momentum with the quantum number . Therefore they had actually expected a splitting into partial beams, but the undeflected central partial beam did not appear. ${\displaystyle l=1}$ ${\displaystyle 2l+1=3}$

Gerlach informed Stern, who was in Rostock, of the result in a telegram with the words: Bohr is right after all . In a telegram of congratulations to Gerlach dated February 17, 1922, Wolfgang Pauli expressed the hope that Stern would now also be convinced of directional quantization.

Directional quantization as a real, observable effect had been proven experimentally, but the interpretation of the result had to be corrected later after the concept of electron spin had been introduced in 1925. In 1927 Phipps and Taylor carried out the Stern-Gerlach experiment with hydrogen atoms and also obtained two partial beams.

Albert Einstein commented on the experiment after learning about it in 1922: But the most interesting thing at the moment is the experiment by Stern and Gerlach. The adjustment of the atoms without collisions cannot be understood according to the present methods of reflection through radiation; an adjustment should by law last more than 100 years. I made a little calculation with Ehrenfest about it. Rubens considers the experimental result to be absolutely certain.

Almost all of the original equipment was destroyed during World War II. A reconstruction of the experiment by Horst Schmidt-Böcking with some originals - a microscope owned by Stern (given to Schmidt-Böcking by a niece of Stern in 2009) and vacuum pumps - was shown in 2014 at an anniversary exhibition of the University of Frankfurt.

Stern and Gerlach were nominated several times (82 nominations for Stern, 30 for Gerlach) for the Nobel Prize for the experiment. As the Nobel Prize nominations progressed, the laureate increasingly focused on Stern. z. B. recommended as "leading spirit of investigations".

When it was awarded to Stern in 1944 (retrospectively for the year 1943), the experiment was not explicitly mentioned, but Stern's contribution to the development of the molecular beam method and the discovery of the magnetic moment of the proton. However, the Stern-Gerlach experiment was highlighted in an appreciation by Nobel Prize Committee member Erik Hulthén in the presentation of the Nobel Prize ceremony on Swedish radio on December 10, 1944. Gerlach was passed over for the award, although he had been nominated for the Nobel Prize 30 times, most recently in 1944 by the influential Nobel Prize Committee member Manne Siegbahn , probably because of his prominent role in German physics research during the Second World War.

application

Each of the two partial beams in the Stern-Gerlach experiment is polarized . Therefore, the principle of the experiment is used in some sources for generating a polarized beam of ions - mostly protons or deuterons - for particle accelerators . The atomic beam passes through a quadrupole or sextupole magnet instead of the dipole magnet . Such a magnet focuses atoms with one of the two angular momentum positions towards the center onto its axis, while defocusing the other atoms, i.e. scattering them outwards. A polarized ion beam can be obtained from the focused atoms by impact ionization in a weak external magnetic field by utilizing hyperfine splitting .

The experiment with other particles

atoms

A beam of diamagnetic atoms initially shows no splitting, since their electron shells have no magnetic moment. At very high resolution, however, a splitting can be seen, which is caused by the nuclear spin with its much smaller magnetic moment. For paramagnetic atoms, any splitting caused by the electron shell is further split by the magnetic moment of the nucleus.

neutrons

Beam splitting in the inhomogeneous magnetic field has occasionally been used with success to measure the polarization of a beam of slow neutrons .

charged particles

A Stern-Gerlach experiment with charged particles, such as free electrons, is usually regarded as impossible because the Lorentz force on the charge is much greater than the force on the magnetic moment; Due to the inhomogeneous field, even the transverse dimensions of the jet and small differences in speed would lead to a smearing that would cover the spin-related splitting. In 1997 Batelaan and M. doubted this statement from a theoretical point of view. They consider it fundamentally possible to build a polarizer for electron beams based on the principle of the Stern-Gerlach experiment. Other researchers have contradicted these considerations.

Such a possibility is even more remote for protons or other ions than for electrons, because their magnetic moment is two to three powers of ten smaller.

literature

• Gerthsen, Kneser, Vogel: Physics . Springer-Verlag, 15th edition, 1986, ISBN 3-540-16155-4 , pp. 615–616
• H. Haken, H. Chr. Wolf: Atomic and Quantum Physics . 8th edition, Springer 2004, ISBN 3-540-02621-5 , pages 196–197
• W. Demtröder: Atoms, Molecules and Photons . Springer, 2010, ISBN 978-3-642-10297-4 , pages 175–176

web links

• Bretislav Friedrich and Dudley Herschbach, "Stern and Gerlach: How a Bad Cigar Helped Reorient Atomic Physics", Physics Today 56, 53-59 (2003) https://doi.org/10.1063/1.1650229

itemizations

1. ^ ^{a b} Stern, Otto (1888-1969) | Frankfurter Lexikon. October 22, 2019, retrieved October 29, 2021 . 
2. ↑ Gerlach, Walther Frankfurter Lexikon. October 22, 2019, retrieved October 29, 2021 . 
3. ↑ Experiment in Physics > Appendix 5: Right Experiment, Wrong Theory: The Stern-Gerlach Experiment (Stanford Encyclopedia of Philosophy). Retrieved October 29, 2021 . 
4. ↑ Walther Gerlach and Otto Stern: The experimental proof of directional quantization in the magnetic field . In: Journal of Physics . tape 9 , 1922, p. 349-352 , doi : 10.1007/BF01326983 .
5. ↑ Debye, Quantum Hypothesis and Zeeman Effect, News Akad. Wiss. Göttingen, Math-Phys. Klasse, 1916. p. 142, and Physical Journal, volume 17, 1916, p. 507.
6. ↑ P. Debye: Quantum hypothesis and Zeemann effect . In: News from the Society of Sciences in Göttingen, Mathematical-Physical Class . tape 1916 , 1916, p. 142–153 ( eudml.org [accessed 29 October 2021]).
7. ↑ Sommerfeld, On the theory of the Zeeman effect of the hydrogen lines, with an appendix on the Stark effect, Physical Journal , Volume S. 17, 1916, pp. 491-507
8. ↑ Wolfgang Pauli: Sommerfeld's contributions to quantum theory . In: Physics and Epistemology . Vieweg+Teubner Verlag, Wiesbaden 1984, ISBN 978-3-528-08563-6 , p. 32–41 , doi : 10.1007/978-3-322-88799-3_5 ( springer.com [accessed 29 October 2021]).
9. ↑ Stern, A way to experimentally test directional quantization in the magnetic field , Z. f. Physics, Volume 7, 1921, pp. 249-253
10. ↑ Gerlach, Memories of Albert Einstein 1908-1930, Physical Sheets Volume 35, 1979, Issue 3, p. 97f
11. ↑ Astrid Ludwig, The Forgotten Nobel Prize Winner , Frankfurter Rundschau, December 28, 2010, Horst Schmidt-Böcking on Otto Stern
12. ↑ Walther Gerlach and Otto Stern: The magnetic moment of the silver atom . In: Journal of Physics . tape 9 , 1922, p. 353-355 , doi : 10.1007/BF01326984 .
13. ^ ^{a b} Wolfgang Gentner, Words of Remembrance for Walther Gerlach , Order Pour le Mérite, Speeches and Words of Remembrance, Volume 16, 1980, pp. 47–53, telegram from Gerlach to Stern, p. 48, postcard from Pauli, p. 49
14. ↑ TE Phipps, JB Taylor: The Magnetic Moment of the Hydrogen Atom. Physical Review Vol. 29 (1927) pp. 309-320
15. ↑ Einstein, Born, Exchange of letters, Langen-Müller, p. 102f, letter no. 42 (undated)
16. ↑ Nomination archive - Otto Stern. Nobel Prize Outreach AB, April 1, 2020, retrieved October 29, 2021 (US English). 
17. ↑ Nomination archive - Walter Gerlach. April 1, 2020, retrieved October 29, 2021 (American English). 
18. ↑ Otto Stern's Collected Letters - Volume 2 . 2019, p. 293 , doi : 10.1007/978-3-662-58837-6 .
19. ↑ Daniel Kleppner: Our Enduring Legacy from Otto Stern . In: Molecular Beams in Physics and Chemistry . Springer International Publishing, Cham 2021, ISBN 978-3-03063962-4 , p. 97–117 , doi : 10.1007/978-3-030-63963-1_7 ( springer.com [accessed 29 October 2021]).
20. ↑ The Nobel Prize in Physics 1943. Retrieved October 29, 2021 (American English). 
21. ↑ Josef Georg Huber, Horst Schmidt-Böcking, Bretislav Friedrich: Walther Gerlach (1889–1979): Precision Physicist, Educator and Research Organizer, Historian of Science . In: Molecular Beams in Physics and Chemistry . Springer International Publishing, Cham 2021, ISBN 978-3-03063962-4 , p. 119–161 , doi : 10.1007/978-3-030-63963-1_8 ( springer.com [accessed 29 October 2021]).
22. ↑ Horst Schmidt-Böcking, Alan Templeton, Wolfgang Trageser (eds.), Otto Sterns Collected Letters, Volume 2, Springer 2019, p. 344. According to the authors, however, the connection cannot be proven.
23. ↑ G. Clausnitzer, R. Fleischmann, H. Schopper, Journal of Physics Volume 144 (1956) p. 336
24. ↑ H. Paetz gen. Schieck: Nuclear Physics with Polarized Particles. Heidelberg etc.: Springer, 2012. ISBN 978-3-642-24225-0
25. ↑ Gerthsen, Kneser, Vogel (see bibliography)
26. ↑ S. Barkan et al.: Measurement of the Polarization of Thermal Neutron Beams of Mixed Velocities. Review of Scientific Instruments Vol. 39 (1968) p. 101. doi : 10.1063/1.1683079
27. ↑ JE Sherwood, TE Stephenson, Seymour Bernstein: Stern-Gerlach Experiment on Polarized Neutrons . In: Physical Review . tape 96 , no. 6 , December 15, 1954, p. 1546–1548 , doi : 10.1103/PhysRev.96.1546 ( aps.org [accessed 29 October 2021]).
28. ↑ ^{a b} H Batelaan, TJ Gay, JJ Schwendiman: Stern-Gerlach Effect for Electron Beams . In: Physical Review Letters . tape 79 , no. 23 , December 8, 1997, p. 4517–4521 , doi : 10.1103/PhysRevLett.79.4517 ( aps.org [accessed 29 October 2021]).
29. ↑ George H. Rutherford, Rainer Grobe: Comment on Stern-Gerlach Effect for Electron Beams . In: Physical Review Letters . tape 81 , no. 21 , November 23, 1998, p. 4772–4772 , doi : 10.1103/PhysRevLett.81.4772 ( aps.org [accessed 29 October 2021]).
30. ↑ RW: At the heart of the antimatter mystery. MPG May 28, 2014, retrieved October 29, 2021 .