Stern-Gerlach Experiment: Difference between revisions

Latest revision as of 20:21, 5 December 2015

Written by Hunter Legerton

In 1922, German physicists Otto Stern and Walther Gerlach sent silver atoms through a non-uniform magnetic field into a detector screen. Based on their understanding of the orientation of magnetic dipoles, Stern and Gerlach expected the atoms to be deflected varying amounts, creating an even range of impacts on the detector screen. However, the atoms were deflected either up or down to two points of accumulation. This experiment, now known as the Stern-Gerlach Experiment, demonstrated angular momentum quantization and the quantum property spin.

The Main Idea

File:Quantum spin and the Stern-Gerlach experiment.ogv

When a beam of silver atoms were sent through the non-uniform magnetic field, Stern and Gerlach expected the atoms to act as magnetic dipoles and, depending on their orientation, to be deflected in a continuous range. However, it was proven that the atoms had a quantum property, spin, that determined the angular momentum of the electrons as either up or down, much like a classically spinning object but only for certain values (specifically spin +ħ/2 or spin −ħ/2 where ħ is the reduced Planck Constant, h / 2π)

Therefore, we know that magnetic materials get their magnetic dipole moments from electron spin, and therefore many materials with up/down pairs of electrons do not have magnetic dipole moments.

A Mathematical Model

The Stern-Gerlach Experiment relies heavily on the uncertainty principle,

[math]\displaystyle{ \sigma_{x}\sigma_{p} \geq \frac{\hbar}{2} }[/math]

the Dirac equation, which describes spin-1/2 particles (such as an electron with +1/2 or -1/2 spin)

[math]\displaystyle{ \left(\beta mc^2 + c\left(\sum_{n \mathop =1}^{3}\alpha_n p_n\right)\right) \psi (x,t) = i \hbar \frac{\partial\psi(x,t) }{\partial t} }[/math]

and the Pauli equation, which works with the Dirac equation to describe the effects of electromagnetic field on spin:

[math]\displaystyle{ \left[ \frac{1}{2m}(\boldsymbol{\sigma}\cdot(\mathbf{p} - q \mathbf{A}))^2 + q \phi \right] |\psi\rangle = i \hbar \frac{\partial}{\partial t} |\psi\rangle }[/math]

And it is known that the magnetic dipole moment is related to angular momentum (L = r x p),

[math]\displaystyle{ μ=\frac{1}{2} \frac{e}{m} L ≈ \frac{1}{2} \frac{e}{m} ℏ }[/math]

Connectedness

The Stern-Gerlach had immense implications on the discovery and understanding of quantized properties. Many later developments of modern physics heavily relied on the conclusions of this experiment. Several later experiments aimed to extend the Stern-Gerlach findings and eventually led to the science behind atomic clocks and Magnetic Resonance Imaging (MRI) Machines.

Norman Foster Ransey, Jr.'s experiments with Isidor Rabi's Rabi oscillations led to the discovery that atomic states can be changed using radio frequency fields, the basis for atomic clock timekeeping.

History

Otto Stern and Walther Gerlach conducted the experiment in Frankfurt, Germany, in 1922. At the time of the experiment, the Bohr model was the predominant atomic model describing electron atomic orbitals. The specified energy levels at which electrons exist is known as space quantization, just as the specified angular momentum of electrons is spin quantization. The experiment was actually conducted before the theory of electron spin was proposed by Uhlenbeck and Goudsmit in 1926. The experiment, along with laying the foundation for electron spin, has been called the most direct evidence of quantization in quantum mechanics and the best demonstration of quantum measurement.

https://en.wikipedia.org/wiki/Stern%E2%80%93Gerlach_experiment https://en.wikipedia.org/wiki/Quantization_(physics) https://en.wikipedia.org/wiki/Measurement_in_quantum_mechanics https://en.wikipedia.org/wiki/Magnetic_moment

Chabay, R., & Sherwood, B. (2015). Matter & interactions (4th ed., Vol. 2). Hoboken, New Jersey: Wiley.

[Magnetic Dipole Moment]

@@ Line 1: / Line 1: @@
-A work in progress by Hunter Legerton
+Written by Hunter Legerton
 [[File:Stern-Gerlach_experiment.PNG|thumb|Silver atoms travel through the non-uniform magnetic field and are deflected to only two specific locations rather than in a continuous range]]
 In 1922, German physicists Otto Stern and Walther Gerlach sent silver atoms through a non-uniform magnetic field into a detector screen. Based on their understanding of the orientation of magnetic dipoles, Stern and Gerlach expected the atoms to be deflected varying amounts, creating an even range of impacts on the detector screen. However, the atoms were deflected either up or down to two points of accumulation. This experiment, now known as the Stern-Gerlach Experiment, demonstrated angular momentum quantization and the quantum property spin.
@@ Line 5: / Line 5: @@
 ==The Main Idea==
 [[File:Quantum spin and the Stern-Gerlach experiment.ogv|thumb|upright=1.5|Video explaining quantum spin versus classical magnet in the Stern–Gerlach experiment]]
 When a beam of silver atoms were sent through the non-uniform magnetic field, Stern and Gerlach expected the atoms to act as magnetic dipoles and, depending on their orientation, to be deflected in a continuous range. However, it was proven that the atoms had a quantum property, spin, that determined the angular momentum of the electrons as either up or down, much like a classically spinning object but only for certain values (specifically spin +ħ/2 or spin −ħ/2 where ħ is the reduced [https://en.wikipedia.org/wiki/Planck_constant Planck Constant], ''h'' / 2''π'')
+Therefore, we know that magnetic materials get their magnetic dipole moments from electron spin, and therefore many materials with up/down pairs of electrons do not have magnetic dipole moments.
 ===A Mathematical Model===
-What are the mathematical equations that allow us to model this topic.  For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.
+The Stern-Gerlach Experiment relies heavily on the uncertainty principle,
-===A Computational Model===
+:: <math>\sigma_{x}\sigma_{p} \geq \frac{\hbar}{2}</math>
-How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]
+the Dirac equation, which describes spin-1/2 particles (such as an electron with +1/2 or -1/2 spin)
-==Examples==
+:: <math>\left(\beta mc^2 + c\left(\sum_{n \mathop =1}^{3}\alpha_n p_n\right)\right) \psi (x,t) = i \hbar \frac{\partial\psi(x,t) }{\partial t} </math>
-Be sure to show all steps in your solution and include diagrams whenever possible
+and the Pauli equation, which works with the Dirac equation to describe the effects of electromagnetic field on spin:
-===Simple===
+:: <math>\left[ \frac{1}{2m}(\boldsymbol{\sigma}\cdot(\mathbf{p} - q \mathbf{A}))^2 + q \phi \right] |\psi\rangle = i \hbar \frac{\partial}{\partial t} |\psi\rangle  </math>
-===Middling===
-===Difficult===
+And it is known that the magnetic dipole moment is related to angular momentum (L = r x p),
+:: <math>μ=\frac{1}{2} \frac{e}{m} L ≈ \frac{1}{2} \frac{e}{m} ℏ  </math>
 ==Connectedness==
-#How is this topic connected to something that you are interested in?
+The Stern-Gerlach had immense implications on the discovery and understanding of quantized properties. Many later developments of modern physics heavily relied on the conclusions of this experiment. Several later experiments aimed to extend the Stern-Gerlach findings and eventually led to the science behind atomic clocks and [[Magnetic Resonance Imaging]] (MRI) Machines.
-#How is it connected to your major?
-#Is there an interesting industrial application?
+[https://en.wikipedia.org/wiki/Norman_Foster_Ramsey,_Jr. Norman Foster Ransey, Jr.]'s experiments with [https://en.wikipedia.org/wiki/Isidor_Rabi Isidor Rabi]'s [https://en.wikipedia.org/wiki/Rabi_Oscillation Rabi oscillations] led to the discovery that atomic states can be changed using radio frequency fields, the basis for atomic clock timekeeping.
 ==History==
-Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
+[https://en.wikipedia.org/wiki/Otto_Stern Otto Stern] and [https://en.wikipedia.org/wiki/Walter_Gerlach Walther Gerlach] conducted the experiment in Frankfurt, Germany, in 1922. At the time of the experiment, the Bohr model was the predominant atomic model describing electron atomic orbitals. The specified energy levels at which electrons exist is known as space quantization, just as the specified angular momentum of electrons is spin quantization. The experiment was actually conducted before the theory of electron spin was proposed by Uhlenbeck and Goudsmit in 1926. The experiment, along with laying the foundation for electron spin, has been called the most direct evidence of quantization in quantum mechanics and the best demonstration of quantum measurement.
 == See also ==
-Are there related topics or categories in this wiki resource for the curious reader to explore?  How does this topic fit into that context?
+The Stern-Gerlach experiment had huge implications on [https://en.wikipedia.org/wiki/Measurement_in_quantum_mechanics atomic measurement], [https://en.wikipedia.org/wiki/Quantization_(physics) quantization], and our understanding of [https://en.wikipedia.org/wiki/Magnetic_moment magnetic moment].
 ===Further reading===
+[[File:Quantum spin and the Stern-Gerlach experiment.ogv]]
-Books, Articles or other print media on this topic
+[[File:Quantum spin and the Stern-Gerlach experiment.ogv|thumb|upright=1.5|Video explaining quantum spin versus classical magnet in the Stern–Gerlach experiment]]
 ===External links===
-[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]
+https://www.youtube.com/watch?v=rg4Fnag4V-E
+==References==
-==References==
+https://www.youtube.com/watch?v=rg4Fnag4V-E
+https://www.youtube.com/watch?v=waK4eKNXB4A
+https://en.wikipedia.org/wiki/Stern%E2%80%93Gerlach_experiment
+https://en.wikipedia.org/wiki/Quantization_(physics)
+https://en.wikipedia.org/wiki/Measurement_in_quantum_mechanics
+https://en.wikipedia.org/wiki/Magnetic_moment
-This section contains the the references you used while writing this page
+Chabay, R., & Sherwood, B. (2015). Matter & interactions (4th ed., Vol. 2). Hoboken, New Jersey: Wiley.
-[[Category:Which Category did you place this in?]]
+[Magnetic Dipole Moment]

Stern-Gerlach Experiment: Difference between revisions

Latest revision as of 20:21, 5 December 2015

Contents

The Main Idea

A Mathematical Model

Connectedness

History

See also

Further reading

External links

References

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