Stern-Gerlach Experiment

A work in progress by Hunter Legerton

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.

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]

A Computational Model

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Connectedness

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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.

See also

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Further reading

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

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

External links

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References

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