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Chapter 8: Q3CQ (page 338)

Summarize the connection between angular momentum quantization and the stem-Gerlach experiment.

Short Answer

Expert verified

The quantized magnetic moment of the electron manifests as a splitting of the atomic beam.

Step by step solution

01

Summarize the experiment

The Stern-Gerlach experiment was to test the Bohr-Sommerfeld hypothesis that the direction of the angular momentum of the silver atom is quantized.

Electrons rotating in the hydrogen atom possess quantized angular momentum, which gives quantized magnetic moment. In the Stem-Gerlach experiment, silver atoms are sent through a non-uniform magnetic field.

02

Explanation

This impacts a force proportional to the magnetic moment. Here, a quantized magnetic moment of the electron manifests as a splitting of the atomic beam.

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Most popular questions from this chapter

Show that the symmetric and anti symmetric combinations of (8−19)and(8−20)are solutions of the two. Particle Schrödinger equation(8−13)of the same energy asψn(x1)ψm(x2), the unsymmetrized product(8−17).

The 21cm Line: One of the most important windows to the mysteries of the cosmos is the 21cm line. With it astronomers map hydrogen throughout the universe. An important trait is that it involves a highly forbidden transition that is, accordingly, quite long-lived. But it is also an excellent example of the coupling of angular momentum. Hydrogen's ground state has no spin-orbit interaction—forl=0there is no orbit. However, the proton and electron magnetic moments do interact. Consider the following simple model.

(a) The proton seesitself surrounded by a spherically symmetric cloud of 1s electron, which has an intrinsic magnetic dipole moment/spin that of course, has a direction. For the purpose of investigating its effect the proton, treat this dispersed magnetic moment as behaving effectively like a single loop of current whose radius isa0then find the magnetic field at the middle of the loop in terms of e,ℏ,me , μ0anda0.

(b) The proton sits right in the middle of the electron's magnetic moment. Like the electron the proton is a spin−12particle, with only two possible orientations in a magnetic field. Noting however, that its spin and magnetic moment are parallel rather than opposite, would the interaction energy be lower with the proton's spin aligned or anti-aligned with that of the electron?

(c) For the protongρ.is 5.6. Obtain a rough value for the energy difference between the two orientations.

(d) What would be the wavelength of a photon that carries away this energy difference?

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