Chapter 8: Q2CQ (page 338)
Does circulating charge require both angular momentum and magnetic? Consider positive and negative charges simultaneously circulating and counter circulating.
No, the circulating charge does not require both angular momentum and magnetic.
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A beam of identical atoms in their ground state is sent through a Stem-Gerlach apparatus and splits into three lines. Identify possible sets of their total spin and total orbital angular momentum? Ignore possibilities in which sT is 2 or higher.
The Line: One of the most important windows to the mysteries of the cosmos is the 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 interactionโforthere 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 isthen find the magnetic field at the middle of the loop in terms of e,, , and.
(b) The proton sits right in the middle of the electron's magnetic moment. Like the electron the proton is a spinparticle, 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 proton.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?
Question: Huge tables of characteristic X-rays start at lithium. Why not hydrogen or helium?
Using the general rule for adding angular momenta discussed in Section 8.7 and further in Exercise 66, Find the allowed values offor three spin fermions. First add two, then add the third.
The line in copper is a very common one to use in X-ray crystallography. To produce it, electrons are accelerated through a potential difference and smashed into a copper target. Section 7.8 gives the energies in a hydrogen like atom as . Making the reasonable approximation that an electron in copper orbits the nucleus and half of its fellow electron, being unaffected by the roughly spherical cloud of other electrons around it. Estimate the minimum accelerating potential needed to make a hole in copper'sKshell.
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