The 21 cm Line: One of the most important windows to the mysteries of the cosmos is the 21 cm 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 momenta. Hydrogen's ground state has no spin-orbit interaction—for ℓ =0 there is no orbit. However, the proton and electron magnetic moments do interact. Consider the following simple model, (a) The proton sees itself 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 on the proton, treat this dispersed magnetic moment as behaving effectively like a single loop of current whose radius is a0, then find the magnetic field at the middle of the loop in terms of e, ħ, me, μ0, and a0. (b) The proton sits right in the middle of the electron's magnetic moment. Like the electron, the proton is a spin½ particle, 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 antialigned with that of the electron? (c) For the proton, g 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?
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.