The "selection rule" for x-ray emission requires a change in orbital angular momentum to be Delta L= 1. Thus, the K alpha emission line corresponds to the 2p rightarrow 1s transition. However, spin angular momentum. S. also spins the K alpha emission into K alpha1 and K alpha2 lines via the spin-orbit interaction. lambda L S. where lambda is a positive constant. Although this is a relatively small effect, it is easily observable in x-ray diffraction experiments using tube sources. For example, the splitting is roughly 0.02 keV out of 8keV for Cu K alpha. Consider the total angular momentum. J. of single electron states. What are the transitions (in terms of the relevant angular momentum quantum numbers) within 2p rightarrow 1s that occur due to the spin-orbit interaction? What are the degeneracies? Consider matrix elements for the above transitions to show that the emission line wavelength of K alpha1 is shorter than K alpha2. Which of the above transitions corresponds to K alpha1 and K alpha2?