9. (a) Find the wavelength of the emitted photon when a Hydrogen atom transitions from n=4 to n=2. List the possible pairs of initial and final states including angular momentum, and draw the energy-level diagram and show the 3 allowed transitions with arrows on the diagram. One of these transitions results in a meta-stable state - which one? Why?
(b) To a first-order approximation, all of the above transitions have the same energy. Qualitatively explain which of these transitions would have the largest energy when spin-orbit coupling is taken into account. Use the nLj notation to specify the exact initial and final states.