1. The problem statement, all variables and given/known data for my comp physics course, we have to create a program that outputs all the possible electron transitions in hydrogen in the for n2 -> n1, where n1 < n2, and n2 < 21. We also have to determine the number of allowed pathways for the transition, and the energy and wavelength of the emitted photon. 2. Relevant equations n= 1,2,3,...,20 l= 0,1,2,...,19 m= -l,...,0,...,l (angular momentum quantum numbers) 3. The attempt at a solution I figured out how to do everything but the allowed pathways. I know the calculation of them has something to do with the angular momentum quantum numbers, but I can't even figure out how the number of pathways are determined, let alone create a program to determine them. All I know is that the output should be 3 for 2 -> 1, 3 for 3 -> 1, 15 for 3 -> 2, 15 for 4 -> 2, etc. Any help would be greatly appreciated.