Why is it much harder to explain the line spectra of polyelectronic atoms and ions than it is to explain the line spectra of hydrogen and hydrogen-like ions

Two people each hold the end of a rope and create waves by moving their arms up and down. this wave is best classified as a transverse wave because a) both the rope particles and the wave are moving in the same direction. b) the wave is moving up and down as the particles of the rope move horizontally. c) the wave is moving horizontally as the particles of the rope move up and down. eliminate d) the wave is moving in a parallel direction with the motion of the person's arms.