Question

a) According to the Rydberg equation, the line with the shortest wavelength in the emission spectrum of atomic hydrogen is predicted to lie at a wavelength (in nm) of _____

b) According to the Rydberg equation, the longest wavelength (in nm) in the series of H-atom lines produced when the electron falls to the state n = 3 is ____

Answer 1

1/wavelength = R(1/n^2 - 1/n^2) where the two n symbols are n1 for the first one and n2 for the second.
So the shortest wavelength (the most energy) will come when an electron falls from the outside most energy level to the inner most energy level. Therefore, plug in n1 = 1 and n2 = 0 and solve for wavelength. That will be the Lyman series limit which you probably have in your text.

2. The longest wavelength when n1 = 3 (it falls to 3) would be for it to start at n =4. So n1 = 3 and n2 = 4. Remember n1<n2 so in my mind this is backwards but you gotta go with the flow. It's because the energy levels have - energy and when the electron is at an infinite distance that's when energy = 0