Clouds of hot, glowing interstellar hydrogen gas can be found in some parts of our galaxy. In some of the hydrogen atoms, electrons may be excited to quantum levels with n = 100 or more.

(a) Calculate the wavelength that would be observed on Earth if electrons fell from the level with n = 100 to that with n = 2. 

(b) In what series would this transition be found?

(c) Some of these high-energy electrons fall to intermediate states, such as n = 90. Would the wavelengths of a transition from a state with n = 100 to one with n = 90 be longer or shorter than those in the Balmer series? Explain your reasoning.