In extremely energetic systems such as the Sun, hydrogen emission lines can be seen from shells as high as n = 40.

The spectrum emitted is quite striking because the energy levels become spaced quite closely.

(a) Calculate the difference in energy (in J) between the n = 2 and n = 3 levels, and compare it with the difference in energy between the n = 32 and n = 33 levels.

(b) Calculate the largest energy difference (in J) that can be observed in the hydrogen atom.

(c) Explain why there is a limit to the energy difference.

(d) Is there a physical phenomenon that corresponds to this difference? Explain your answer.