A student in a physics laboratory observes a hydrogen spectrum with a diffraction grating for the purpose of measuring the wavelengths of the emitted radiation. In the spectrum, she observes a yellow line and finds its wavelength to be 589 nm.

(a) Assuming this is part of the Balmer series, determine , the principal quantum number of the initial state.

(b) What is unreasonable about this result? 

(c) Which assumptions are unreasonable or inconsistent?