8.6 Exercise 24

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, they observe a yellow line and find its wavelength to be 589 nm. (a) Assuming that this is part of the Balmer series, determine $n_{\text{i}} ,$ the principal quantum number of the initial state. (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?