In the Balmer series for the atomic emission of hydrogen, emission lines with n going from 3 → 2, 4 → 2, 5 → 2, and 6 → 2 are in the visible spectrum.

(a) What are the wavelengths of the light emitted in these transitions?

(b) A spectrometer is a device that disperses light into its constituent wavelengths, and provides a means of measuring these wavelengths. You and your team are designing a simple spectrometer using a transmission grating with 1500 lines/cm. A collimated beam of light from a hydrogen discharge tube (which emits light from all possible hydrogen atomic transitions) passes through the grating. At what second-order angles (m = 2) do you expect each of the emission lines calculated in (a) to appear?

(c) You place a screen with a coating that fluoresces when exposed to ultraviolet light in the light emerging from the grating, and you observe another line at ???? = 6.84°. Calculate the wavelength of this light. Does it come from the Balmer series?