A vapor of an unknown element X is electrically excited inside a sealed tube. Four bound-state energies (relative to the free-electron level) are known for element X:
• Level 1: E1=−12.0eV (ground state)
• Level 2: E2=−8.4eV
• Level 3: E3=−5.0eV
• Level 4: E4=−3.3eV
Two bright spectral lines are observed at wavelengths 365 nm and 254 nm when the vapor is viewed directly through a spectroscope.
(a) Calculate the photon energy (in electron-volts) corresponding to each of the two observed wavelengths.
(b) Using the tabulated energy levels, identify the pair of levels involved in each observed transition. Show all reasoning and calculations.
(c) Explain why the two lines observed in this electrically excited vapor appear in emission rather than absorption.
(d) Suppose instead that white light is shined through a cool sample of element X in its ground state. Predict which, if any, of the two wavelengths is most likely to produce a strong absorption line, and justify your prediction.