An introductory astronomy reference book includes verbal descriptions of the…
PHYSICS · Multi-part · A Level · Physics · Particles and radiation · Particles and radiation
Problem
An introductory astronomy reference book includes verbal descriptions of the low-lying electronic structures of two neutral atoms.
• Element A has a ground-state energy of −13.6 eV and its first three excited stationary states lie at −3.4 eV, −1.5 eV, and −0.9 eV.
• Element B has a ground-state energy of −24.6 eV and its first three excited stationary states lie at −5.5 eV, −2.9 eV, and −1.2 eV.
A laboratory spectrograph records the bright-line emission spectrum of an unknown low-pressure gas, then compares it to the tabulated information above.
Answer the following questions about the physical basis for identifying the gas sample.
(a) Describe, without performing detailed calculations, why the two elements listed must generate different sets of photon wavelengths when they return from excited states to the ground state. In your answer, explicitly reference energy conservation and the numerical values given.
(b) Explain why a photon produced by the transition from the −3.4 eV state to the ground state of Element A could also appear as a dark line (rather than a bright line) in a spectrum under different experimental conditions. Clearly articulate the physical process involved.
(c) Outline a logical procedure for deciding whether the unknown gas is Element A, Element B, or neither, using only the information provided and qualitative comparisons between observed and reference spectra. Your explanation should indicate the key spectral features you would focus on and justify how those features lead to an unambiguous identification.