An isolated cloud of cold hydrogen gas in space is illuminated from behind by a hot
PHYSICS · Multi-part · A Level · Physics · Particles and radiation · Particles and radiation
Problem
An isolated cloud of cold hydrogen gas in space is illuminated from behind by a hot, dense star. When the spectrum of starlight that has passed through the cloud is examined, a dark line is seen at a wavelength of 121.6 nm.
Selected energy levels for the hydrogen atom are listed below (energies are relative to the zero of an unbound electron).
• n=1:−13.6eV
• n=2:−3.40eV
• n=3:−1.51eV
• n=4:−0.85eV
(a) Calculate the energy, in electron-volts, of a photon whose wavelength is 121.6 nm.
(b) Using the tabulated energy levels, determine the initial and final principal quantum numbers that account for the 121.6 nm line. Show your work.
(c) Explain why the 121.6 nm line appears as a dark (absorption) line in the spectrum described, rather than as a bright (emission) line.