Molecular vibrational energy levels:
(a) A HCl molecule can be considered to be a quantized harmonic oscillator, with quantized vibrational energy levels
that are evenly spaced. Make a rough estimate of this uniform energy spacing in electron volts (where 1 eV = 1.6 ×
10−19 J). You will need to make some rough estimates of atomic properties based on prior work. For comparison
with the spacing of these vibrational energy states, note that the spacing between quantized energy levels for
“electronic” states such as in atomic hydrogen is of the order of several electron volts.
(b) List several photon energies that would be emitted if a number of these vibrational energy levels were occupied due
to electron excitation. To what region of the spectrum (x-ray, visible, microwave, etc.) do these photons belong? (See
Figure 8.1 at the beginning of the chapter.)