b/1. The molecule N 2. 2. The
nucleus^178 Hf.
14.2 Rotation and vibration
14.2.1 Types of excitations
Figure a shows the visible-light spectrum of the molecule N 2. Be-
cause this particular chemical bond is unusually strong, the molecule
does not break apart, even at the high temperature of a gas discharge
tube, so we see the spectrum of the molecule, not of monoatomic
nitrogen. This spectrum is more complex than the spectrum of the
hydrogen atom, and that’s not surprising, because the number of
different states grows exponentially with the number of particles
(here, 14 electrons plus 2 nuclei).a/Visible spectrum of N 2. Violet
is on the left, red on the right.
What is more surprising is that there are some clear, simple pat-
terns in this spectrum — patterns simpler than any that we would
see in the spectrum of a monoatomic gas with the same number of
particles. To start to understand this, we note that N 2 lacks the
spherical symmetry of an individual atom, but it does have an axis
of symmetry, b/1. These properties are also possessed by many nu-
clei, e.g., b/2. We now consider three different ways in which an
excited energy state could occur in N 2 :- Individualparticles(electrons) can be raised to a higher energy
level. - The molecule canvibratealong its long axis, so that the nu-
clei (which have nearly all the inertia) move back and forth,
elongating and compressing the system. - The molecule canrotate.
14.2.2 Vibration
Particle excitations would produce the type of very complex, dis-
organized spectrum that we normally see in atoms that have many
electrons, so that isn’t what we’re seeing in figure a. What about
vibrations? For a classical harmonic oscillator, we know that the
frequency of vibration is independent of the amplitude. If a clas-
sical oscillator contains electric charge, it will emit electromagnetic
radiation at this frequency, smoothly and continuously draining it-
self of energy. As the energy is lost, the frequency stays the same.960 Chapter 14 Additional Topics in Quantum Physics