a billion billion times more likely for light having wavelength of 300.0 nm
than a wavelength of 21.0 cm.Before we get to lasers themselves, we need to jump ahead a little (to
Chapters 17 and 18). The basic idea is that thermal energy may be sufficient to
cause excited quantum states to be populated to a significant degree—
depending on the amount of thermal energy available and the amount of energy
necessary to reach the excited state. It will be shown later that if an energy level
is Eenergy units (typically, joules) above the ground state, then the fraction of
the total species,labeled F, that is in the excited state is given by the equation
Fe^ E/kT (15.34)
where Tis the absolute temperature and kis Boltzmann’s constant. We are as-
suming that the two energy states involved are nondegenerate. Otherwise, de-
generacy must be included (see Chapters 17 and 18). If the molar energy were
used, then the equation would be
Fe^ E/RT
where Ris the ideal gas law constant. For example, rotational levels in gas-
phase molecules can be thermally excited, so that the most populated rota-
tional eigenstate is not the J0 state (see Chapter 14). Vibrational energy
states are often thermally populated. Electronic energy levels are rarely ther-
mally populated because most ambient temperatures are so low relative to the
amount of excitation energy that practically all systems are in the ground elec-
tronic state. Systems whose atoms or molecules follow equation 15.34 are said
to be at thermal equilibrium.Each possible energy level has a certain fraction
of molecules having that energy level. The energy levels are said to have a cer-
tain populationof systems inhabiting that energy. A system at thermal equilib-
rium is illustrated in Figure 15.27.
Now, to lasers. Because there is both spontaneous and stimulated emission,
systems in thermal equilibria usually have more molecules in a lower-energy
electronic state than in a higher-energy electronic state. Suppose, however, that
a certain electronic state decays rather slowly. We call this a long-livedor
metastable excited state.Suppose too that we can excite the atoms or molecules
into the metastable excited state faster than that excited state decays. Under
those circumstances, we can populate the excited state over and above the frac-
tion dictated by thermal equilibrium, which is given by equation 15.34. Such a
situation is called a population inversionand is illustrated in Figure 15.28.
Population inversions can be achieved by light excitation, by electrical dis-
charge, or even by chemical reaction. Typically, at least three energy levels are
needed to establish a population inversion. There is the lowest-energy initial
state (sometimes but not always the ground state), and an initial excited state
that decays rather quickly into a second, lower-energy, long-lived excited state.
It is between the lower-energy excited state and the ground state that the pop-
ulation inversion is established.
Even when a population inversion is established and maintained, both spon-
taneous and stimulated emission still occur. However, the stimulated emission
is the key. A photon of a particular wavelength stimulates the emission of an-
other photon of the same wavelength, which can stimulate the emission of a
photon of the same wavelength, which can stimulate the emission of a photon
of the same wavelength, which can... and so the building up of a collection15.12 Lasers 553Figure 15.27 Thermal equilibrium is charac-
terized by this type of population of excited states
that might be accessed by thermal energy alone.
The higher the energy level, the smaller the pop-
ulation. Statistical analysis indicates that the de-
crease in population of the energy levels is expo-
nential in nature.
Figure 15.28 A population inversion is
achieved when higher energy levels are more pop-
ulated than is predicted by a thermal equilibrium
(see Figure 15.27). Here, the third energy level is
experiencing a population inversion. Population
inversions are not normally encountered, but can
be easily engineered. All lasers require a popula-
tion inversion as part of the laser process.