Albert Einstein used statistical mechanics (Chapter 8) to show that:
(14.23)
Thus the rate of stimulated absorption and stimulated emission are equal
and there is a net rate of absorption because there are more electrons in
the lower states:
Wnet=(N−N′)Bρ (14.24)
Lasers
The design of lasers is critically based upon the balance of the number
of electrons in two electronic states. By establishing a larger number of
electrons in the higher-energy state, it is possible to create a net emission
of photons, all of which have the same frequency. The creation of a larger
number in the higher-energy state is called population inversion. To achieve
a population inversion it is necessary to provide energy into the system
that can specifically change the energies of the electrons. In the simplest
version, consider a total of four electronic levels (Figure 14.9). The goal
BB′==A
h
c
and B
8 3
3
πυ
Figure 14.9A schematic diagram of the transitions that occur in a laser and
the physical layout of a laser. After pumping of electrons from level 1 to
level 2, the excited electrons can make a radiationless transition to level 3,
followed by the laser transition to level 4 and relaxation back to level 1.
300 PART 2 QUANTUM MECHANICS AND SPECTROSCOPY
Pump
Energy
Laser
transition
Dye
Excitation radiation
Partially transmitting
mirror
Laser
output
Radiationless
transition
3
4
2
1
Relaxation
