Physical Chemistry , 1st ed.

but the timescale is much faster than the normal human perception.

Phosphorescence, in terms of our own physical perception, is a much longer

lasting phenomenon than fluorescence.)

Most glow-in-the-dark objects use the phosphorescence phenomenon be-

cause it is longer lasting. (Old watch dials with glow-in-the-dark watch faces

actually relied on the fluorescence phenomenon, where a small amount of

radium was mixed with zinc sulfide (a material that fluoresced) to provide a

permanently glowing timepiece. Such radium-doped products are no longer

made.) Glow-in-the-dark paint is made possible by a phosphorescence phe-

nomenon, whereas Day-Glo or other so-called fluorescent paints take advan-

tage of fluorescence.

15.12 Lasers

Lasers are a widespread and recognizable part of the modern technical soci-

ety. They also represent such an unusual example of how electronic energy

levels are utilized that a discussion of how (some) lasers work should be con-

sidered in this chapter. The very word “laser” is an example of how technol-

ogy affects vocabulary. Originally an acronym for light amplification by stim-

ulated emission of radiation, it has become a word in its own right. The maser

(microwave.. .) preceded the laser, but it worked in the microwave region of

the spectrum and was invisible to the eye and relatively low in energy. The

fundamental theory behind lasers (and masers) was developed by Albert

Einstein (Figure 15.25) around 1917.

In trying to understand the interactions between light and matter, Einstein

defined three mechanisms. In order for an atomic or molecular system to go

from a lower-energy state to an excited energy state, it must absorb a photon

having a certain frequency (or wavelength or energy). Such absorption

processes do not occur spontaneously, but must be stimulated by the presence

of just the right photon. Einstein called this stimulated absorption,and noted

that the rate of absorption must be proportional to the density of photons that

have the right energy, labeled (), and the concentration of atoms or mole-

cules in the lower state,clower:

rate () clower

The photon density () can be determined from Planck’s theory of light, as-

suming perfect blackbody behavior. Einstein introduced a proportionality con-

stant B, now called the Einstein coefficient of stimulated absorption:

rate of stimulated absorption B() clower (15.27)

In addition, Einstein noted that a photon having the same energy can also in-

duce, or stimulate,a transition in the opposite direction, from higher-energy

state to lower-energy state. In doing so, the photon of just the right frequency

causes a transition that emits another photon having the same energy. Einstein

called this stimulated emission,and by the same arguments that led to equation

15.27 defined the Einstein coefficient of stimulated emission, B:

rate of stimulated emission B() chigher (15.28)

where chigheris the concentration of species in the excited state. Einstein was

able to show that BB. Finally, he recognized another way a system can

go from an excited state to a lower-energy state, a mechanism that excita-

tions do not have: there could be a spontaneous emissionof a photon of the

550 CHAPTER 15 Introduction to Electronic Spectroscopy and Structure

Singlet manifold

Triplet manifold

Radiationless

transition

Intersystem

crossing

T 1

T 2

S 0

S 1

Excitation

Radiationless

transition

Phosphorescence

Figure 15.24 Phosphorescence occurs when

there is a quantum-mechanically forbidden inter-

system crossing (that is, when S0 occurs)

and a state of different multiplicity is occupied.

Because the transition from the triplet excited

state to the singlet ground state is also formally

forbidden, the transition from the T 1 state to the

S 0 state takes a long time on the atomic or mole-

cular timescale; phosphorescence is a relatively

slow process.