bei48482_FM

Stimulated

emission

Spontaneous

emission

Stimulated

absorption

Nj atoms

Ni atoms

NiBiju(
) NjAji NjBjiu(
)

Ej

Ei

h
 h
 h
 h

h
 h
 = E

j − Ei

Solution

We begin by finding the total power Pradiated by the sun. The area of a sphere whose radius

reis that of the earth’s orbit is 4re^2. Since solar radiation falls on this sphere at a rate ofPA

1.4 kW/m^2 ,

P(4e^2 )(1.4 103 W/m^2 )(4)(1.5 1011 m)^2 3.96 1026 W

Next we find the radiation rate Rof the sun. If rsis the sun’s radius, its surface area is 4rs^2 and

R6.43 107 W/m^2

The emissivity of a blackbody is e1, so from Eq. (9.41) we have

T

1  4

 

1  4

5.8 103 K

9.7 EINSTEIN’S APPROACH

Introducing stimulated emission

The stimulated emission of radiation was mentioned in Sec. 4.9 as the key concept

behind the laser. In a 1917 paper Einstein introduced stimulated emission and used it

to arrive at the form of Planck’s radiation law in an elegantly simple manner. By the

early 1920s this idea together with what had become known about the physics of the

atom would have enabled the laser to have been invented then, but somehow nobody

connected the dots until over thirty years later.

Let us consider two energy states in a particular atom, a lower one iand an upper

one j(Fig. 9.9). If the atom is initially in state i, it can be raised to state jby absorb-

ing a photon of frequency

 (9.42)

Now we imagine an assembly of Niatoms in state iand Njatoms in state j, all in

thermal equilibrium at the temperature Twith light of frequency and energy density

u( ). The probability that an atom in state iabsorbs a photon is proportional to the

EjEi



h

6.43 107 W/m^2



(1)(5.67 10 ^8 W/m^2 K^4

R



e

3.96 1026 W



(4)(7.0 108 m)^2

P



4 rs^2

power output



surface area

P



A

318 Chapter Nine

Figure 9.9Three kinds of transi-

tion between states of energies Ei

and Ejin an atom. In spontaneous

emission, the photon leaves the

atom in a random direction. In

stimulated emission, the photons

that leave are in phase with each

other and with the incident pho-

ton, and all the photons move in

the same direction. The number

of atoms that undergo each tran-

sition per second is indicated,

where the quantity u( ) is the

density of photons of frequency

and Aji, Bij, and Bjiare constants

that depend on the properties of

the atomic states.

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