is excited up to a higher level (i.e., the stimulated absorption). (ii) The higher-level
electron may spontaneously lose its energy and return back to the ground state (the
spontaneous emission). (iii) The higher-level electron may also lose its energy and
return back to the ground state. Unlike (ii), however, the excited electron has to be
stimulated by being irradiated by light quanta having an energy corresponding to the
energy difference between the ground state and excited state (the stimulated emission). Figure 9.2 schematically depicts the optical processes of the Einstein model.
Under those postulates, Einstein dealt with the problem probabilistically. Suppose that the ground state and excited state have energies E 1 and E 2 . Einstein
assumed that light quanta having an energy equaling E 2 À E 1 take part in all the
above three transition processes. He also propounded the idea that the light quanta
have an energy that is proportional to its (angular) frequency. That is, he thought that
the following relation should hold:
ħω 21 ¼ E 2 À E 1 ,
ð9:38Þ
where ω 21 is an angular frequency of light that takes part in the optical transitions.
For the time being, let us follow Einstein’s postulates.
(i) Stimulated absorption: This process is simply said to be an “absorption.” Let W a
[s
À1 ] be the transition probability that the electron absorbs a light quantum to be
excited to the excited state. W a is described as
W a ¼ N 1 B 21 ρ ω 21
ð Þ,
ð9:39Þ
where N 1 is the number of atoms occupying the ground state; B 21 is a proportional constant; ρ(ω 21 ) is due to (9.33). Note that in (9.39) we used ω 21 instead
of ω in (9.33). The coefficient B 21 is called Einstein B coefficient; more
specifically one of Einstein B coefficients. Namely, B 21 is pertinent to the
transition from the ground state to excited state.
ℏ
=
−
,
(
)
(
)
Stimulated
absorption
Stimulated
emission
Spontaneous
emission
,
Fig. 9.2 Optical processes
of Einstein two-level atom
model
346
9 Light Quanta: Radiation and Absorption
electron may spontaneously lose its energy and return back to the ground state (the
spontaneous emission). (iii) The higher-level electron may also lose its energy and
return back to the ground state. Unlike (ii), however, the excited electron has to be
stimulated by being irradiated by light quanta having an energy corresponding to the
energy difference between the ground state and excited state (the stimulated emission). Figure 9.2 schematically depicts the optical processes of the Einstein model.
Under those postulates, Einstein dealt with the problem probabilistically. Suppose that the ground state and excited state have energies E 1 and E 2 . Einstein
assumed that light quanta having an energy equaling E 2 À E 1 take part in all the
above three transition processes. He also propounded the idea that the light quanta
have an energy that is proportional to its (angular) frequency. That is, he thought that
the following relation should hold:
ħω 21 ¼ E 2 À E 1 ,
ð9:38Þ
where ω 21 is an angular frequency of light that takes part in the optical transitions.
For the time being, let us follow Einstein’s postulates.
(i) Stimulated absorption: This process is simply said to be an “absorption.” Let W a
[s
À1 ] be the transition probability that the electron absorbs a light quantum to be
excited to the excited state. W a is described as
W a ¼ N 1 B 21 ρ ω 21
ð Þ,
ð9:39Þ
where N 1 is the number of atoms occupying the ground state; B 21 is a proportional constant; ρ(ω 21 ) is due to (9.33). Note that in (9.39) we used ω 21 instead
of ω in (9.33). The coefficient B 21 is called Einstein B coefficient; more
specifically one of Einstein B coefficients. Namely, B 21 is pertinent to the
transition from the ground state to excited state.
ℏ
=
−
,
(
)
(
)
Stimulated
absorption
Stimulated
emission
Spontaneous
emission
,
Fig. 9.2 Optical processes
of Einstein two-level atom
model
346
9 Light Quanta: Radiation and Absorption