Environmental Engineering Reference
In-Depth Information
Ta b l e A . 4
Conversion factors in formulas for radiative transitions between atomic states.
Number
Formula
C
Units
10
15
eV
in s
1
1
ε
D
C
ω
4.1347
ω
10
34
J
in s
1
6.6261
ω
10
15
s
1
2
ω
D
C
ε
1.519
ε
in eV
10
11
s
1
1.309
ε
in K
10
15
s
1
3
ω
D
C
/
λ
1.884
ε
in eV
4
ε
D
C
/
λ
1.2398 eV
λ
in
μ
m
d
2
g
10
17
in s
1
,
d
in D
a
f
0
D
C
5
ω
1.6126
ω
in eV,
d
in D
a
Δ
ε
D„
ω
0.02450
Cd
2
g
m,
d
in D
a
f
0
D
6
/
λ
0.03038
λ
in
μ
3
d
2
g
0
10
40
s
1
in s
1
,
d
in D
a
7
1/
τ
0
D
C
ω
3.0316
ω
10
6
s
1
in eV,
d
in D
a
1.06312
Δ
ε
D„
ω
Cd
2
g
0
/
3
10
6
s
1
m,
d
in D
a
8
1/
τ
0
D
λ
2.0261
λ
in
μ
2
g
0
f
0
/
g
10
23
s
1
in s
1
,
d
in D
a
9
1/
τ
0
D
C
ω
1.8799
ω
10
7
s
1
in eV,
d
in D
a
4.3393
Δ
ε
D„
ω
2
)
10
7
s
1
m,
d
in D
a
10
1/
τ
0
D
Cf
0
g
0
/(
g
λ
6.6703
λ
in
μ
10
18
CGSE.
a
Disdebye,1D
D
ea
0
D
2.5418
ε
D„
ω
1 The photon energy
,where
ω
is the photon frequency.
2 The photon frequency is
ω
D
ε
/
„
.
3 The photon frequency is
ω
D
2
π
c
/
λ
,where
λ
is the wavelength and
c
is the light speed.
4 The photon energy is
.
5 The oscillator strength for a radiative transition from the lower 0 to the upper
ε
D
2
π
„
c
/
λ
state of an atomic
particle that is averaged over lower states 0 and is summed over upper states of the group
according to (2.113) is
f
0
D
is the matrix element for
the operator of the dipole moment of an atomic particle taken between transition states. Here
m
e
and
2
m
e
ω
/(3
„
e
2
)
d
2
g
,where
d
Dh
0
j
D
ji
„
are atomic parameters,
g
is the statistical weight of the upper state, and
ω
D
(
ε
ε
0
)/
„
ε
are the energies of the transition states.
6 The oscillator strength for radiative transition is given by [2-5]
is the transition frequency, where
ε
0
and
e
2
)
d
2
g
.Here
f
0
D
4
π
cm
e
/(3
„
λ
is the transition wavelength; other notation is the same as above.
7 The rate of the radiative transition (2.112) is 1/
λ
3
/(3
c
3
)
d
2
g
0
,where
B
is the
τ
0
D
B
0
D
4
ω
„
Einstein coefficient; other notation is as above.
8 The rate of radiative transition is given by 1/
3
/(
3
)
d
2
g
0
,where
τ
0
D
B
0
D
32
π
„
λ
λ
is the
wavelength of this transition; other notation is the same as above.
9 The rate of radiative transition according to (2.112) is 1/
2
e
2
g
0
/
m
e
c
3
g
f
0
.
τ
0
D
2
ω
2
g
0
/
„
2
c
f
0
.
D
g
λ
10 The rate of radiative transition (2.112) is given by 1/
τ
0
8
π
