2.3 Solutions
117
Further from (2) d(Δω) = dω. The relative distribution of Doppler shift is
dN
N
=
exp
−
Δω
Δω D
2
√
π
dω
Δω D
(6)
Thus a Gaussian distribution is produced in the Doppler shift due to the
random thermal motion of the source (Fig. 2.4).
The intensity of radiation is
I (ω) =
exp
−
Δω
Δω D
2
Δω D
√
π
(7)
centered around the unshifted frequency ω 0 . The width of the distribution at
the frequencies where I (ω) falls to half the central intensity I (ω 0 ) is known as
the half width
Doppler half width = 2(ln2)
1/2
Δω D
= 2ω 0
2kT ln2
Mc 2
1/2
(8)
Thermal broadening is most pronounced for light atoms such as hydrogen and
high temperatures, for example the H α line (6,563 ˚
A) has a Doppler width of
0.6 ˚
A at 400 K.
2.49 Lande’ g-factor is
g = 1 + j( j + 1) + s(s + 1) − l(l + 1)/2 j( j + 1)
For the term
2 P 3/2 , l = 1, J =
3
2
, s =
1
2
and g =
4
3
For
2 S 1/2 , l = 0, j =
1
2
, s =
1
2
and g = 2
Fig. 2.5 Anamolous Zeeman
effect in an alkali atom. The
lines are not equidistant
117
Further from (2) d(Δω) = dω. The relative distribution of Doppler shift is
dN
N
=
exp
−
Δω
Δω D
2
√
π
dω
Δω D
(6)
Thus a Gaussian distribution is produced in the Doppler shift due to the
random thermal motion of the source (Fig. 2.4).
The intensity of radiation is
I (ω) =
exp
−
Δω
Δω D
2
Δω D
√
π
(7)
centered around the unshifted frequency ω 0 . The width of the distribution at
the frequencies where I (ω) falls to half the central intensity I (ω 0 ) is known as
the half width
Doppler half width = 2(ln2)
1/2
Δω D
= 2ω 0
2kT ln2
Mc 2
1/2
(8)
Thermal broadening is most pronounced for light atoms such as hydrogen and
high temperatures, for example the H α line (6,563 ˚
A) has a Doppler width of
0.6 ˚
A at 400 K.
2.49 Lande’ g-factor is
g = 1 + j( j + 1) + s(s + 1) − l(l + 1)/2 j( j + 1)
For the term
2 P 3/2 , l = 1, J =
3
2
, s =
1
2
and g =
4
3
For
2 S 1/2 , l = 0, j =
1
2
, s =
1
2
and g = 2
Fig. 2.5 Anamolous Zeeman
effect in an alkali atom. The
lines are not equidistant