Elements of Modern Physics
156
10
20
30
40
50
60
70
80
Z
70
60
50
40
30
20
10
(h /E )
n 0
1/2
0
K a 1
K a 2
Fig. 5.9 Moseley diagram for the plot of (hv/E 0 )
1/2
against Z for the K a lines.
hv ≈ |E 0 |
2
2
2
2
(
)
(
)
− σ
− σ
−
f
l
i
Z
Z
nf
n
...(5.51)
where E 0 is the energy of the ground state of the hydrogen atom. This expression
may be written in the approximate form in conformity with the experimentally
hv ≈ |E 0 |
2
2
1
i
nf
n
1 −
(Z – σ)
2
(5.52)
observed relation in Eq. (5.50). It is found that σ n ≈ 1 for the ground state n = 1
and σ n ≈ 7.5 for n = 2. It may also be noted that the separation between K σ1 and
K σ2 lines, being related to the spin-relativity separation, increases rapidly as Z
increases.
X-ray Absorption Spectrum
X-rays can pass through matter. The intensity is reduced in the process, the
reduction depending upon the nature of the material (which forms the basis of
many practical applications), and on the frequency. High frequency x-rays are
generally absorbed less than low frequency x-rays.
The amount of absorption of x-rays by a given material is studied in terms
of the mass absorption coefficient which is defined by the relation
dI = – µ ρ I dx
(5.53)
156
10
20
30
40
50
60
70
80
Z
70
60
50
40
30
20
10
(h /E )
n 0
1/2
0
K a 1
K a 2
Fig. 5.9 Moseley diagram for the plot of (hv/E 0 )
1/2
against Z for the K a lines.
hv ≈ |E 0 |
2
2
2
2
(
)
(
)
− σ
− σ
−
f
l
i
Z
Z
nf
n
...(5.51)
where E 0 is the energy of the ground state of the hydrogen atom. This expression
may be written in the approximate form in conformity with the experimentally
hv ≈ |E 0 |
2
2
1
i
nf
n
1 −
(Z – σ)
2
(5.52)
observed relation in Eq. (5.50). It is found that σ n ≈ 1 for the ground state n = 1
and σ n ≈ 7.5 for n = 2. It may also be noted that the separation between K σ1 and
K σ2 lines, being related to the spin-relativity separation, increases rapidly as Z
increases.
X-ray Absorption Spectrum
X-rays can pass through matter. The intensity is reduced in the process, the
reduction depending upon the nature of the material (which forms the basis of
many practical applications), and on the frequency. High frequency x-rays are
generally absorbed less than low frequency x-rays.
The amount of absorption of x-rays by a given material is studied in terms
of the mass absorption coefficient which is defined by the relation
dI = – µ ρ I dx
(5.53)