294 12 Characterization of Nanomaterials
Figure 12.12 Simplified structure of an atom. This graph indicates the different electron
shells, their names, and the most important electron transitions leading to the emission of
X-rays. The denomination of the emitted X-rays is also indicated.
n = 1; K shell
n = 2; L shell
n = 3; M shell
Nucleus
Kα
Kβ
Lα
Table 12.1 Denomination and main quantum numbers of electron shells of atoms and the most important
transitions leading to X-ray emission. The notation of the emitted X-ray lines is also given.
Shell of the initial electron
vacancy
Shell donating the electron
to fill the vacancy
Notation of the
emission lines
series
Difference of principal
quantum numbers
Designation
Principal
quantum
number
Designation
Principal
quantum
number
K
1
L
2
Kα
1
K
1
M
3
Kβ
2
K
1
N
4
Kγ
3
. . .. . .. . ..
L
2
M
3
Lα
1
L
2
N
4
Lβ
2
. . .. . ..
M
3
N
4
Mα
1
the line system. Moseley’s law lastly says that the energy (which is proportional to
the frequency) of the emitted X-rays increases quadratically with the atomic
number. From Table 12.1 it is obvious that there is a sequence in the energy of
the emitted X-ray lines.
E
E E
K
L
M
> > ,
(12.18)
where E K , E L , and E M are the energies of the K, L, and M emission lines. Besides
information about the element, the emitted X-rays carry information about the