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Basic Spectroscopy 193

‘‘covered up’’ (10=11) of the nuclear charge of the Na nucleus. However, the effective nuclear
charge is greater than þ1 by a considerable amount. This can be interpreted as ‘‘imperfect
screening’’ of the nuclear charge by the first 10 electrons (the Ne core). We can see from the
formula for the Bohr radius that the radius increases as the square of the quantum number ‘‘n,’’ and
so, as the orbits of the n ¼ 2 shell get larger than the n ¼ 1 shell, their ability to be between the outer
electron and the nuclear charge of the core is reduced so the outer electron experiences more of the
uncovered nuclear charge. Thus, the Bohr model can give a qualitative explanation for the concept
of electron screening. We emphasize that this result departs from the precision of six-figure accuracy
of the spectroscopic measurements but provides a valuable concept.

X-RAY EMISSION
Here is another way in which the simple Bohr model can be used to give qualitative ideas about
electronic structure that is tantalizingly semiquantitative. X-rays were discovered by W. C. Roentgen
(1845–1923), a German physicist who carried out the first experiments in 1895 and was awarded the
very first Nobel Prize in Physics in 1901. A process called Auger x-ray emission spectroscopy is due
to the use of an electron beam to knock electrons out of inner orbitals of atoms whereupon the outer
electrons of the formerly neutral atoms ‘‘fall’’ down in a cascade of steps to again fill the lowest
orbitals. When this happens, electromagnetic radiation is given off just as the yellow flame emission
occurs due to an outer electron of Na. This process was studied by Pierre Victor Auger (1899–
1993), a French physicist who found that electrons are emitted (and scattered) as well as x-rays.
Since the n ¼ 1 level is the lowest level, the energy gap between the n ¼ 2 and n ¼ 1 levels is large
enough to produce the emitted radiation in the x-ray range. X-rays from the (n ¼ 2 ! n ¼ 1)
transition are called K a and those from (n ¼ 3 ! n ¼ 1) K b .
As one proceeds to heavier elements, the number of electrons increases but the increasing nuclear
charge pulls the inner orbitals closer to the nucleus as the Bohr radius decreases. According to the
Bohr model of circular shells, the extension to more electrons went as K, L, M, N, . . . shells
containing 2, 8, 8, 18, 18, . . . electrons respectively. The point is that for elements beyond Cd
(Z ¼ 48), the L shell as well as the innermost K shell are pulled in tightly, so that x-rays can be easily
observed from electrons falling into a partially empty L shell from the M and N shells. The Bohr
model advocates justified the 2, 8, 8, 18, . . . sequence using just the one ‘‘n’’ Bohr quantum number
from the atomic numbers of the rare gas atoms and we can use the 2, 8, 8 sequence for the innermost
shells. You can also see that for high values of Z, the inner L shell might be partly empty and
electrons could cascade from the M and N shells. Thus, transitions from (n ¼ 3 ! n ¼ 2) are called
L a and those from (n ¼ 4 ! n ¼ 2) are called L b . While K a transitions can still be created for
Z > 48, a higher energy electron beam is needed, so it has been found that reducing the excitation
beam energy to 20,000 V or even just 10,000 V allows use of the same dispersive system and
detectors for the L a of Z > 48 as for the K a transitions of elements with Z < 49.
We are emphasizing x-ray wavelengths to make the connection to the Bohr theory that originated
from wavelength data. However, most modern x-ray fluorescence (XRF) data is reported in kilo-
electron volt energies from a detector under a high voltage potential (Figure 9.5). Of course, we
12,398
will give us an accurate conversion between electron volts and wavelength
DE(eV)
know l (A ˚ ) ¼
in angstroms, so we can convert from one representation to the other. However, the table of x-ray
data was last reported as wavelengths in the CRC Handbook in the 1976 edition. Another recent
consideration is that in order to keep the range of x-rays within a given order of diffraction and
detector limits the longer wavelength M a and M b , x-rays can be used for heavier elements.
However, the M a,b transitions are less easily assigned in terms of clean integers. We will see that
even the L a,b transitions are subject to non-integer screening of the nuclear charge so the M a,b
transitions are identified and cataloged as empirical data and we will not attempt an analysis of the