Page 236 - Essentials of physical chemistry

198 Essentials of Physical Chemistry

TABLE 9.2
Nuclear Screening of the K Shell and a Partial
L Shell in Selected Elements
Element Z L a (eV) l L a (Å) Z eff KL screen
Sn 50 3.444 3.600 42.6904 7.3096
Cs 55 4.286 2.892 47.6302 7.3698
Nd 60 5.230 2.370 52.6147 7.3853
Tb 65 6.2728 1.977 57.6074 7.3926
Yb 70 7.4140 1.672 62.6417 7.3538
Re 75 8.6150 1.433 67.6641 7.3359
Hg 80 9.987 1.241 72.7103 7.2897
Rn 86 11.724 1.057 78.7851 7.3149
Th 90 12.966 0.956 82.8424 7.1576
Pu 94 14.279 0.868 86.9404 7.0560

This can be interpreted as the effective charge out of the bare nuclear charge of 49 that is not
covered by the K shell and what there is of the L shell. Thus, (49 41.7057) ¼ 7.2943 so the clean
formula of the one-electron Bohr atom is now muddled up with internal electron–electron repulsion
and the idea that as the shell radius gets large the electrons get spread out more and cannot
completely cover up the nuclear charge on a 1:1 basis. The same effect is almost constant across
the periodic chart for the L a transitions from atomic number 49 (In) to the data for Pu (Z ¼ 94) as
seen for selected elements in Table 9.2. This result also indicates that the electron giving off the
x-ray energy is not falling into an empty L shell and that may be a function of how hard the atom
was hit with the incoming electron, because this effective charge number indicates there are
definitely some other electrons in the L shell. Assuming the number of electrons is an integer, the
noninteger effective charge means that as the electrons move they cannot be everywhere at once.
Thus, even if the electrons are very fast, both the K shell and what there is of the L shell cannot
completely cover an integer amount of the nuclear charge. These considerations are useful to
increase our appreciation of what is going on inside an atom. Historically, this is probably as far
as one can push the Bohr model without including electron–electron repulsion and a better
description of the orbitals but it is interesting to see that the K- and L-Auger transitions behave
almost like the one-electron Bohr model when the model is adjusted for an effective nuclear charge.
Although our short list implies that the average value of the screening might be 7.3, previous
work by Moseley soon after 1913 preferred a value of 7.4 [6]. Mosely was a brilliant British chemist
who was tragically killed in action in WWI at the Battle of Gallipoli at the age of 27. Some writers
have said that Bohr’s shell model was not believed until the work of Mosely; note concurrent dates
of discovery.

X-RAY FLUORESCENCE

While Auger processes do lead to x-ray emission, there is a variation in the technique that offers
more sensitivity and generality. Overall, x-ray emission techniques are not as sensitive as some
other analytical methods but offer simple sample preparation and simultaneous imaging of very
small samples and elemental analysis. An application combining these advantages is the ability to
check the elemental composition of doped microelectronic devices. Forensic samples such as shot or
bullets offer an abundant sample size, so the element ratios within a strong signal is the desired
information. These examples can use the Auger emission of the SEM beam or reduce the voltage to
measure L a transitions. With the standard SEM method, scattered Auger electrons require a
grounding connection to the sample in some cases to bleed off the secondary scattered electrons