Page 234 - Essentials of physical chemistry

196 Essentials of Physical Chemistry

So we see that the K a x-ray emission of a Cu target can be calculated from the simple Bohr
model but there is an error of about 6.2% compared to the experimental value of 1.541 Å; not
exactly the six figure accuracy of the Rydberg value but close. Note, we have reversed the sign of
the energy difference for an emission. The answer is sufficiently close to the experimental value
that we are confident that our simple model has captured the main principle of the phenomenon.
For further use later, let us ask what the effective nuclear charge is that would produce the correct
wavelength:

s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
12, 398 eV A ˚
¼ 28:0791,
Z eff ffi
(1:541 A ˚ )(0:75)(13:6057 eV)
not the bare nuclear charge of 29.
That is quite revealing and suggests that the n ¼ 1 shell is not completely empty. Using modern
information about electron spin and the idea that orbitals can contain two electrons with opposite
spin, it appears that there is still one electron in the n ¼ 1 orbital and only one is missing. The Bohr
theory postulates that the orbital occupancy should be 2, 8, 8, 18, . . . with no reason given except
that the periodic chart implies that occupancy, so the n ¼ 1 orbital should have two electrons and the
K a data implies there is still one electron in the n ¼ 1 orbital.
Today, most computer monitors and TV screens are some variant of a flat screen but not so long
ago all TV screens and computer monitors were a picture tube in which a beam of electrons moved
across the screen and excited phosphors on the inside of an evacuated ‘‘cathode ray tube.’’ That
meant that you were facing an electron beam hitting the inside of a glass tube with energy of 20,000 V
or so. What about K a x-rays from cathode ray screens? While the heaviest (highest Z) element in
glass (SiO x ) would be Si (Z ¼ 14), the early green phosphors were a form of ZnO, so Zn was present
(Z ¼ 30). Later, color TV tubes had lanthanide salts for various colors such as Eu 2 O 3 for the red
color and so some Eu was present (Z ¼ 63). While the impact of the electron beam with Si atoms
produced only ‘‘soft x-rays,’’ the heavier elements could produce x-rays with shorter wavelengths
capable of breaking bonds in biological compounds. Thus, there was a safety issue with cathode ray
tubes, especially for young developing children sitting close to the picture tube. Now, flat screen
picture screens are not only more convenient but they also have eliminated an x-ray hazard that
accompanied the use of cathode ray tubes.
This author is old enough to have purchased new shoes at a time when department stores had
‘‘fluoroscopes,’’ which were real-time x-ray machines with inlets for your feet, and you could ‘‘show
your mother’’ on a small TV-like screen that the shoes were big enough by wiggling your toes to
show the space inside the new shoes. It is now known that high exposure to x-rays can cause
sterility, so by now those old fluoroscopes are long gone. Fortunately, shoes tend to last a year or
more so children’s exposure to x-rays was infrequent. Modern radiology technicians work behind a
lead–glass wall and wear a film badge to monitor the extent of exposure on any given day.

FORENSIC=ANALYTICAL USE OF AUGER X-RAYS

One of the most interesting recent forensic developments is alloy analysis applied to bullets and
metal shell casings. It has been found that with the sensitivity of modern instrumentation it is
possible to analyze the alloys in forensic samples to match bullets to a particular box of cartridges
due to slight variations in the alloy composition. A variety of techniques are available for alloy
analysis such as various forms of optical emission spectra and mass spectroscopy but to continue
our survey of applications of the Bohr equation, we want to discuss XRF [5]. The overall
Auger process of aiming a beam of high energy electrons to knock inner electrons out of atoms
produces scattered ‘‘Auger electrons’’ as well as x-ray emission due to outer electrons ‘‘falling’’ into