Chapter 5 – Detection and Imaging Tools that Use Nonoptical Waves 173
for optical microscopy (see Chapter 3). This gives rise to Kα (transition from principal
quantum number n = 2–1) and less intense Kβ (transition from principal quantum number
n = 3–1) x-ray emission lines, respectively, at a wavelength of ~10−10 m (see Table 5.1 for typ
ical wavelengths for Kα). Other shell transitions are possible to the n = 2 level, or L-shells are
designated as L x-rays (e.g., n = 3 → 2 is Lα, n = 4 → 2 is Lβ, etc.), but in general, all but the
most intense Kα transitions are filtered out from the final emission output from an x-ray tube
collected at right angles to the incident electron beam.
The choice of target in an x-ray tube is a trade-off against the x-ray emission wavelengths
desired, the intensity of Kα emission lines, and the target metal having a sufficiently high
melting point (since ~99% of the energy from the accelerated electrons is actually converted
into heat). Melting point has no clear overall trend across the periodic table, though there is
some periodicity to melting point with the atomic number Z and all of the common target
metals used are clustered into regions of high melting point on the periodic table. In terms of
wavelength of the emission lines, this can be modeled by Moseley’s law, which predicts that
the frequency ν of emission scales closely to ~Z2:
(5.7)
v
k
Z
k
=
−
(
)
1
2
where k1 and k2 are constants relating to the type of electron shell transition; however, for all
Kα transitions k1 = k2 and the equation can be rewritten as
(5.8)
v
Z
=
×
(
)×
−
(
)
−
2 5
10
1
15
2
.
Hz
The alternative x-ray generation mechanism to x-ray fluorescence is that which produces
Bremsstrahlung radiation. Bremsstrahlung radiation is a continuum of electromagnetic
wave emission output across a range of wavelengths. When a charged particle is slowed
down by the effects of other nearby charged particles, some of the lost kinetic energy can be
converted into an emitted photon of Bremsstrahlung radiation. In the raw output from the
metal target in an x-ray tube, this emission is present as a background underlying the x-ray
fluorescence emission peaks (Figure 5.2d), though in most modern biophysical applications,
Bremsstrahlung radiation is filtered out.
Most x-rays generated for use in biophysical research today are generated from a syn
chrotron. The principle of generating synchrotron radiation is similar to that of a cyclo
tron; in that, it involves accelerating charged particles using radiofrequency voltages and
multiple electromagnet B-field deflectors to generate circular motion, here of an electron
(Figure 5.2e). These bending magnet deflectors alter the path of electrons in the storage ring.
The theory of synchrotron radiation is nontrivial but is confirmed both in classical physics
and at the quantum mechanical levels. In essence, a curved trajectory of a charged particle
results in warping of the shape of the electric dipole force field to produce a strongly for
ward peaked distribution of electromagnetic radiation, which is highly collimated; this is
synchrotron radiation.
However, synchrotrons use radiofrequency (f) values that, unlike cyclotrons, are not
fixed and also operate over much larger diameters than the few tens of meters of a cyclo
tron, more typically a few hundred meters. The United States has several large synchro
tron facilities including the National Synchrotron Light Source at Brookhaven, with the
United Kingdom also investing substantial funds in the DIAMOND synchrotron national
facility, with 100 other synchrotron facilities around the world, at the time of writing.
Note the largest particle accelerator as such, though not explicitly designed as a synchro
tron source of x-rays, is 27 km in diameter, which is the Large Hadron Collider near
Geneva, Switzerland.
Equating magnetic and centripetal forces on an electron of mass m and charge q, traveling
at speed v with kinetic energy E in a circular orbit of radius r implies simply