Physics of X-RAY Production
When fast-moving electrons slam into a metal object, x-rays are produced.
The kinetic energy of the electron is transformed into electromagnetic
energy. The function of the x-ray machine is to provide a sufficient
intensity of electron flow from the cathode to anode in a controlled
manner. The three principal segments of an x-ray machine - ca control
panel, a high-voltage power supply, and the x-ray tube are all designed
to provide a large number of electrons focused to a small spot in such
a manner that when the electrons arrive at the target, they have acquired
high kinetic energy.
Kinetic
energy is the energy of motion. Stationary objects have no kinetic energy;
objects in motion have kinetic energy proportional to their mass and
the square of their velocity.
The
equation used to calculate kinetic energy is:
where
m is the mass in kilograms, v is the velocity in meters per second,
and KE is the kinetic energy in joules. In determining the magnitude
of the kinetic energy of a projectile, the velocity is more important
than the mass.
In
a x-ray tube, the projectile is the electron. As its kinetic energy
is increased, both the intensity (number of x-rays) and the energy (their
ability to penetrate) of the created x-rays are increased.
The
x-ray machine is a remarkable instrument. It conveys to the target an
enormous number of electrons at a precisely controlled kinetic energy.
At 100 mA, for example, 6 x 1017 electrons travel from the
cathode to the anode of the x-ray tube every second.
The
distance between the filament and the target is only about 1 to 3 cm.
Imagine the intensity of the accelerating force required to raise the
velocity of the electrons from zero to half the speed of light in so
short a distance.
The
electrons traveling from the cathode to anode in a vacuum tube comprise
the x-ray current and are sometimes called projectile electrons. When
these projectile electrons impinge on the heavy metal atoms of the target,
they interact with these atoms and transfer their kinetic energy to
the target. These interactions occur within a very small depth of penetration
into the target. As they occur, the projectile electrons slow down and
finally come nearly to rest, at which time they can be conducted through
the x-ray anode assembly and out into the associated electronic circuitry.
The
projectile electron interacts with either the orbital electrons or the
nuclei of target atoms. The interactions result in the conversion of
kinetic energy into thermal energy and electromagnetic energy in the
form of x-rays.
By
far, most of the kinetic energy of projectile electrons is converted
into heat. The projectile electrons interact with the outer-shell electrons
of the target atoms but do not transfer sufficient energy to these outer-shell
electrons to ionize them. Rather, the outer-shell electrons are simply
raised to an excited, or higher, energy level. The outer-shell electrons
immediately drop back to their normal energy state with the emission
of infrared radiation. The constant excitation and restabilization of
outer-shell electrons is responsible for the heat generated in the anodes
of x-ray tubes.
Generally,
more than 99% of the kinetic energy of projectile electrons is converted
to thermal energy, leaving less than 1% available for the production
of x-radiation. One must conclude, therefore, that, sophisticated as
it is, the x-ray machine is a very inefficient apparatus.
The
production of heat in the anode increases directly with increasing tube
current. Doubling the tube current doubles the quantity of heat produced.
Heat production also varies almost directly with varying kVp.
The
efficiency of x-ray production is independent of the tube current. Regardless
of what mA is selected, the efficiency of x-ray production remains constant.
The efficiency of x-ray production increases with increasing projectile-electron
endery. At 60 kVp, only 0.5% of the electron kinetic energy is converted
to x-rays; at 120 MeV, it is 70%.
Characteristic
Radiation
If
the projectile electron interacts with an inner-shell electron of the
target atom rather than an outer-shell electron, characteristic x-radiation
can be produced. Characteristic x-radiation results when the interaction
is sufficiently violent to ionize the target atom by total removal of
the inner-shell electron. Excitation of an inner-shell electron does
not produce characteristic x-radiation.
When
the projectile electron ionizes a target atom by removal of a K-shell
electron, a temporary electron hole is produced in the K shell. This
is a highly unnatural state for the target atom and is corrected by
an outer-shell electron falling into the hole in the K shell. The transition
of an orbital electron from an outer shell to an inner shell is accompanied
by the emission of an x-ray photon. the x-ray has energy equal to the
difference in the binding energies of the orbital electrons involved.
Example:
A K-shell electron is removed from a tungsten atom and is replaced by
an l_shell electron. What is the energy of the characteristic x-ray
that is emitted?
Answer:
For tungsten, K electrons have binding energies of 69.5 keV, and L electrons
are bound by 12.1 keV. Therefore, the characteristic x-ray emitted has
energy of:
In
summary, characteristic x-rays are produced by transitions of orbital
electrons from outer to inner shells. Since the electron binding energy
for every element is different, the characteristic x-rays produced in
the various elements are also different. This type of x-radiation is
called characteristic radiation because it is characteristic of the
target element. The effective energy characteristic x-rays increases
with increasing atomic number of the target element.
Discrete
X-ray Spectrum
We
saw earlier that characteristic x-rays have precisely fixed, or discrete,
energies and that these energies are characteristic of the differences
between electron binding energies of a particular element. A characteristic
x-ray from tungsten, for example, can have one of fifteen energies and
no others.
Bremsstrahlung Radiation
The production of heat and characteristic x-rays involves
interactions between the projectile electrons and the electrons of target
atoms. A third type of interaction in which the projectile electron
can lose its kinetic energy is an interaction with the nucleus of a
target atom. In this type of interaction, the kinetic energy of the
projectile electron is converted into electromagnetic energy.
A projectile electron that completely avoids the orbital electrons on
passing through an atom of the target may come sufficiently close to
the nucleus of the atom to come under its influence. Since the electron
is negatively charged and the nucleus is positively charged, there is
an electrostatic force of attraction between them. As the projectile
electron approaches the nucleus, it is influenced by a nuclear force
much stronger than the electrostatic attraction. As it passes by the
nucleus, it is slowed down and deviated in its course, leaving with
reduced kinetic energy in a different direction. This loss in kinetic
energy reappears as an x-ray photon. These types of x-rays are called
bremsstrahlung radiation, or bremsstrahlung x-rays. Bremsstrahlung
is the German word for slowing down or braking; bremsstrahlung radiation
can be considered radiation resulting from the braking or projectile
electrons by the nucleus.
A projectile electron can lose any amount of its kinetic energy in an
interaction with the nucleus of a target atom, and the bremsstrahlung
radiation associated with the loss can take on a corresponding range
of values. For example, an electron with kinetic energy of 70 keV can
lose all, none, or any intermediate level of that kinetic energy in
a bremsstrahlung interaction; the bremsstrahlung x-ray produced can
have an energy in the range of 0 to 70 keV. This is different from the
production of characteristic x-rays that have specific energies.
Continuous X-ray Spectrum
If it were possible to identify and quantitative the
energy contained in each bremsstrahlung photon emitted from an x-ray
tube, one would find that these energies extend from that associated
with the peak electron energy all the way down to zero. In other words,
when an x-ray tube is operated at 70 kVp, bremsstrahlung photons with
energies ranging from 0 to 70 keV are emitted. Thus, creating a typical
continuous, or bremsstrahlung, x-ray emission spectrum.
This emission spectrum is sometimes called the continuous emission spectrum
because, unlike in the discrete spectrum, the energies of the photons
emitted may range anywhere from zero to some maximum value. The general
shape of the continuous x-ray spectrum is the same for all x-ray machines.
The maximum energy that an x-ray can have is numerically equal to the
kVp of operation. The greatest number of x-ray photons is emitted with
energy approximately one-third of the maximum photon energy. The number
of x-rays emitted decreases rapidly at very low photon energies and
below 5 keV nearly reaches zero.
