Introduction
Modern atomic and
nuclear physics is among the most impressive scientific achievements of the
last century. Both the theories and techniques of atomic and nuclear physics
have played an important role in the life sciences. The theories provided a
solid foundation for understanding the structure and interaction of organic
molecules, and the techniques provided many tools for both experimental and
clinical work. Contributions from this field have been so numerous and
influential that it is impossible to do them justice in a single chapter. We
will present a brief description of the atom and the nucleus, which will lead
into a discussion of the applications of atomic and nuclear physics to the life
sciences.
1) Early Models of the Atom
By 1912, through the work of J.
J. Thompson, E. Rutherford, and their colleagues, a number of important facts
had been discovered about atoms which make up matter:
· Atoms
contain small negatively charged electrons and relatively heavier positively
charged protons.
charged protons.
·
The proton is about 2000 times heavier than the
electron, but the magnitude of the
charge on the two is the same.
charge on the two is the same.
·
There are as many positively charged protons in
an atom as negatively charged
electrons. The atom as a whole is, therefore, electrically neutral.
electrons. The atom as a whole is, therefore, electrically neutral.
·
The identity of an atom is determined by the
number of protons it has. For example,
hydrogen has 1 proton, carbon has 6 protons, and silver has 47 protons.
hydrogen has 1 proton, carbon has 6 protons, and silver has 47 protons.
Through a series of ingenious
experiments, Rutherford explained his
astonishing results by developing a new atomic model which was presented as
follows:
·
The positive charge in the atom was concentrated
in a region that was small relative to
the size of the atom. He called this concentration of positive charge the nucleus of the
atom.
the size of the atom. He called this concentration of positive charge the nucleus of the
atom.
· Any
electrons belonging to the atom were assumed to be in the relative large volume
outside the nucleus. To explain why these electrons where not pulled into the nucleus
by the attractive electric force, Rutherford modeled them as moving in orbits around
the nucleus in the same manner as the planets orbit the Sun. For this reason, this model
is often referred to as the planetary model of the atom (Figure 1).
outside the nucleus. To explain why these electrons where not pulled into the nucleus
by the attractive electric force, Rutherford modeled them as moving in orbits around
the nucleus in the same manner as the planets orbit the Sun. For this reason, this model
is often referred to as the planetary model of the atom (Figure 1).
·
It was subsequently discovered that the nucleus
also contains another particle, the
neutron, which has approximately the same mass as the proton but is electrically
neutral.
neutron, which has approximately the same mass as the proton but is electrically
neutral.
·
Although the nucleus contains most of the atomic
mass, it occupies only a small part of
the total atomic volume. The diameter of the whole atom is on the order of 10−8 cm,
but the diameter of the nucleus is only about 10−13 cm.
the total atomic volume. The diameter of the whole atom is on the order of 10−8 cm,
but the diameter of the nucleus is only about 10−13 cm.
Figure
1: Rutherford
′s planetary model of the atom
Two basic difficulties exist with
Rutherford ′s planetary model:
1. The
first difficulty is that, an atom emits (and absorbs) certain frequencies of
electromagnetic radiation and no others, which Rutherford′ s model cannot explain
this phenomenon.
electromagnetic radiation and no others, which Rutherford′ s model cannot explain
this phenomenon.
2. The
second difficulty is that Rutherford’s
electrons are undergoing a centripetal
acceleration, but centripetally accelerated charges revolving with frequency ƒ should
radiate electromagnetic waves of the same frequency ƒ.
acceleration, but centripetally accelerated charges revolving with frequency ƒ should
radiate electromagnetic waves of the same frequency ƒ.
Unfortunately,
this classical model leads to a prediction of self- destruction when applied to
the atom. As the electron radiates, energy is carried away from the atom, the
radius of the electron′ s orbit steadily decrease as this radiation is given
off and its frequency of revolution increases. This process would lead to an
ever-increasing frequency of emitted radiation and the electron should eventually
spiral into the nucleus and finally an ultimate collapse of the atom occurs.
2) Bohr′s Model of the Hydrogen Atom
In 1913, the Danish physicist
Niels Bohr proposed a model for the atom that circumvented the difficulties of Rutherford's planetary model, and explained many
observations that were puzzling scientists at that time. The most surprising
observed property of atoms was the light emitted by them. When an element is
put into a flame, it emits light at sharply defined wavelengths, called spectral
lines. Each element emits its own characteristic spectrum of light. Prior
to Bohr, scientists could not explain why these colors were emitted by atoms. Bohr's
model of the atom explained the reason of the sharp spectra. The basic ideas of
the Bohr Theory as it applies to the hydrogen atom were expressed by the
following assumption:
1. The electron
moves in circular orbits around the proton under the influence of the
electric force of attraction as shown in Figure 2.
electric force of attraction as shown in Figure 2.
Figure
2: Diagram representing Bohr′s model
of hydrogen atom. The orbiting electron is allowed to be
only in specific discrete radii.
only in specific discrete radii.
2. Only certain
electron orbits are stable. When in one of these stationary states,
as Bohr
called them, the electron does not emit energy in the form of radiation. Hence the total
called them, the electron does not emit energy in the form of radiation. Hence the total
energy level of the atom remains constant
and classical mechanics can be used to
describe the electron’s motion. This representation claims that the centripetally
accelerated electron does not continuously emit radiation, losing energy and
eventually spiraling into the nucleus, as predicted by Rutherford ′s planetary model.
describe the electron’s motion. This representation claims that the centripetally
accelerated electron does not continuously emit radiation, losing energy and
eventually spiraling into the nucleus, as predicted by Rutherford ′s planetary model.
3. Radiation
is emitted by the atom when the electron makes a transition from a more
energetic initial orbit to a lower-energy orbit. This transition can not be visualized.
Bohr was able to calculate the radii of these allowed orbits and shows that, the
radiation or spectral lines are emitted as a consequence of orbital restrictions. The
orbital restrictions are most easily illustrated with the simplest atom hydrogen,
which has a single proton nucleus and one electron orbiting around it. Unless energy
is added to the atom, the electron is found in the allowed orbit closet to the nucleus. If
energy is added to the atom, the electron may “jump” to one of the higher allowed
orbits farther away from the nucleus, but the electron can never occupy the regions
between the allowed orbits (Figure 3).
energetic initial orbit to a lower-energy orbit. This transition can not be visualized.
Bohr was able to calculate the radii of these allowed orbits and shows that, the
radiation or spectral lines are emitted as a consequence of orbital restrictions. The
orbital restrictions are most easily illustrated with the simplest atom hydrogen,
which has a single proton nucleus and one electron orbiting around it. Unless energy
is added to the atom, the electron is found in the allowed orbit closet to the nucleus. If
energy is added to the atom, the electron may “jump” to one of the higher allowed
orbits farther away from the nucleus, but the electron can never occupy the regions
between the allowed orbits (Figure 3).
Figure
3: Bohr model for the hydrogen atom.
The electron orbits about the nucleus and can occupy only
discrete orbits with radii 1, 2, 3, and so on.
discrete orbits with radii 1, 2, 3, and so on.
4. The Bohr model was very
successful in explaining many of the experimental
observations for the simple hydrogen atom. But to describe the behavior of atoms
with more than one electron, it was necessary to impose an additional restriction on
the structure of the atom; the number of electrons in a given orbit cannot be greater
than 2n2, where n is the order of the orbit from the nucleus, trough which the
maximum number of electrons in each orbit can be calculated according to the
following:
observations for the simple hydrogen atom. But to describe the behavior of atoms
with more than one electron, it was necessary to impose an additional restriction on
the structure of the atom; the number of electrons in a given orbit cannot be greater
than 2n2, where n is the order of the orbit from the nucleus, trough which the
maximum number of electrons in each orbit can be calculated according to the
following:
The
first allowed orbit = 2 x (1)2 = 2
The
second allowed orbit = 2 x (2)2 = 8
The third allowed orbit = 2 x (3)2
= 18 and so on.
The atoms are found to be constructed in
accordance with these restrictions. Helium
has two electrons, and, therefore, its first orbit is filled. Lithium has three electrons,
two of which fill the first orbit; the third electron, therefore, must be in the second
orbit. This simple sequence is not completely applicable to the very complex atoms,
but basically this is the way the elements are constructed.
has two electrons, and, therefore, its first orbit is filled. Lithium has three electrons,
two of which fill the first orbit; the third electron, therefore, must be in the second
orbit. This simple sequence is not completely applicable to the very complex atoms,
but basically this is the way the elements are constructed.
5. A specific amount of energy
is associated with each allowed orbital configuration of
the electron. Therefore, instead of speaking of the electron as being in a certain orbit,
we can refer to it as having a corresponding amount of energy. Each of these allowed
values of energy is called an energy level. An energy level diagram for an atom is
shown in Figure 4. Note that every element has its own characteristic energy level
structure. The electrons in the atom can occupy only specific energy states; that is, in a
given atom the electron can have energy E1, E2, E3, and so on, but cannot have energy
between these two values. This is a direct consequence of the restrictions on the
allowed electron orbital configurations.
the electron. Therefore, instead of speaking of the electron as being in a certain orbit,
we can refer to it as having a corresponding amount of energy. Each of these allowed
values of energy is called an energy level. An energy level diagram for an atom is
shown in Figure 4. Note that every element has its own characteristic energy level
structure. The electrons in the atom can occupy only specific energy states; that is, in a
given atom the electron can have energy E1, E2, E3, and so on, but cannot have energy
between these two values. This is a direct consequence of the restrictions on the
allowed electron orbital configurations.
Figure
4: Energy Level for an Atom.
6. The
lowest energy level that an electron can occupy is called the ground state.
This
state is associated with the orbital configuration closest to the nucleus. The higher
allowed energy levels, called excited states, are associated with larger orbits and
different orbital shapes. Normally the electron occupies the lowest energy level but it
can be excited into a higher energy state by adding energy to the atom.
state is associated with the orbital configuration closest to the nucleus. The higher
allowed energy levels, called excited states, are associated with larger orbits and
different orbital shapes. Normally the electron occupies the lowest energy level but it
can be excited into a higher energy state by adding energy to the atom.
7. An
atom can be excited from a lower to a higher energy state in a number of
different
ways. The two most common methods of excitation are:
ways. The two most common methods of excitation are:
(a) Electron impact.
(b) Absorption of electromagnetic
radiation.
(a) Excitation by electron impact
occurs most frequently in a gas discharge; if a
current is passed through a gas of atoms, the colliding electron is slowed down and
the electron in the atom is promoted to a higher energy configuration. When the
excited atoms fall back into the lower energy states, the excess energy is given off
as electromagnetic radiation. Each atom releases its excess energy in a single
photon. Therefore, the energy of the photon is simply the difference between the
energies of the initial state Ei and the final state Ef of the atom. The frequency ƒ of
the emitted radiation is given by
current is passed through a gas of atoms, the colliding electron is slowed down and
the electron in the atom is promoted to a higher energy configuration. When the
excited atoms fall back into the lower energy states, the excess energy is given off
as electromagnetic radiation. Each atom releases its excess energy in a single
photon. Therefore, the energy of the photon is simply the difference between the
energies of the initial state Ei and the final state Ef of the atom. The frequency ƒ of
the emitted radiation is given by
ƒ= Energy of
photon / Planck constant = (Ei −
Ef) / h (1)
Where
h is a Planck′ s constant with a value = 6.626 x 10-34 J. s
Transition between each pair of energy levels
results, in the emission of light at a
specific frequency, called transition or resonance frequency. Therefore, a group of
highly excited atoms of a given element emit light at a number of well-defined
frequencies which constitute the optical spectrum for that element.
specific frequency, called transition or resonance frequency. Therefore, a group of
highly excited atoms of a given element emit light at a number of well-defined
frequencies which constitute the optical spectrum for that element.
(b) An atom in a given energy level
can also be excited to a higher level by light at a
specific frequency. The frequency must be such that each photon has just the right
amount of energy to promote the atom to one of its higher allowed energy states.
Atoms, therefore, absorb light only at the specific transition frequencies, given by
Equation 1. Light at other frequencies is not absorbed. If a beam of white light
(containing all the frequencies) is passed through a group of atoms of a given species,
the spectrum of the transmitted light shows gaps corresponding to the absorption of
the specific frequencies by the atoms. This is called the absorption spectrum of the
atom. In their undisturbed state, most of the atoms are in the ground state. The
absorption spectrum, therefore, usually contains only lines associated with transitions
from the ground state to higher allowed states (Figure 5). Optical spectra are produced
by the outer electrons of the atom. The inner electrons, those closer to the nucleus, are
bound more tightly and are consequently more difficult to excite. However, in a
highly energetic collision with another particle, an inner electron may be excited.
When in such an excited atom an electron returns to the inner orbit, the excess energy
is again released as a quantum (photon) of electromagnetic radiation. Because the
binding energy here is about a thousand times greater than for the outer electrons, the
frequency of the emitted radiation is correspondingly higher. Electromagnetic
radiation in this frequency range is called X - rays.
specific frequency. The frequency must be such that each photon has just the right
amount of energy to promote the atom to one of its higher allowed energy states.
Atoms, therefore, absorb light only at the specific transition frequencies, given by
Equation 1. Light at other frequencies is not absorbed. If a beam of white light
(containing all the frequencies) is passed through a group of atoms of a given species,
the spectrum of the transmitted light shows gaps corresponding to the absorption of
the specific frequencies by the atoms. This is called the absorption spectrum of the
atom. In their undisturbed state, most of the atoms are in the ground state. The
absorption spectrum, therefore, usually contains only lines associated with transitions
from the ground state to higher allowed states (Figure 5). Optical spectra are produced
by the outer electrons of the atom. The inner electrons, those closer to the nucleus, are
bound more tightly and are consequently more difficult to excite. However, in a
highly energetic collision with another particle, an inner electron may be excited.
When in such an excited atom an electron returns to the inner orbit, the excess energy
is again released as a quantum (photon) of electromagnetic radiation. Because the
binding energy here is about a thousand times greater than for the outer electrons, the
frequency of the emitted radiation is correspondingly higher. Electromagnetic
radiation in this frequency range is called X - rays.
Figure 5:
The absorption Spectrum
8. The
Bohr model also explained qualitatively the formation of chemical bonds. The
formation of chemical compounds and matter in bulk is due to the distribution of
electrons in the atomic orbits. When an orbit is not filled to capacity (which is the
case for most atoms), the electrons of one atom can partially occupy the orbit of
another. This sharing of orbits draws the atoms together and produces bonding
between atoms. As an example we show in Figure 6, the formation of a hydrogen
molecule from two hydrogen atoms.
formation of chemical compounds and matter in bulk is due to the distribution of
electrons in the atomic orbits. When an orbit is not filled to capacity (which is the
case for most atoms), the electrons of one atom can partially occupy the orbit of
another. This sharing of orbits draws the atoms together and produces bonding
between atoms. As an example we show in Figure 6, the formation of a hydrogen
molecule from two hydrogen atoms.
(a)
(b)
Figure
6: A schematic representation for the formation
of a hydrogen molecule.
(a) Two separate hydrogen atoms.
(b) When the two atoms are
close together, the electrons share each other’s orbit, which results
in the binding of the two atoms into a molecule.
in the binding of the two atoms into a molecule.
Figure
6 indicate that:
(a)In
the orbit of each of the hydrogen atoms, there is room for another electron.
(b)A
completely filled orbit is the most stable configuration; therefore, when two
hydrogen atoms are close together, they share each other’s electrons, in this way
the orbit of each atom is completely filled part of the time. This shared orbit can
be pictured as a rubber band pulling the two atoms together.
hydrogen atoms are close together, they share each other’s electrons, in this way
the orbit of each atom is completely filled part of the time. This shared orbit can
be pictured as a rubber band pulling the two atoms together.
Therefore,
the sharing of the electrons binds the atoms into a molecule. While the
sharing of electrons pulls the atoms together, the repulsion force of the nuclei tends
to keep them apart. The equilibrium separation between atoms in a molecule is
determined by these two counter forces. In a similar way, more complex molecules,
and ultimately bulk matter, are formed. Atoms with completely filled orbits (these
are atoms of the so-called noble gases) as helium, neon, argon, krypton, and xenon,
cannot share electrons with other elements and are, therefore, chemically most inert.
sharing of electrons pulls the atoms together, the repulsion force of the nuclei tends
to keep them apart. The equilibrium separation between atoms in a molecule is
determined by these two counter forces. In a similar way, more complex molecules,
and ultimately bulk matter, are formed. Atoms with completely filled orbits (these
are atoms of the so-called noble gases) as helium, neon, argon, krypton, and xenon,
cannot share electrons with other elements and are, therefore, chemically most inert.
9.
Molecules also have characteristic spectra both in emission and in absorption.
Because molecules are more complicated than atoms, their spectra are
correspondingly more complex. In addition to the electronic configuration, these
spectra also depend on the motion of the nuclei. Still the spectra can be interpreted
and are unique for each type of molecule.
Because molecules are more complicated than atoms, their spectra are
correspondingly more complex. In addition to the electronic configuration, these
spectra also depend on the motion of the nuclei. Still the spectra can be interpreted
and are unique for each type of molecule.
2) Spectroscopy
Spectroscopy is the study of the
wavelength distribution of radiation from a sample. The absorption and emission
spectra of atoms and molecules are unique for each species. They can serve as
fingerprints in identifying atoms and molecules in various substances.
Spectroscopic techniques were first used in basic experiments with atoms and
molecules, but they were soon adopted in many other areas, including the life
sciences as:
·
In biochemistry, spectroscopy is used to
identify the products of complex chemical
reactions.
reactions.
·
In medicine, spectroscopy is used routinely to
determine the concentration of certain
atoms and molecules in the body. From a spectroscopic analysis of urine, for example,
one can determine the level of mercury in the body. Blood sugar level is measured by
first producing a chemical reaction in the blood sample which results in a colored
product. The concentration of this colored product, which is proportional to the blood-
sugar level, is then measured by absorption spectroscopy.
atoms and molecules in the body. From a spectroscopic analysis of urine, for example,
one can determine the level of mercury in the body. Blood sugar level is measured by
first producing a chemical reaction in the blood sample which results in a colored
product. The concentration of this colored product, which is proportional to the blood-
sugar level, is then measured by absorption spectroscopy.
The basic principles of spectroscopy are simple and characterized
by two different forms:
2.1)
Emission Spectroscopy
In emission spectroscopy the sample under investigation is
excited by an electric current or a flame. The emitted light is then examined
and identified. Emission spectra can provide information about the
concentration of the various components in the substance. In emission
spectroscopy, the intensity of the emitted light in the spectrum is proportional
to the number of atoms or molecules of the given species.
2.2)
Absorption Spectroscopy
In absorption spectroscopy, the sample is placed in the
path of a beam of white light. Examination of the transmitted light reveals the
missing wavelengths which identify the
components in the substance. The absorption spectra can also provide information about the concentration of all the components in a substance. In absorption spectroscopy, the amount of absorption can be related to the concentration.
components in the substance. The absorption spectra can also provide information about the concentration of all the components in a substance. In absorption spectroscopy, the amount of absorption can be related to the concentration.
2.3) The
Spectrometer
The instrument used to analyze the spectra is called a spectrometer.
This device records the intensity of light as a function of wavelength. A
spectrometer, in its simplest form, consists of a focusing system, a prism, and
a detector for light as shown in Figure 7.
Figure 7: The measurement of spectra.
2.3.1The Measurement of Spectra
The focusing system forms a parallel beam of light which
falls on the prism. The prism, which can be rotated, breaks up the beam into
its component wavelengths. At this point, the fanned-out spectrum can be
photographed and identified as follows:
·
The narrow exit slit intercepts only a portion
of the spectrum, through which a small
section of the spectrum is detected at a time.
section of the spectrum is detected at a time.
·
As the prism is rotated, the whole spectrum is
swept sequentially past the slit. The
position of the prism is calibrated to correspond with the wavelength impinging on the
slit.
position of the prism is calibrated to correspond with the wavelength impinging on the
slit.
·
The light that passes through the slit is
detected by a photo detector which produces an
electrical signal proportional to the light intensity. The intensity of the signal as a
function of wavelength can be displayed on a chart recorder.
electrical signal proportional to the light intensity. The intensity of the signal as a
function of wavelength can be displayed on a chart recorder.
Spectrometers used in routine clinical work are automated
and can be operated by relatively unskilled personnel. The identification and
interpretation of the spectra produced by less well-known molecules, however,
require considerable training and skill. In addition to identifying the
molecule, such spectra also yield information about the molecular structure.
3) Quantum
Mechanics
3.1) Overview
Quantum
mechanics is the study of mechanical systems whose
dimensions are close to or below the atomic scale, such as molecules, atoms,
electrons, protons and other subatomic particles.
Quantum mechanics is a fundamental branch of physics with wide applications. Quantum theory
generalizes classical mechanics
and provides accurate
descriptions for many previously unexplained phenomena such
as stable electron orbits.
The effects of quantum mechanics are typically not observable on macroscopic scales, but become evident at the atomic
and subatomic
level. The word “quantum”
came from the Latin word which means "what quantity". In quantum
mechanics, it refers to a discrete unit that quantum theory assigns to certain
physical quantities, such as the energy of an atom at rest. The discovery
that waves have discrete energy packets (called quanta) that behave in a manner similar to particles led
to the branch of physics that deals with atomic and subatomic systems
which we today call quantum mechanics.
As mentioned earlier, quantum mechanics is essential to understand the
behavior of systems at atomic length scales and smaller. For example,
if Newtonian mechanics
governed the workings of an atom, electrons would rapidly travel towards and
collide with the nucleus, making
stable atoms impossible. However, in the natural world the electrons normally
remain in an unknown orbital path around the nucleus (Figure 8).
Figure 8: The electrons
orbiting the atomic nucleus in different orbits, with different energy
levels.
This branch of physics was initially developed to provide a better
explanation of the atom, especially the spectra of light emitted by
different atomic species.
The quantum theory of the atom was developed as an explanation for the electron's
staying in its orbital, which could not be explained by Newton's
laws of motion and by Maxwell's laws of classical electromagnetism. In the
formalism of quantum mechanics, the state of a system at a given time is described
by a complex wave function
(sometimes referred to as orbital in the case of atomic electrons), and more
generally, elements of a complex vector space.
This abstract mathematical object allows for the calculation of probabilities
of outcomes of concrete experiments. For example, it allows one to compute the probability
of finding an electron in a particular region around the nucleus at a
particular
time. Contrary to classical mechanics, one can never make simultaneous predictions of conjugate variables, such as position and momentum, with arbitrary accuracy. For instance, electrons may be considered to be located somewhere within a region of space, but with their exact positions being unknown. Contours of constant probability, often referred to as “clouds” may be drawn around the nucleus of an atom to conceptualize where the electron might be located with the most probability (Figure 8).
time. Contrary to classical mechanics, one can never make simultaneous predictions of conjugate variables, such as position and momentum, with arbitrary accuracy. For instance, electrons may be considered to be located somewhere within a region of space, but with their exact positions being unknown. Contours of constant probability, often referred to as “clouds” may be drawn around the nucleus of an atom to conceptualize where the electron might be located with the most probability (Figure 8).
The other exemplar that led to
quantum mechanics was the study of electromagnetic waves
such as light. When it was found in 1900 by Max Planck that the energy of waves
could be described as consisting of small packets or quanta, Albert Einstein exploited this idea to show that
an electromagnetic wave such as light could be described by a particle
called the photon with a discrete energy dependent on its
frequency. This led to a theory of unity
between subatomic particles and electromagnetic waves called wave –particle
duality in which particles and waves were neither one nor the other,
but had certain properties of both...
3.2) The Wave
Properties of Particles
In 1924
Louis de Broglie postulated that because photons have both wave and particle
characteristics, perhaps all forms of matter have both properties. According
to de Broglie, electrons, just like light, have a dual particle - wave nature.
Because the photon wavelength can be specified by its momentum: λ = h/p,
De Broglie suggested that material particles of momentum p have a
characteristic wavelength that is given by the same expression. Thus the de
Broglie wavelength of a particle is
λ = h / p = h / m v
(2)
From equation 2, the magnitude of the momentum
p of a particle of mass m and speed v is p = m v.
Furthermore,
in analogy with photons, de Broglie postulated that a particle obey the
Einstein relation E = h ƒ (Equation 1), where E is the
total energy of the particle. Then the frequency of a particle is
ƒ = E / h
The
dual nature of matter is apparent in these last two equations, because each
contains both particle concepts (m v and E) and wave concepts (λ
and ƒ).
4) The Electron Microscope
It was pointed out earlier, that
the size of the smallest object observable by a microscope is about half the
wavelength of the illuminating radiation. In light microscopes, this limits the
resolution to about 200 nm (2000 A˚). Because of the wave properties of
electrons, it is possible to construct microscopes with a resolution nearly
1000 times smaller than this value. It is relatively easy to accelerate
electrons in an evacuated chamber to high velocities so that their wavelength
is less than 10−10 m (1A˚). Furthermore, the direction of motion of
the electrons can be altered by electric and magnetic fields. Thus, suitably
shaped fields can act as lenses for the electrons. The short wavelength of
electrons coupled with the possibility of focusing them has led to the
development of electron microscopes that can observe objects 1000 times smaller than are visible with light microscopes.
development of electron microscopes that can observe objects 1000 times smaller than are visible with light microscopes.
The basic construction of an
electron microscope is shown in Figure 9. The similarities between the electron
and the light microscope are evident; both have the same basic configuration of
two lenses which produce two-stage of magnification.
Figure
9: The electron Microscope
4.1) Measurements
·
Electrons are emitted from a heated filament, and
are then accelerated and collimated
into a beam.
into a beam.
·
The beam passes through the thin sample under examination
which diffracts the
electrons in much the same way as light is diffracted in an optical microscope. But
because of their short wavelength, the electrons are influenced by much smaller
structures within the sample.
electrons in much the same way as light is diffracted in an optical microscope. But
because of their short wavelength, the electrons are influenced by much smaller
structures within the sample.
·
The transmitted electrons are focused into a
real image by the objective lens.
·
This image is then further magnified by the
projector lens, which projects the final
image onto film or a fluorescent screen.
image onto film or a fluorescent screen.
Although it is possible to produce
electrons with a wavelength much less than 10−10m (1˚A), the theoretical
optimum resolution implied by such short wavelengths has not yet been realized.
At present, the best resolution of electron microscopes is about 5 x 10−10
m (5A˚).
4.1.1 The Optimum Measuring Conditions
a)Because electrons are
scattered by air, the microscope must be contained in an
evacuated chamber.
evacuated chamber.
b)The samples under
examination must be dry and thin.
These conditions, of course,
present some limitations in the study of biological materials. The samples have
to be specially prepared for electron microscopic examination. They must be
dry, thin, and in some cases coated. Nevertheless, electron microscopes have
yielded beautiful pictures showing details in cell structure, biological
processes, and recently even large molecules such as DNA in the process of
replication.
5) X-rays
Introduction
X-rays are part of the
electromagnetic spectrum. X-rays were first observed and documented in 1895 by
Wilhelm Conrad Roentgen, a German scientist who found them quite by
accident when experimenting with electron beams in a gas discharge tube.
Roentgen noticed that, a fluorescent
screen in his lab started to glow when the electron beam was turned on. This
response in itself was not so surprising. Fluorescent material normally glows
in reaction to electromagnetic radiation, but Roentgen's tube was surrounded by
heavy black cardboard. Roentgen assumed this has blocked most of the radiation.
Roentgen placed various objects between the tube and the screen, and the screen
still glowed. A week later, he took an
X-ray photograph of his wife's hand which clearly revealed her wedding ring and
her bone as shown in Figure 10. The photograph electrified the general public
and aroused great scientific interest in the new form of radiation. Roentgen
called it "X" to indicate it was an unknown type of
radiation.
5.1) X-Ray Spectra
X-rays are emitted when
high-energy electrons or any other charged particles bombard a metal target.
The x-rays spectrum typically consists of a broad continuous band containing a
series of sharp lines, as shown in Figure 11.
5.1.1 Bremsstrahlung X-Rays (Broad band)
As we mentioned earlier, that an
accelerated electric charge emits electromagnetic radiation. The x-rays in
Figure 11 are the result of the slowing down of high-energy electrons as they
strike the target. The electron loses all of its kinetic energy after several
interactions with the atoms of the target. The amount of kinetic energy lost in
any given interaction varying from zero up to the entire kinetic energy of the
electron. Therefore, the wavelength of radiation from these interactions lies
in a continuous range from some minimum value up to infinity. It is this
general slowing down of the electrons that
provide the continuous curve in Figure 11, which shows the cutoff of x-rays below a minimum wavelength value that depends on the kinetic energy of the incoming electrons. X-ray radiation with its origin in the slowing down of electrons or continuous spectrum shown in the Figure is called Bremsstrahlung, the German word for “braking radiation.”
provide the continuous curve in Figure 11, which shows the cutoff of x-rays below a minimum wavelength value that depends on the kinetic energy of the incoming electrons. X-ray radiation with its origin in the slowing down of electrons or continuous spectrum shown in the Figure is called Bremsstrahlung, the German word for “braking radiation.”
Figure
11: The x – rays spectrum of a metal
target consists of a broad continuous spectrum plus a number
of sharp lines, which are due to characteristic x-rays. The data shown were obtained when 37-
ke V electrons bombarded a molybdenum target.
of sharp lines, which are due to characteristic x-rays. The data shown were obtained when 37-
ke V electrons bombarded a molybdenum target.
5.1.2 Characteristic X- rays
(Sharp lines)
The discrete lines shown in Figure
11 called Characteristic x-rays which can be produced according to the
following steps:
·
A bombarding electron collides with a target
atom.
·
The electron with high energy, removes an electron
from an innermost shell (K shell, n
= 1) of the atom.
= 1) of the atom.
·
An electron from a next higher orbit (L shell, n
= 2) drops down to fill the vacancy.
The time interval for this to happen is very short, less than 10-9 s.
The time interval for this to happen is very short, less than 10-9 s.
·
This transition is accompanied by the emission of
a photon whose energy is equal to
the energy difference between the two levels. Thus the photon emitted has an energy
corresponding to the K α, the characteristic x-ray line on the curve in Figure 11.
the energy difference between the two levels. Thus the photon emitted has an energy
corresponding to the K α, the characteristic x-ray line on the curve in Figure 11.
[In this notation K refers
to the final level of the electron and the subscript α, refers to
the initial level as the first one above the final level. Thus Kα indicates that, a
transition occur from energy level L (n = 2) to energy level K (n = 1)].
the initial level as the first one above the final level. Thus Kα indicates that, a
transition occur from energy level L (n = 2) to energy level K (n = 1)].
·
If the vacancy in the K (n = 1) shell is
filled with electron dropping from the M shell (n
= 3), the Kβ line in Figure 11 is produced.
= 3), the Kβ line in Figure 11 is produced.
[K β
is a transition from level M (n = 3) to level K (n=1)]
Typically, the energy of such
transition is greater than 1 000 eV, and the emitted photons have wavelengths
in the range of 0.01 nm to 1 nm.
Other characteristic x-rays lines
are formed when electrons drop from upper levels to vacancies other than those
in the K shell. For example, L lines are produced when vacancies in the L shell
are filled by electrons dropping from higher shells. An Lα
lines is produced as an electron drops from M shell (n = 3) to the
L shell (n = 2), and an Lβ is produced by a transition from the N
shell (n = 4) to the L (n = 2) shell.
5.2) X-Rays
Machines
The heart of an X-ray machine is an electrode pair, a
cathode and an anode that sits inside a glass vacuum tube. The cathode is a
heated filament. The machine passes current through the filament, heating it
up. The heat sputters electrons off of the filament surface. The
positively-charged anode, a flat disc made of tungsten, draws the electrons
across the tube as shown in Figure 12.
Figure 12: The X - Ray Machine
The voltage difference between the cathode and anode is
extremely high, so the electrons fly through the tube with a great deal of
force. When a speeding electron collides with a tungsten atom, it knocks loose
an electron in one of the atom’s lower orbital. An electron in a higher orbital
immediately falls to the lower energy level, releasing its extra energy in the
form of a photon. It’s a big drop, so the photon has a high energy level; it is
an X-ray photon (Figure 13).
Figure
13: The free electron collides with
the tungsten atom, knocking an electron out of a lower orbital.
A higher orbital electron fills the empty position, releasing its excess energy as a photon.
A higher orbital electron fills the empty position, releasing its excess energy as a photon.
The high-impact collisions involved in x-ray production
generate a lot of heat. A motor
rotates the anode to keep it from melting (the electron beam isn’t always
focused on the same area). A cool oil bath surrounding the envelope also
absorbs heat. The entire mechanism is surrounded by a thick lead shield. This
keeps the x-rays from escaping in all directions. A small window in the shield
lets some of the x-ray photons escape in a narrow beam. The beam passes through
a series of filters on its way to the patient. A camera on the other side of
the patient records the pattern of x-ray light that passes all the way through
the patient’s body (Figure 12).
Generally,
doctors keep the film image as a negative. That is, the areas that
are exposed to more light appear darker and the areas that are exposed to less
light appear lighter. Hard material, such as bone, appears white, and
softer material appears black or gray.
Finally, from the preceding
discussion, one can show that two different processes give rise to radiation of
x-ray frequency:
· In
one process; radiation is emitted by the high - speed electrons themselves as
they
are slowed or even stopped in passing near the positively charged nuclei of the anode
material. This is the Brehmsstrahlung radiation.
are slowed or even stopped in passing near the positively charged nuclei of the anode
material. This is the Brehmsstrahlung radiation.
·
In a second process; radiation is emitted
by the electrons of the anode atoms when
incoming electrons from the cathode knock electrons near the nuclei out of orbit and
they are replaced by other electrons from outer orbits. X - rays produced in this way
have definite energies just like other line spectra from atomic electrons. They are
Characteristic x-rays. The spectral lines generated depend on the target (anode)
element used and thus are called characteristic lines.
incoming electrons from the cathode knock electrons near the nuclei out of orbit and
they are replaced by other electrons from outer orbits. X - rays produced in this way
have definite energies just like other line spectra from atomic electrons. They are
Characteristic x-rays. The spectral lines generated depend on the target (anode)
element used and thus are called characteristic lines.
In medical applications, the
target (anode) is usually tungsten or a more crack resistant alloy of rhenium (5%) and
tungsten (95%), but sometimes molybdenum for more specialized applications, such as when
soft x-rays are needed as in mammography.
In general, the spectrum of
frequencies given off with any particular anode material thus consists of a
continuous range of frequencies emitted in the first process, and superimposed
on it a number of sharp peaks of intensity corresponding to discrete frequencies
at which x- rays are emitted in the second process.
5.3) X-Rays
Techniques
5.3.1 Medicine
1. X-ray Picture:
Within three weeks of Roentgen’s announcement, two French
physicians, Oudin and Barthelemy, obtained x-rays of bones in a hand. Since then, x-
rays have become one of the most important diagnostic tools in medicine. With
current techniques, it is even possible to view internal body organs that are quite
transparent to x-rays. This is done by injecting into the organ a fluid opaque to x-
rays. The walls of the organ then show up clearly by contrast.
physicians, Oudin and Barthelemy, obtained x-rays of bones in a hand. Since then, x-
rays have become one of the most important diagnostic tools in medicine. With
current techniques, it is even possible to view internal body organs that are quite
transparent to x-rays. This is done by injecting into the organ a fluid opaque to x-
rays. The walls of the organ then show up clearly by contrast.
2. X-ray Computerized
Tomography (CT scan): The usual x-ray picture does not
provide depth information. The image represents the total attenuation as the x-ray
beam passes through the object in its path. For example, a conventional x-ray of the
lung may reveal the existence of a tumor, but it will not show how deep in the lung the
tumor is located. Several tomographic techniques (CT scans) have been developed to
produce slice-images within the body which provide depth information. Presently the
most commonly used of these is x-ray computerized tomography (CT scan) developed
in the 1960. The basic principles of the technique in its simplest form illustrated in
Figure 14 are:
provide depth information. The image represents the total attenuation as the x-ray
beam passes through the object in its path. For example, a conventional x-ray of the
lung may reveal the existence of a tumor, but it will not show how deep in the lung the
tumor is located. Several tomographic techniques (CT scans) have been developed to
produce slice-images within the body which provide depth information. Presently the
most commonly used of these is x-ray computerized tomography (CT scan) developed
in the 1960. The basic principles of the technique in its simplest form illustrated in
Figure 14 are:
·
A thin beam of x-rays passes through the plane
we want to visualize and is detected by
a diametrically opposing detector.
a diametrically opposing detector.
·
For a given angle with respect to the object (in
this case the head), the x-ray source-
detector combination is moved laterally scanning the region of interest as shown by the
arrow in Figure 14 (a).
detector combination is moved laterally scanning the region of interest as shown by the
arrow in Figure 14 (a).
·
At each position, the detected signal carries
integrated information about x-ray
transmission properties of the full path in this case A−B.
transmission properties of the full path in this case A−B.
·
The angle is then changed by a small amount (about
1˚) and the process is repeated full
circle around the object.
circle around the object.
As indicated in Figure 14(b), by rotating the
source-detector combination, information can be obtained about the intersection
points of the x-ray beams. The Figure shows schematically the scanning beam at
two angles with two lateral positions at each angle. While at each position,
the detected signal carries integrated information about the full path, two
paths that intersect contain common information about the one point of
intersection. In the Figure, four such points are shown at the intersection of
the beams A − B, A′ − B′, C − D, and C′−D.
The multiple images obtained by translation and rotation contain information
about the x-ray transmission properties of each point
within the plane of the object to be studied. These signals are stored and by a rather complex computer analysis a point by point image is constructed of the thin slice scanned within the body.
within the plane of the object to be studied. These signals are stored and by a rather complex computer analysis a point by point image is constructed of the thin slice scanned within the body.
Figure 14: (a) Basic principle of computed axial tomography.
(b)Rotation of the source-detector combination
provides information about the x-ray
transmission properties of each point within the plane of the object to be studied.
transmission properties of each point within the plane of the object to be studied.
The visualized slices within the body
obtained in this way are typically about 2 mm
thick. In the more recent versions of the instrument, a fan rather than a beam of x-rays
scans the object, and an array of multiple detectors is used to record the signal. Data
acquisition is speeded up in this way yielding an image in a few seconds.
thick. In the more recent versions of the instrument, a fan rather than a beam of x-rays
scans the object, and an array of multiple detectors is used to record the signal. Data
acquisition is speeded up in this way yielding an image in a few seconds.
5.3.2 Biology
Crystallography: x-rays
have also provided valuable information about the structure of biologically
important molecules. The technique used here is called crystallography and can
be expressed as follows:
The wavelength of x-rays is on the order of 10−10 m,
about the same as the distance between atoms in a molecule or crystal.
Therefore, if a beam of x- rays is passed through a crystal, the transmitted
rays produce a diffraction pattern that contains information about the
structure and composition of the crystal. The diffraction pattern consists of
regions of high and low x-ray intensity which when photographed show spots of varying brightness (Figure 15).
regions of high and low x-ray intensity which when photographed show spots of varying brightness (Figure 15).
Figure 15: Arrangement
for detecting diffraction of X-rays by a crystal.
Diffraction studies are most successfully done with
molecules that can be formed into a regular periodic crystalline array. Many
biological molecules can in fact be crystallized under the proper conditions.
It should be noted, however, that the diffraction pattern is not a unique,
unambiguous picture of the molecules in the crystal. The pattern is a mapping
of the collective effect of the arrayed molecules on the x-rays that pass
through the crystal. The structure of the individual molecule must be deduced
from the indirect evidence provided by the diffraction pattern.
If the crystal has a simple structure such as sodium
chloride, the x-ray diffraction pattern is also simple and relatively easy to interpret.
Complicated crystals, however, such as those synthesized from organic
molecules, produce very complex diffraction patterns. But, even in this case,
it is possible to obtain some information about the structure of the molecules forming
the crystal. To resolve the three-dimensional features of the molecules,
diffraction patterns must be formed from thousands of different
angles. The patterns are then analyzed, with the aid of a computer. These types
of studies provided critical information for the determination of the structure
for penicillin, vitamin B12, DNA, and many other biologically
important molecules.
5.4) Medical Applications of X-Ray
X- Ray radiation, used in
medicine into two different ways:
1. Diagnosis (imaging)
2. Therapy [The treatment
of neoplastic disease (abnormal growth of cells) by using x-
rays to prevent or to slow the proliferation of malignant cells by decreasing the rate of
mitosis or impairing DNA synthesis].
rays to prevent or to slow the proliferation of malignant cells by decreasing the rate of
mitosis or impairing DNA synthesis].
5.4.1 Diagnostic Imaging
X-ray radiation is used for imaging
internal body structures, hard and soft tissue, for diagnosis; x-rays hard tissues
such as bones and teeth absorb more x-rays and show as lighter areas on x-ray
film; A contrast
medium can be used to highlight soft tissues in
still x-ray pictures, or can be followed on x-ray motion-picture films as it moves through the body or part of the body to record body processes.
still x-ray pictures, or can be followed on x-ray motion-picture films as it moves through the body or part of the body to record body processes.
Contrast Medium; in a
normal x-ray picture, most soft tissue doesn't show up clearly. To focus in on
organs, or to examine the blood vessels that make up the circulatory system,
doctors must introduce contrast media into the body. Contrast media are liquids
that absorb x-rays more effectively than the surrounding tissue. To bring
organs in the digestive and endocrine systems into focus, a patient will
swallow a contrast media mixture, typically a barium compound. If the doctors
want to examine blood vessels or other elements in the circulatory system, they
will inject contrast media into the patient's bloodstream.
Arthrography (Joint x-ray):
Arthrography is the x-ray examination of joint that uses a special form
of x-ray called fluoroscopy and a contrast material containing iodine. Fluoroscopy
makes it possible to see internal organs in motion. When iodine is injected into
the joint space, it coats the inner lining of the joint structures and appears
bright white on an arthrogram, allowing the radiologist to assess the anatomy and function of
the joint (areas where the dye leaks out indicate a tear in the tendons). Arthrographic
images help physicians evaluate alterations in structure and function of a
joint and help to determine the possible need for treatment, including surgery
or joint replacement. The procedure is most often used to identify
abnormalities within the shoulder, wrist, hip, knee (Figure 16), and ankle.
Figure
16: C T Arthrogram of the knee.
Catheter Angiography: In
catheter angiography, a thin plastic tube, called a catheter,
is inserted into an artery through a small incision in the skin. Once the
catheter is guided to the area being examined, a contrast material is injected
through the tube and images are captured using a small dose of ionizing
radiation (x-rays).
Catheter angiography is used to examine blood vessels in key areas of the body
including the brain, kidneys, pelvis, legs, lungs, heart, and neck.
Mammography: Mammography
is a specific type of imaging that uses a low dose x-ray system to examine breasts. A mammography exam,
called a mammogram, is used to aid in the diagnosis of breast diseases.
Bone X-ray: A bone x-ray shows
images of bones in the body, including the hand (Figure 17), wrist, arm, foot,
ankle, knee and leg. A bone x-ray is used to determine whether a bone has been fractured
or if a joint is dislocated. It also can ensure that a fracture has been
properly aligned and stabilized for healing following treatment. The image can
show whether there is a build up of fluid in the joint or around a bone. It can
also evaluate injury or damage from conditions such as infection, arthritis, abnormal bone growths or other bone
diseases, such as osteoporosis. This technique is also used to assist
in the detection and diagnosis of cancer.
Figure
17: X-ray showing frontal view of
both hands.
Lower Gastrointestinal Tract
X-ray: Lower gastrointestinal tract radiography, also called a lower GI, is
an x-ray examination of the large intestine (colon)
as shown in Figure 18. This includes the examination of the right or ascending
colon, the transverse colon, the left or descending colon and the rectum. The appendix and a portion of the small intestine
may also be included. The lower GI use x-ray (fluoroscopy) and a contrast material (barium). A physician may order a lower GI
examination to detect; ulcers, benign tumors, cancer, and signs of other intestinal diseases.
Figure
18: This image shows the right side
of the large intestine. Air (dark) distends the bowel and barium
(white) coats the inner lining.
(white) coats the inner lining.
Renal Examination: X-raying
the kidneys, are usually done after injecting a contrast medium into a vein. A
series of x-rays is then taken to show the renal outline
and collecting system and structures of the kidneys, as well as ureters and the
bladder.
Hysterosalpingography: Hysterosalpingography
is primarily used to examine women, who
have difficulty to become pregnant by allowing
the radiologist to evaluate the shape and structure of the uterus, the openness of the fallopian tubes. The procedure can be used to
investigate repeated miscarriages that result from congenital abnormalities of the uterus, and to
determine the presence and severity of these abnormalities, including: tumor
masses or adhesions uterine fibroids (The word hystero means uterus, while salpingo
means tubes in latin).
Dental X-rays: Structures that are dense (such as silver fillings
or metal restoration) will block most of the photons and will appear
white on developed film. Air beneath the teeth will be black on
film, teeth and tissue will appear as
shades of gray. The test is performed
in the dentist's clinics. There are four types of x-rays:
1. Bite-wing: The bite-wing is when the patient bites on a paper tab and
shows the crown
portions of the upper and lower teeth together (Figure19).
portions of the upper and lower teeth together (Figure19).
Figure 19: Bite-Wings X-rays are some of the most typical x-rays a Dentist will take. These types
of x-
rays are very effective at discovering tooth decay. It is called Bitewing because the x-ray
film holder provides a surface to bite down on and hold the x-ray securely in place.
rays are very effective at discovering tooth decay. It is called Bitewing because the x-ray
film holder provides a surface to bite down on and hold the x-ray securely in place.
2. Periapical X-rays: The periapical x-rays shows one or two complete teeth
from crown
to root (Figure 20).
to root (Figure 20).
Figure 20: Periapical X-rays are taken to get a more effective examination of the
entire tooth area from
crown to root. These types of x-rays provide a complete side view and typically a complete
set consists of 14 films with each tooth appearing in two different films from two different
angles.
crown to root. These types of x-rays provide a complete side view and typically a complete
set consists of 14 films with each tooth appearing in two different films from two different
angles.
3. Occlusal X-rays: Occlusal x-ray captures the
upper or the lower teeth in one shot,
while the film rests on the biting surface of the teeth (Figure 21).
while the film rests on the biting surface of the teeth (Figure 21).
Figure 21: Occlusal X-rays
are less common than either Bite-Wing or Periapical X-rays. These types of
x-rays are taken to show the lower or the upper jaw.
x-rays are taken to show the lower or the upper jaw.
4. Panoramic: Panoramic x-ray requires a special machine that
rotates around the head.
The x-ray captures the entire jaws and teeth in one shot. It's used to plan treatment for
dental implants, check for impacted wisdom teeth, and detect jaw problems. A
panoramic x-ray is not good for detecting cavities, unless the decay is very advanced
and deep( Figure 22).
The x-ray captures the entire jaws and teeth in one shot. It's used to plan treatment for
dental implants, check for impacted wisdom teeth, and detect jaw problems. A
panoramic x-ray is not good for detecting cavities, unless the decay is very advanced
and deep( Figure 22).
Figure 22: Panoramic or Panorex (a type of film) X-ray is also very commonly done on an "initial"
visit
of a dentist. As the name suggests, a Panoramic X-ray makes a complete half circle from ear
to ear to produce a complete two dimensional representation of all teeth. Panoramic X-rays
give the dentist an overall picture of all your teeth and jaw bones.
of a dentist. As the name suggests, a Panoramic X-ray makes a complete half circle from ear
to ear to produce a complete two dimensional representation of all teeth. Panoramic X-rays
give the dentist an overall picture of all your teeth and jaw bones.
In General, dental x-rays may be used to identify the number, size, and
position of teeth, unemerged or impacted
teeth, the presence and extent of dental cavities, bone damage (such
as from periodontitis),
abscessed teeth, fractured jaw.
5.4.2 X-ray Therapy Radiation Treatment
This kind of treatment is based
on the uses of high energy, penetrating waves or particles such as x-rays to destroy cancer
cells or keep them from reproducing. One of the
characteristics of cancer cells is that they grow and divide faster than normal cells. Radiation also damages normal cells, but because normal cells are growing more slowly, they are better able to repair radiation damage than are cancer cells. In order to give normal cells time to heal and reduce side effects, radiation treatments are often given in small doses over a six or seven week period. It is used in more than half of all cancer cases. Radiation therapy can be used in different ways:
characteristics of cancer cells is that they grow and divide faster than normal cells. Radiation also damages normal cells, but because normal cells are growing more slowly, they are better able to repair radiation damage than are cancer cells. In order to give normal cells time to heal and reduce side effects, radiation treatments are often given in small doses over a six or seven week period. It is used in more than half of all cancer cases. Radiation therapy can be used in different ways:
·
Alone to kill cancer.
·
During surgery to kill cancer cells that may
remain in surrounding tissue after the surgery.
·
After surgery to kill cancer cells remaining in
the body.
·
To shrink an inoperable
tumor in order to reduce pain and improve quality of life in combination with chemotherapy.
6) Lasers
In this section, we will explore
the nature of laser light and apply our knowledge of atomic structure to describe
the mechanism involved in the operation of laser. This will be followed by
describing a variety of applications of lasers in our technological society.
6.1) The Nature of Laser Light.
6.1.1 Properties of Laser
Light
The
primary properties of laser that make it useful in these technological
applications are:
·
Laser light is
coherent; the individual rays in a laser beam maintain a fixed phase
relationship with each other.
relationship with each other.
·
Laser light is
monochromatic; light in a laser beam has a very narrow range of
wavelengths.
wavelengths.
·
Laser light has a
small angle of divergence: the beam spreads out very little, even over
long distances.
long distances.
6.1.2 Lasers – Operation
In
order to understand the origin of these properties, let us combine our
knowledge of atomic energy levels from this chapter with some special
requirements for the atoms that emit laser light.
We have
described, how an incident photon can cause atomic energy level transitions
either upward (stimulated absorption) or downward (stimulated emission). The two
situations are equally probable. When light is incident on a collection of
atoms, a net absorption of energy usually occurs because when the system is in
thermal equilibrium, many more atoms are in the ground state than in the
excited states. The situation can be inverted so that more atoms are in excited
states than in the ground state, a net emission of photons can result. Such a
condition is called population inversion.
Population
inversion is, in fact, the fundamental principle involved in the operation of a
laser (an acronym for light amplification by stimulated
emission of radiation). The full name indicates one of the
requirements for laser light: this means that, to achieve laser action, the process
of stimulated emission must occur.
Suppose an atom is in the excited state E2,
as in Figure 23, when a photon with energy hƒ= E2 –
E1 is incident on it, we can show that:
·
The incoming photon
can stimulate the excited atom to return to the ground state and thereby emit a
second photon having the same energy hƒ and traveling in the same
direction. The incident photon is not absorbed, so after the stimulated
emission, there are two identical photons: the incident photon and the emitted
photon. The emitted photon is in phase with the incident photon.
·
These photons can
stimulate other atoms to emit photons in a chain of similar processes. The many
photons produced in this fashion are the source of the intense, coherent light
in a laser.
Figure 23: Stimulated
emission of a photon by an incoming photon of energy hƒ = E2
– E1.
Initially, the atom is in the excited state. The incoming photon stimulates the atom to emit a
second photon of energy given by hƒ = E2 – E1.
Initially, the atom is in the excited state. The incoming photon stimulates the atom to emit a
second photon of energy given by hƒ = E2 – E1.
6.1.3
Conditions for Build-Up of Photons
For the
stimulated emission to result in laser light there must be a buildup of photons
in the system. The following three conditions must be satisfied in order to
achieve this buildup:
1. The system must be in a state of population inversion; there
must be more atoms in an
excited state than in the ground state. That must be true because the number of
photons emitted must be greater than the number absorbed.
excited state than in the ground state. That must be true because the number of
photons emitted must be greater than the number absorbed.
2. The excited state of the system must be a metastable
state; which means that its
lifetime must be long compared with the usually short lifetimes of excited state, which
are typically 10-8s. In this case, the population inversion can be established and
stimulated emission is likely to occur before spontaneous emission as shown in
Figure 24.
lifetime must be long compared with the usually short lifetimes of excited state, which
are typically 10-8s. In this case, the population inversion can be established and
stimulated emission is likely to occur before spontaneous emission as shown in
Figure 24.
[Spontaneous
emission; Once an atom is in an excited state, the excited atom can
make a transition to a lower energy level, because this process happens naturally, it is
known as spontaneous emission].
make a transition to a lower energy level, because this process happens naturally, it is
known as spontaneous emission].
Figure 24: Spontaneous emission of a photon by an
atom that is initially in the excited state E2.
When the atom falls to the ground state, it emits a photon of energy hƒ = E2 – E1.
When the atom falls to the ground state, it emits a photon of energy hƒ = E2 – E1.
3. The emitted photons must be confined in the system long
enough to enable them to
stimulate further emission from other excited atoms. That is achieved by using
reflecting mirrors at the ends of the system. One end is made totally reflecting, and the
other is partially reflecting. A fraction of the light intensity passes through the
partially reflecting end, forming the beam of laser light (Figure 25).
stimulate further emission from other excited atoms. That is achieved by using
reflecting mirrors at the ends of the system. One end is made totally reflecting, and the
other is partially reflecting. A fraction of the light intensity passes through the
partially reflecting end, forming the beam of laser light (Figure 25).
Figure 25: Schematic diagram of a laser design.
The tube contains the atoms that are the
active medium. An external source of energy (for
example, an optical or electrical device) pumps the atoms to the excited states. The parallel end
mirrors confine the photons to the tube, but mirror 2 is only partially reflective.
example, an optical or electrical device) pumps the atoms to the excited states. The parallel end
mirrors confine the photons to the tube, but mirror 2 is only partially reflective.
6.2) Laser Construction
A laser is effectively a machine
that makes billions of atoms pump out trillions of photons all at once so they
line up to form a really concentrated light beam.
A red laser contains a long
crystal made of ruby as shown in Figure 26 as a red bar with a flash tube
(yellow zig-zag lines) wrapped around it. The flash tube looks a bit like a
fluorescent strip light, only it's coiled around the ruby crystal and it flashes every so often like a camera's flash gun.
fluorescent strip light, only it's coiled around the ruby crystal and it flashes every so often like a camera's flash gun.
Figure
26: A construction for
laser light by using a crystal and a flash tube.
The following
represents how the flash tube and the crystal make laser light:
1. A high-voltage electric
supply makes the tube flash on and off.
2. Every time
the tube flashes, it "pumps" energy into the ruby crystal. The flashes
it
makes inject energy into the crystal in the form of photons.
makes inject energy into the crystal in the form of photons.
3. Atoms in the ruby crystal
(large green blobs) soak up this energy in an absorption
process. When an atom absorbs a photon of energy, one of its electrons jumps
from a low energy level to a higher one. This puts the atom into an excited state, but
makes it unstable. Because the excited atom is unstable, the electron can stay in the
higher energy level only for a few milliseconds. It falls back to its original level,
living off the energy it absorbed as a new photon of light radiation (small blue blob).
This is the spontaneous emission process.
process. When an atom absorbs a photon of energy, one of its electrons jumps
from a low energy level to a higher one. This puts the atom into an excited state, but
makes it unstable. Because the excited atom is unstable, the electron can stay in the
higher energy level only for a few milliseconds. It falls back to its original level,
living off the energy it absorbed as a new photon of light radiation (small blue blob).
This is the spontaneous emission process.
4.
The photons that atoms give off zoom up and down inside the ruby crystal,
traveling
at the speed of light.
at the speed of light.
5.
Every so often, one of these photons hits an already excited atom. When this
happens,
the excited atom gives off two photons of light instead of one. This is the stimulated
emission described earlier. Now one photon of light has produced two and the light
has been amplified (increased in strength). In other words, "light amplification" (an
increase in the amount of light) has been caused by "stimulated emission of radiation"
(hence the name "laser", because that's exactly how a laser works!)
the excited atom gives off two photons of light instead of one. This is the stimulated
emission described earlier. Now one photon of light has produced two and the light
has been amplified (increased in strength). In other words, "light amplification" (an
increase in the amount of light) has been caused by "stimulated emission of radiation"
(hence the name "laser", because that's exactly how a laser works!)
6. A mirror at one
end of the laser tube keeps the photons bouncing back and forth inside
the crystal.
the crystal.
7. A partial mirror at the
other end of the tube bounces some photons back into the
crystal but lets some escape.
crystal but lets some escape.
8. The escaping photons form a
very concentrated beam of powerful laser light.
6.3) Classifications
of Lasers
Lasers are classified into four broad areas depending on the potential for
causing biological damage. Safety thresholds for lasers are expressed in
terms of Maximum
Permissible Exposure (MPE). When you use a laser, it should be labeled with one of these four classes designations:
Permissible Exposure (MPE). When you use a laser, it should be labeled with one of these four classes designations:
Class 1
These lasers cannot emit laser radiation at known hazard
levels under normal operating conditions, because they are completely
enclosed (prohibit or limits access to the laser radiation). Examples of this
class are: laser printers and laser disc players.
Class 1a
This is a special designation that applies only to lasers that are
"not intended for viewing," such as a supermarket laser scanner. The
upper power limit of class1a is 4.0 mW.
Class 2
These are low-power visible lasers that emit above class 1 levels but at a
radiant power not above 1 mW. The concept is that the human aversion reaction
to bright light will protect a person and are capable of creating eye
damage through chronic exposure. The human eye blink reflex, which occurs
within 0.25 seconds of exposure to Class 2 laser beam. Examples are:
Helium-Neon lasers and some laser pointers.
Class 3a
These are intermediate - power lasers from 1 to 5
mW, which are hazardous only for intra-beam viewing. A warning label
shall be placed on or near the laser in a conspicuous location of caution
users, to avoid staring into the beam or directing the beam toward the eye of
individuals. Example of this type of laser: Helium-Neon lasers, some solid
state laser pointers and most
pen-like pointing lasers are in this class.
Class 3b
These are moderate-power lasers from 5 mW to 500 mW . These lasers
will produce an eye hazard if viewed directly.
Class 4
These are high-power lasers from 500 mW if continuous wave (cw), or 10 J/cm2
if pulsed, which are hazardous to view under any condition.
6.4) Types of
Lasers
There are many different types of
lasers. The laser medium can be a solid, gas, liquid or semiconductor. A laser
concentrates high energies into an intense narrow beam of no divergent
monochromatic electromagnetic radiation; Lasers using various substances (ruby,
argon, krypton, neodymium, helium-neon, carbon dioxide) are available. Lasers
are commonly designated by the type of lasing material employed.
Solid-State Lasers: is a high-power laser
operating in the infrared, used for cutting,
welding and marking of metals and other materials, have lasing material
distributed in a solid matrix (such as the ruby or neodymium: yttrium-aluminum
garnet "YAG" lasers).
Gas Lasers: helium and helium-neon, He-Ne are the most common
gas lasers, have a primary output of visible red light. CO2 lasers
emit energy in the far-infrared, 10.6 micrometer, and are used for cutting hard
materials.
Excimer Lasers: Use reactive gases, such as chlorine and
fluorine, mixed with inert gases such as argon, krypton or xenon. When
electrically stimulated, a pseudomolecule or dimmer is produced. When lased,
the dimmer produces light in the ultraviolet range (the name excimer is
derived from the terms excited and dimmers).
Dye Lasers: use complex organic dyes, such as rhodamine 6G,
in liquid solution or suspension as lasing media. They are tunable over a broad
range of wavelengths
Semiconductor Lasers: sometimes called diode lasers, are not solid-
state lasers. These electronic devices are generally very small and use low
power. They may be built into larger arrays, such as the writing source in some
laser
printers , laser pointers or CD players.
6.5) Applications
There are many scientific, military, medical and commercial
laser applications which have been developed since the invention of the
laser in the 1958. The coherency, high monochromatic,
and ability to reach extremely high powers, are all properties which allow for
these specialized applications of laser.
Commercial: The most widespread use of
lasers is in optical storage devices
such as compact disc and DVD players, in which the laser (a few millimeters in size) scans the surface of the disc. Other common applications of lasers are bar code readers, laser printers and laser pointers.
such as compact disc and DVD players, in which the laser (a few millimeters in size) scans the surface of the disc. Other common applications of lasers are bar code readers, laser printers and laser pointers.
Medicine: Bloodless surgery, laser healing, surgical treatment,
kidney
stone treatment, eye treatment, dentistry.
Defense: Marking targets, guiding munitions, missile defense, electro-optical countermeasures (EOCM) and
alternative to radar.
Research: Spectroscopy, laser ablation, laser annealing, laser scattering, laser interferometer.
Industry: Lasers
are used for cutting and welding the steel and other metals and for
inscribing patterns (such as the letters on computer Key boards).
6.5.1 Medical Applications
Because various laser wavelengths
can be absorbed in specific biological tissues, lasers have a number of medical
applications:
·
Certain laser procedures have greatly reduced
blindness in patients with glaucoma and
diabetes. Glaucoma is a widespread eye condition characterized by a high fluid
pressure in the eye, a condition that can lead to destruction of the optic nerve. A simple
laser operation, (iridectomy) can “burnˮ open a tiny hole in a clogged membrane relieving the destructive pressure. A serious side effect of diabetes is neovascularization, the proliferation of weak blood vessels, which often leak blood. When neovascularization occurs in the retina, vision deteriorates (diabetic retinopathy) and finally is destroyed. Today, it is possible to direct the green light from an argon ion laser through the clear eye lens and eye fluid, focus on the retina edges, and photocoagulate the leaky vessels. Even people who have only minor vision defects such as nearsightedness are benefiting from the use of lasers to reshape the cornea,
changing its focal length and reducing the need for eyeglasses.
diabetes. Glaucoma is a widespread eye condition characterized by a high fluid
pressure in the eye, a condition that can lead to destruction of the optic nerve. A simple
laser operation, (iridectomy) can “burnˮ open a tiny hole in a clogged membrane relieving the destructive pressure. A serious side effect of diabetes is neovascularization, the proliferation of weak blood vessels, which often leak blood. When neovascularization occurs in the retina, vision deteriorates (diabetic retinopathy) and finally is destroyed. Today, it is possible to direct the green light from an argon ion laser through the clear eye lens and eye fluid, focus on the retina edges, and photocoagulate the leaky vessels. Even people who have only minor vision defects such as nearsightedness are benefiting from the use of lasers to reshape the cornea,
changing its focal length and reducing the need for eyeglasses.
·
Laser surgery is now an everyday occurrence at
hospitals and medical clinics around the word. Infrared light at 10 μ m
from a carbon dioxide laser can cut through muscle tissue, primarily by
vaporizing the water contained in cellular material. Laser power of
approximately 100 W is required in this technique. The advantage of the “laserˮ
knife over conventional methods is that laser radiation cut tissue and
coagulates blood at the same time, leading to a substantial reduction in blood
loss. In addition, the technique virtually eliminates cell migration, an
important consideration when tumors are being removed.
·
A laser beam can be trapped in fine optical
fiber light guides (endoscopes) by means of total internal reflection. An
endoscope can be introduced through natural orifices, conducted around internal
organs, and directed to specific interior body locations, eliminating the need
for invasive surgery. For example, bleeding in the gastrointestinal tract can
be optically cauterized by endoscopes inserted through the patient's mouth.
·
In medical and biological research, it is often
important to isolate and collect unusual cells for study and growth. A laser
cell separator exploits the tagging of specific cells with fluorescent dyes.
All cells are then dropped from a tiny charged nozzle and laser- scanned for
the dye tag. If triggered by the correct light-emitting tag, a small voltage
applied to parallel plates deflects the falling electrically charged cell into
a collection beaker.
6.5.2 Laser surgery
Before lasers could be successfully used in surgical procedures, a wide
range of studies had to be conducted to understand the effect of intense light
on various types of tissues. Further, technology had to be developed for
precise control of light intensity and duration and for accurate positioning of
the focal point. While the surgical use of lasers is growing in many areas of
medicine and dentistry, the positional accuracy of laser tissue-removal is
particularly important in neurosurgery and eye surgery where a fraction of a
millimeter offset can make the difference between success and failure.
Dermatology
In
laser skin resurfacing, a laser is used to remove areas of damaged or wrinkled
skin, layer by layer. The procedure is most commonly used to minimize the
appearance of fine lines, especially around the mouth and the eyes. However, it
is also effective in treating facial scars or areas of uneven pigmentation, sun damaged skin, acne scars, broken blood vessels,
wrinkles, (Figure 27 (a), (b) and (c)) and facial redness. Laser resurfacing may be performed on the whole face or
in specific regions.
(a)
(b)
(c)
Figure 27: (a) Acne Scars, (b) Broken Blood Vessels, and (c)
Wrinkles.
Ophthalmology
Ophthalmologists were among the first to use
lasers for a wide range of procedures. Figure 28 describes the treatment
of the disorder of the eye to restore normal vision (lasik eye surgery).
(a) The cornea is the transparent part of the
eye that covers the iris. It is also the main
light bending part of the eye.
light bending part of the eye.
(a)
(b) Anesthetic eye drops are given to numb the eye, and the surgeon marks
the cornea
with water-soluble ink to guide replacement of the corneal flap.
with water-soluble ink to guide replacement of the corneal flap.
(b)
(c) The surgeon performs a keratectomy which creates a corneal flap. The
flap is lifted
and reflected exposing the cornea beneath (A keratectomy is a procedure that uses a
small instrument that makes a cut in the cornea as it moves across it).
and reflected exposing the cornea beneath (A keratectomy is a procedure that uses a
small instrument that makes a cut in the cornea as it moves across it).
(c)
(d) A computer-controlled laser
reshapes the cornea to the prescribed shape for clear
vision.
vision.
(d)
(e) The corneal flap is repositioned and bonds to the cut edge of
the cornea quickly.
(e)
Figure 28: Lasik Eye Surgery.
Oncology
Laser procedure promises to
eliminate the need for radiation, preserve speech, shorten treatment time and
significantly improve care in other ways for many patients whose cancer is
diagnosed early. The therapy uses heat
from laser to destroy the tumor’s
blood supply and cancer cells, which damages surrounding tissues far less than
radiation and different types of lasers.
Otolaryngology
Otolaryngology
is the use of laser systems for excising skin tumors, cancers, birthmarks and
other disorders of the head and neck; problems of the voice box, throat, mouth,
nose and ear may be amenable to different laser treatments. Nodules or polyps
on the larynx and blood vessel defects in the upper airway are disorders that
could be treated with laser. In another instance, laser surgery might be
performed to remove the stapes from the middle ear for treatment of
otosclerosis. A new outpatient could eliminate the need for radiation in
treating early cancer of the larynx, or voice box. Pulses of green laser light
selectively destroy blood vessels feeding the tumor without burning the vocal
cords as shown in Figure 29.
Figure
29: The use of laser in treating
tumor in the voice box.
Finally, laser Surgery is often referred to as "bloodless
surgery," laser procedures usually involve less bleeding than conventional
surgery. The heat generated by the laser keeps the surgical site free of germs
and reduces the risk of infection. Because a smaller incision is required,
laser procedures often take less time (and cost less money) than traditional
surgery. Sealing off blood vessels and nerves reduces bleeding, swelling,
scarring, pain, and the length of the recovery period.
Dental Laser
A dental laser (Figure 30) is a type of laser designed specifically
for use in oral surgery or dentistry.
Figure
30: Dental Laser
Lasers are so precise in what they can do; there
are several unique types of lasers used in dentistry for varied purposes in
hard or soft tissue. They are designed with different wavelengths that have
different absorption capabilities that recognize and interact with different
types of human tissue. For example,longer wave lasers such as the Er: YAG
(erbium) lasers, are used for teeth and bone because they have an affinity for
water and can recognize the decayed part of the tooth because of the
differences in water content between solid and decayed tooth structure.
The laser emits light energy either in
continuous or pulsed states. Most dental lasers involve pulsed energy release.
The pulse, or burst of light, delivers the laser’s heat energy quickly (each
pulse lasts only a few ten thousandths of a second) and then allows the tissue
a time to cool before initiating another blast. This heat energy pulse works by
either boiling away water within and between the cells, or by causing micro
expansion of hard tissue, resulting in a tiny explosion that removes the
unwanted tissue. The procedure consists of a series of “pops” that work to
remove decay or cut away tissue or tooth structure.
When laser used for surgical procedures, it acts as a cutting instrument or
a vaporizer of tissue. When used for cutting, a-filling, the laser helps to
strengthen the bond between the filling and the tooth. When used in teeth
whitening procedures, the laser acts as a heat source.
Several variants of dental laser are in use, with the most common being diode
lasers, carbon dioxide lasers and yttrium
aluminum garnet laser. Different lasers use different wavelengths and these
mean they are better suited for different applications. For example, diode in
the 810–900 nm
range are well absorbed by red colored tissues such as the gingival, increasingly
being used in place of electro surgery and standard surgery for soft tissue
applications such as tissue contouring and gingivectomy.
There are many different types of dental lasers, but all can be classified
as one of two kinds of hard or soft tissue dental lasers. Laser
dentistry is a new technique that can
improve the precision of your treatment while minimizing pain and recovery time (Figure 31).
improve the precision of your treatment while minimizing pain and recovery time (Figure 31).
Figure 31: The
use of dental laser in oral surgery.
The application of lasers in
dentistry opens the door for dentists to perform a wide variety of dental
procedures; they otherwise may not be capable of performing as:
·
Benign Tumors: Dental lasers may be used
for the painless and suture-free removal of
benign tumors from the gums, palate, sides of cheeks, and lips.
benign tumors from the gums, palate, sides of cheeks, and lips.
·
Cavity Detector: Low intensity soft
tissue dental lasers may be used for the early
detection of cavities by providing a reading of the by-products produced by decay.
detection of cavities by providing a reading of the by-products produced by decay.
·
Tooth and Gum Tissues: Optical Coherence Tomography (CT scan) is a safer
way to
see inside tooth and gums in real time.
see inside tooth and gums in real time.
·
Cold Sores: Low intensity dental lasers
reduce pain associated with cold sores and
minimize healing time.
minimize healing time.
·
Crown Lengthening: Dental lasers can
reshape gum tissue and bone to expose
healthier tooth structure. Such reshaping called crown lengthening; provides a stronger
foundation for a restoration.
healthier tooth structure. Such reshaping called crown lengthening; provides a stronger
foundation for a restoration.
·
Dental Fillings: Hard tissue dental
lasers may eliminate the need for a local anesthetic
injection and the traditional turbine drill. Lasers used in dental filling procedures are
capable of killing bacteria located in a cavity and this may lead to better long term
tooth restorations.
injection and the traditional turbine drill. Lasers used in dental filling procedures are
capable of killing bacteria located in a cavity and this may lead to better long term
tooth restorations.
·
Soft Tissue Folds (Epulis): Dental lasers
may be used for the painless and suture-free
removal of soft tissue folds often caused by ill-fitting dentures.
removal of soft tissue folds often caused by ill-fitting dentures.
·
Teeth Whitening: Low intensity soft
tissue dental lasers may be used to speed up the
bleaching process associated with teeth whitening and with the use of a whitening gel.
The translucent bleaching gel is applied to the teeth and a laser light is used to activate
the crystals to absorb the energy from the light and penetrate the teeth enamel to
increase the lightening effect on the teeth. The length of time in the cosmetic dentist's
chair depends on the degree of discoloration you have (Figure 32).
bleaching process associated with teeth whitening and with the use of a whitening gel.
The translucent bleaching gel is applied to the teeth and a laser light is used to activate
the crystals to absorb the energy from the light and penetrate the teeth enamel to
increase the lightening effect on the teeth. The length of time in the cosmetic dentist's
chair depends on the degree of discoloration you have (Figure 32).
Figure
32: Before and after using laser for whitening.
·
Temporomandibular Joint Treatment: Dental
lasers may be used to quickly reduce
pain and inflammation of the temporomandibular jaw joint.
pain and inflammation of the temporomandibular jaw joint.
·
Gummy Smile: Dental lasers can reshape
gum tissue to expose healthy tooth structure
and improve the appearance of a gummy smile.
and improve the appearance of a gummy smile.
·
Tooth Sensitivity: Dental lasers may be
used to seal tubules (located on the root of the
tooth) that are responsible for hot and cold tooth sensitivity.
tooth) that are responsible for hot and cold tooth sensitivity.
References:
1)Serway, R. and Jewett, J., Physics for Scientists
and Engineers with ModernPhysics,
7 th Edition,
Thomson , Brooks/COLE 2008.
2)Davidovits, P. Physics in Biology and Medicine, 3rd
Edition, Elsevier 2007.
26)http://www.hep.vanderbilt.edu/~velkovja/VUteach/PHYS117B07/lectures/April20.
2007.ppt#281,3, How X-rays interact with the tissues in your body
2007.ppt#281,3, How X-rays interact with the tissues in your body
39)http://discountxray.com/index.php?option=com_content&task=view&id=1&Itemid=
1
41)http://www.moondragon.org/obgyn/procedures/hsg.html
1
41)http://www.moondragon.org/obgyn/procedures/hsg.html
47)http://healthguide.howstuffworks.com/dental-x-rays-dictionary.htm
111)http://www.uadchicago.com/laser-xray-sports.html
113)http://www.medicinenet.com/lasers_in_dental_care/page2.htm
114)http://geocities. com/muldoon432/Laser_Types_and_Classifications.htm.
Assignment 5
1-Explain the operation of a spectrometer and
describe two possible uses for this device.
2-How are X ray produced?
3-What are the applications of X rays in medicine?
4-Describe the 4 types of X ray images used in
dentistry.
5-Describe the process of X-ray computerized
tomography. What information does this
process provide that ordinary X-ray images do not?
process provide that ordinary X-ray images do not?
6-Calculate the frequency of a photon of
energy 4.8 x 10-19 J;
[ƒ= 7.24 X 1014 Hz]
7-Calculate the de Broglie wavelength for a
proton moving with a speed of 106m/s.
[mass of proton = 1.67 X 10-27 kg]
[mass of proton = 1.67 X 10-27 kg]
[λ = 3.97 X 10-13m]
8-Describe the operation of a laser. Include a
description of the method for obtaining the
inverted population distribution.
inverted population distribution.
9-What are the applications of laser in medicine in
general and in dentistry in particular?
References:
1)Serway, R. and Jewett, J., Physics
for Scientists and Engineers with Modern Physics,
7 th Edition, Thomson , Brooks/COLE 2008.
7 th Edition, Thomson , Brooks/COLE 2008.
2)Davidovits, P. Physics in Biology and Medicine, 3rd
Edition, Elsevier 2007.
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