Fundamentals of Radiation Physics PDF

Fundamentals of radiation Physics Dr. Waleed Salah Abdul Wahab Lecture (1) 1. The Atom Atoms are far too small to see directly, even with the most powerful optical microscopes. But atoms do interact with and under some circumstances emit light in ways...

Fundamentals of radiation Physics Dr. Waleed Salah Abdul Wahab Lecture (1) 1. The Atom Atoms are far too small to see directly, even with the most powerful optical microscopes. But atoms do interact with and under some circumstances emit light in ways that reveal their internal structures in amazingly fine detail. 1.1 Fundamental Particles Diagnostic imaging employs radiations – X, gamma, radiofrequency and sound – to which the body is partly but not completely transparent, and it exploits the special properties of a number of elements and compounds. As ionizing radiations (X-rays and gamma rays) are used most, it is best to start by discussing the structure of the atom and the production of X-rays. Table -1-: Fundamental properties of particulate radiation Relati Mas Approximate particle Symbol ve s Energy charg (am Equivalent e u) (MeV) Neutron n0 0 1.00898 940 2 Proton P, 1H+ +1 1.00759 938 3 Electron (beta e−, β− −1 0.00054 0.511 minus) 8 Positron (beta e+, β+ +1 0.00054 0.511 plus) 8 Alpha α, 4H2+ +2 4.0028 3727 1. 2 Atomic Structure An atom consists mainly of empty space. Its mass is concentrated in a central nucleus which contains a number A of nucleons, where A is called the mass number as shown in figure -1-. 1  Figure -1-: Electron shells in a sodium atom. The nucleons comprise Z protons, where Z is the atomic number of the element, and so (A-Z) neutrons. A nuclide is a species of nucleus characterized by the two numbers Z and A. The atomic number is synonymous with the name of the element. The electron limit per shell can be calculated from the expression: 2n2 where n is the shell number. In each atom, the outermost or valence shell is concerned with the chemical, thermal, optical and electrical properties of the element. X-rays involve the inner shells, and radioactivity concerns the nucleus. …………………………………………………………………………………………………………………… 1.3 Binding Energy Binding energy is defined as amount of energy required to separate a particle from a system of particles or to disperse all the particles of the system. Binding energy is especially applicable to sub atomic particles in atomic nuclei, to electrons bound to nuclei in atoms, and to atoms and ions bound together in crystals. Nuclear binding energy is the energy required to separate an atomic nucleus completely into its constituent protons and neutrons, or, equivalently, the energy that would be liberated by combining individual protons and neutrons into a single nucleus. 2  The hydrogen-2 nucleus, for example, composed of one proton and one neutron, can be separated completely by supplying 2.23 million electron volts (MeV) of energy. Conversely, when a slowly moving neutron and proton combine to form a hydrogen-2 nucleus, 2.23 MeV are liberated in the form of gamma radiation. The total mass of the bound particles is less than the sum of the masses of the separate particles by an amount equivalent (as expressed in Einstein’s mass–energy equation) to the binding energy. Electron binding energy, also called ionization potential, is the energy required to remove an electron from an atom, a molecule, or an ion. In general, the binding energy of a single proton or neutron in a nucleus is approximately a million times greater than the binding energy of a single electron in an atom. An atom is said to be ionized when one of its electrons has been completely removed. The detached electron is negative ion and the remnant atom a positive ion. Together they form an ion pair. The binding energy depends on the shell,(𝐸𝑘 > 𝐸𝐿 > 𝐸𝑀 …. ) and on the element, increasing as the atomic number increases. 1.4 Wave-Particle Duality There are two aspects for Electromagnetic radiation can be regarded as 1- A stream of ‘packets’ or quanta of energy, called photons (i.e. quantum aspects), traveling in straight lines. The photon is the smallest possible packet (quantum) of light; it has zero mass but a definite energy. 2- Electromagnetic radiation can also be regarded as sinusoid ally varying electric and magnetic fields (i.e. wave aspects), traveling with light velocity when in vacuum. They are transverse waves: the electric and magnetic field vectors point at right angles to each other and to the direction of travel of the wave. Einstein is most famous for saying "mass is related to energy". [𝑬 = 𝒎 × 𝑪𝟐 ] E: Energy in Joules m: Mass in Kg C: speed of light 𝑐 = 3𝑥108 𝑚⁄𝑠. Because of the wave-particle duality of light, the energy of a wave can be related to the wave's frequency by the equation: [𝑬 = 𝒉 × 𝒗]. E : Energy (Joules) h : plank s Constant (𝟔. 𝟔𝟐𝟔 × 𝟏𝟎−𝟑𝟒 𝒋. 𝒔) 𝒗: Frequency (𝑯𝒛 𝒐𝒓 𝒔−𝟏 ). There are three measurable properties of wave motion: (a) amplitude, 3  (b) wavelength, and (c) frequency, the number of vibrations per second. The relation between the wavelength λ (Greek lambda) and frequency of a wave 𝒗 (Greek nu) is determined by the propagation velocity (V) ; [𝝀 × 𝒗 = 𝑽] 𝝀 : Wavelength 𝒗: frequency V : velocity. This relation is true of all kinds of wave motion, including sound; although for sound the velocity is about a million times less. More usefully, since frequency is inversely proportional to wavelength, so also is photon energy: E (in keV) =1.24/λ (in nm) For example: Blue light λ=400 nm E=3 eV Typical X- and gamma rays λ=0.1 nm E=140 keV. At any point, the graph of field strength against time is a sine wave, depicted as a solid curve in Figure - 2-. The peak field strength is called the amplitude (A). The interval between successive crests of the wave is called the period (T). The frequency (𝒗) is the number of crests passing a point in a second, and 𝒗 = 𝟏⁄𝑻. The distance between successive crests of the wave is called the wavelength (λ). Wavelength (λ) or Period (T) Amplitude (A) Propagation Velocity Figure -2- : Electromagnetic wave 4  The types of radiation are listed in Table -2- in order of increasing photon energy, increasing frequency, and decreasing wavelength see figure -3-. Table 1.2: Electromagnetic spectrum Electromagnetic Wavelength Frequency Energy Radio waves 30-6 m 10-50 MHz 40-200 neV Infrared 10-0.7 μrn 30-430 THz 0. 2-1.8 eV Visible light 700-400 nm 430-750 THz l.8-3eV Ultraviolet 400-100 nm 750-3000 THz 3-12 eV X- and gamma 60-2.5 pm 5× I06– 120× 20-500 keV 106THz 1.5 Radiation Radiation is energy moving in the form of waves or streams of particles. Understanding radiation requires basic knowledge of atomic structure, energy and how radiation may damage cells in the human body. There are many kinds of radiation all around us. Electromagnetic radiation is a form of energy. Electromagnetic energy is the term given to energy traveling across empty space and used to describe all the different kinds of energies released into space by stars such as the Sun. All forms of electromagnetic radiation (which includes radio waves, light, cosmic rays, etc.) moves through empty space with the same velocity at the speed of 299,792 km per second (very close to 3×108 ms-1) and not significantly less in air, they include: Radio Waves 2. TV waves 3. Radar waves 4. Heat (infrared radiation) 5. Light 6.Ultraviolet Light (This is what causes Sunburns) 7. X-rays (emitted by X-ray tubes) 8.Short waves 9. Microwaves, like in a microwave oven 10.Gamma Rays; gamma rays (emitted by radioactive nuclei) have essentially the same properties of X-rays and differ only in their origin. 5 Figure -3- : The electromagnetic spectrum Not all radiation interacts with matter in the same way. There are two forms of radiation: non-ionizing and ionizing. …………………………………………………………………………………………………………… 6  Lecture (2) 1.6 Non-Ionizing Radiation Non-ionizing radiation is the radiation that has enough energy to move atoms in a molecule around or cause them to vibrate, but not enough to remove electrons. That mean it does not possess enough energy to produce ions. Non-ionising radiation consists of parts of the electromagnetic-spectrum (Figure -3-), which includes radio waves, microwaves, infra-red, visible and ultraviolet light, together with sound and ultrasound. 1.7 Ionizing Radiation Ionizing radiation is a special type of radiation (in the form of either particles or waves) that has enough energy to remove tightly bound electrons out of their orbits around atoms, thus creating ions. In other words, Ionizing radiation is any kind of radiation capable of removing an orbital electron from an atom with which it interacts, the atom is said to be ionized. Ionizing radiation includes the radiation that comes from both natural and man-made radioactive materials. Examples of this kind of ionizing radiation are gamma (γ) and x-rays. 1- Gamma radiation consists of photons that originate from within the nucleus. 2- X-ray radiation consists of photons that originate from outside the nucleus, and are typically lower in energy than gamma radiation. 1.8 Types of Ionizing Radiation Photon radiation can penetrate very deeply and sometimes can only be reduced in intensity by materials that are quite dense, such as lead or steel. In general , there are several types of ionizing radiation. (A) Particle Radiation Particle radiation consists of a stream of charged or neutral particles, both charged ions and subatomic elementary particles. This includes solar wind, cosmic radiation, and neutron flux in nuclear reactors. 7 -1- Alpha Particles Alpha particles (α), helium nuclei, are the least penetrating. Alpha particles are positively charged and made up of two protons and two neutrons from the atom’s nucleus. Some unstable atoms emit alpha particles and comes from the decay of the heaviest radioactive elements, such as uranium, radium and polonium. The health effect from exposure to alpha particles depends greatly on how a person is exposed. Inside the body, however, they can be very harmful. If alpha-emitters are inhaled, swallowed, or get into the body through a cut, the alpha particles can damage sensitive living tissue. -2- Beta Particles Beta particles (β) are fast-moving particles with a negative electrical charge. Beta particles (electrons) are emitted from an atom’s nucleus during radioactive decay with more penetrating, but still can be absorbed by a few millimeters of aluminum. Beta particles are more penetrating than alpha particles but are less damaging to living tissue and DNA because the ionizations they produce are more widely spaced. Some beta particles are capable of penetrating the skin and causing damage such as skin burns. -3- Neutron Radiation - Neutrons are absorbed by nuclei of atoms in a nuclear reaction. This most-often creates a secondary radiation hazard, as the absorbing nuclei transmute to the next-heavier isotope, many of which are unstable. - Neutrons are able to penetrate tissues and organs of the human body when the radiation source is outside the body. Apart from cosmic radiation, spontaneous fission is the only natural source of neutrons. A common source of neutrons is the nuclear reactor, in which the splitting of a uranium or plutonium nucleus is accompanied by the emission of neutrons. 8  Paper wood Lead Figure - 4 -: Penetration abilities of different types of ionizing radiation. (B) Types of Electromagnetic Ionizing Radiation In general, electromagnetic radiation consists of emissions of electromagnetic waves, the properties of which depend on the wavelength. Ionizing radiation has more energy than non-ionizing radiation such that it can cause chemical changes by interacting with an atom to remove tightly bound electrons from the orbit of the atom, causing the atom to become charged or ionized. The types of ionizing electromagnetic radiation are categorized according to their wavelength. -1- Gamma Rays Gamma rays (γ) are weightless packets of energy called photons. Gamma-rays have the smallest wavelengths and but have much higher energy of any other wave in the electromagnetic spectrum. Unlike alpha and beta particles, which have both energy and mass, gamma rays are pure energy. Gamma rays are often emitted along with alpha or beta particles during radioactive decay and in nuclear explosions. Gamma rays are a radiation hazard for the entire body. They can easily penetrate barriers, such as skin and clothing that can stop alpha and beta particles. Gamma rays have so much penetrating power that several inches of a dense material like lead or even a few feet of concrete may be required to stop them. 9 -2- X-Rays Because of their use in medicine, almost everybody has heard of x-rays. X-rays are similar to gamma rays in that they are photons of pure energy. X-rays and gamma rays have the same basic properties but come from different parts of the atom. X-rays are emitted from processes outside the nucleus, but gamma rays originate inside the nucleus. They also are generally lower in energy and, therefore, less penetrating than gamma rays but have higher energy than ultraviolet waves. -3- Ultraviolet The dividing line between ionizing and non-ionizing radiation in the electromagnetic spectrum falls in the ultraviolet portion of the spectrum and while most UV is classified as non-ionizing radiation, the shorter wavelengths from about 150 nm (UV-C or ‘Far’ UV) are ionizing. UV-C from the sun is nearly all absorbed by the ozone layer. 1.9 Inverse Square Law for Radiation Any point source which spreads its influence equally in all directions without a limit to its range will obey the inverse square law. This comes from strictly geometrical considerations. The intensity of the influence at any given radius is the source strength divided by the area of the sphere. Being strictly geometric in its origin, the inverse square law applies to diverse phenomena. Point sources of gravitational force, electric field, light, sound or radiation obey the inverse square law. When light is emitted from a source such as the sun or a light bulb, the intensity decreases rapidly with the distance from the source. X-rays exhibit precisely the same property. The intensity (I) of the radiation is inversely proportional to the square of the distance ( r)from a point source (see figure 1.6) 10 Figure -5-: The inverse square law applying to a point source. As intensity is the power per unit area, Intensity = Power /Area. So, the luminous intensity on a spherical surface a distance from a source radiating a total power P is:\ The luminous intensity is proportional to the inverse of distance: 11  Lecture (3) 3. Basic Requirements for Production of X-Rays X-rays are produced when some form of matter is struck by a rapidly moving electron. To accomplish this, three basic requirements must be met. 3.1 Supply of Electrons - There must be a supply of the electrons. Fortunately, the electrons can be supplied by simply raising the temperature of a suitable material. - As the temperature rises, the electrons become more and more agitated until finally they escape or “boil off” the material, surrounding it in the form of an electron cloud. - This is known as thermionic emission. In an X-ray tube the heated material is known as the filament, which is similar to the filament in a light bulb. Glass Envelope Cloud of electrons Anode Figure – 6 - : Electrons cloud surrounds the filament 3.2 Movement of the Electrons - Movement of the emitted electrons is the second step in producing X-rays. - Electrons are negative charges, thus repel each other. However, a stronger attracting force is needed to accelerate the electrons to a higher velocity. - Therefore, a strong opposite (positive) charge is used to move the electrons from one point to another. - It is important that this movement is conducted in a good vacuum. - Otherwise the electrons collide with air molecules and lose energy through ionization and scattering. 12 3.3 Components and Properties of an X-Ray Tube An x-ray tube consists of two electrodes into an evacuated glass envelope. 1- A negative electrode (cathode) which incorporates a fine tungsten coil or filament. 2- A positive electrode (anode) which incorporates a smooth flat metal target, usually of tungsten. 3- Traditionally the tube has been a glass envelope with a reduced thickness at the window, the point where the x-rays exit, to reduce x-ray absorption. 4- The high vacuum reduces the problem of the electrons colliding with, and being absorbed by, molecules of air and provides electrical insulation between the cathode and anode. 5- In some designs a beryllium window is incorporated to further reduce absorption of the x-ray beam, particularly the lower energies. In many applications glass envelopes are being replaced by metal-ceramic envelopes. 3.3.1 Cathode - Actually, it is a filament or coil of tungsten wire that emits electrons when heated to a high temperature. - But because the filament gives off electrons in all directions, some means must be used to focus them on a target. - A reflector or focusing cup within the cathode. 3.3.2 Anode In radiographic tubes the target material is generally made of tungsten. The choice of tungsten as a target for industrial radiography is based on four material characteristics: 1- High atomic number (74). The higher the atomic number of a material the more efficient is the conversion from electrical energy into X-ray energy. 2- High melting point (690.F*). Most of the energy in the electrons bombarding the target is dissipated in the form of heat. The extremely high melting point of tungsten permits operation of the target at very high temperatures. 3- High thermal conductivity. Permits rapid removal of heat from the target, allowing maximum energy input for a given area size. 13 3.3.3 Processes Occurring in the Anode of an X-Ray Tube - Each electron arrives at the surface of the target with a kinetic energy (in kilo electron volts) equivalent to the kV between the anode and cathode at that instant. - The electrons penetrate several micrometers into the target and lose their energy by a combination of processes: 1- As a large number of very small energy losses, by interaction with the outer electrons of the atoms; constituting unwanted heat and causing a rise of temperature. 2- As large energy losses producing X-rays, by interaction with either the inner shells of the atoms or the field of the nucleus. ………………………………………………………………………………………………………………. Lecture (4) 4.1 Production of X-Rays Over a century ago in 1895, Wilhelm Roentgen discovered the first example of ionizing radiation, X-rays. The key to Roentgens discovery was a device called a Crooke’s tube, which was a glass envelope under high vacuum, with a wire element at one end forming the cathode, and a heavy copper target at the other end forming the anode. 1- When a high voltage was applied to the electrodes, electrons formed at the cathode would be pulled towards the anode and strike the copper with very high energy. 2- When electrons hit this material, some of the electrons will approach the nucleus of the metal atoms where they are deflected , this deflection causes the energy of the electron to decrease, and this decrease in energy then results in forming an x-ray. 3- Only a very small amount of the energy in the electron beam is converted into X radiation ranges from about 0.05% at 30 kV to approximately 10% in the MeV energy range. 4.2 X-Ray Tube X-rays are produced in X-ray tubes such as the one shown in Figure - 7 - 14  High-voltage cables 80 – 140 kV Anode Rotor Vacuum Oil Bearings Cathode Lead shielding Stator windings x-ray beam Figure- 7 -: Fundamentals of X-Ray Tube 1- The high-voltage source is typically of the order of 103 to 106 volts. 2- The filament (cathode) is heated to incandescence and emits electrons by the process of thermionic emission. At such high temperatures (2200 C0). 3- The kinetic energy of the electrons is converted into X-rays (1%) and into heat (99%). Inside the tube, the electrons have a small probability of collision with air molecules since the gas pressure inside the gas is of the order of 0.01 Pa or 10-7 atm. 4.3 Cooling Requirements Most of the electron beam energy is converted into heat. This generation of heat in the X-ray tube target material is one of the limiting factors in the capabilities of the X-ray tube and it is necessary to remove this heat from the target as rapidly as possible. Various techniques are used for removal of heat:- 1- In some instances, the target is comparatively thin, and suitable oil is circulated on the back surface to remove heat. 2- Others use water-antifreeze mixture to conduct heat away from the target. 3- Most X-ray targets are mounted in copper, using the copper as a heat sink. 4.5 Focal Spot - The focal spot is the area of the target that is bombarded by the electrons from the cathode. 15  - The shape and size of the focusing cup of the cathode and the length and diameter of the filament all determine the size and shape of the focal spot. - The size of the focal spot has a very important effect upon the quality of the x-ray image. - Generally, the smaller the focal spot the better the detail of the image. - But as the electron stream is focused to a smaller area, the power of the tube must be reduced to prevent overheating at the tube anode. Generators can be classified as a conventional, minifocus, and microfocus system. a- Conventional units have focal-spots larger than about 0.5 mm. b- minifocus units have focal-spots ranging from 50 microns to 500 microns (0.05 mm to 0.5 mm). c- microfocus systems have focal-spots smaller than 50 microns. 4.6 The Origin of Characteristic X-Rays When a sample is bombarded by an electron beam, some electrons are knocked out of their shells in a process called inner-shell ionization. About 0.1% of the electrons produce K-shell vacancies; most produce heat. Outer-shell electrons fall in to fill a vacancy in a process of self-neutralization. The energy required to produce inner-shell ionization is termed the excitation potential or critical ionization potential. - The kinetic energy 𝑘𝑜 of the incoming electron corresponding to the potential energy of the electric potential between the cathode and the target. 𝑘𝑜 = 𝑒𝑉𝐶𝑎𝑡ℎ𝑜𝑑 →𝑇𝑎𝑟𝑔𝑒𝑡 - The quantization of this radiation the (x-ray) photon has energy ℎ𝑐 ℎ𝑐 𝐸 = ℎ𝑣𝑚𝑎𝑥 = = 𝑒𝑉𝐶𝑎𝑡ℎ𝑜𝑑 →𝑇𝑎𝑟𝑔𝑒𝑡 , hence 𝜆𝑚𝑖𝑛 =. 𝜆𝑚𝑖𝑛 𝑒𝑉𝐶𝑎𝑡ℎ𝑜𝑑 →𝑇𝑎𝑟𝑔𝑒𝑡 The X-ray production can be seeing as a continuous spectrum of radiation superimposed by two peaks of well defined wavelength. These two spectrums are called the(A) continuous X-ray Spectrum and the (B) Characteristic X-ray Spectrum. …………………………………………………………………………………………………………………………………………………………… 16  Lecture (5) 5.1 Continuous X-Ray Spectrum As in figure -8- , if a projectile electron penetrates the K-shell and approaches close to the nucleus. A projectile electron approaches fast and leaves less quickly, losing some or all of its kinetic energy when passing close to the nucleus. The lost energy is carried away as a single photon of X-rays or bremsstrahlung (literally, 'braking radiation')..The 1, 2, and 3 depict incident electrons interacting in the vicinity of the target nucleus, resulting in bremsstrahlung production caused by the deceleration and change of momentum, with the emission of a continuous energy spectrum of x-ray photons.. The continuous spectrum corresponds to the entire radiation spectrum ignoring the two well defined peaks.. If 𝑘𝑜 is the initial kinetic energy of the incident electron. ΔK is the change in energy of the electron, the X-Ray photon has an energy given by |∆𝑘| = ℎ𝑣..The most energetic photon (greatest frequency) corresponds to the case in which the total incident kinetic energy of the electron is transfered into the X-Ray photon:- 𝑘0 𝑐 |∆𝑘 | = |−𝑘0 | = ℎ𝑣𝑚𝑎𝑥 → 𝑣𝑚𝑎𝑥 = but 𝑐 = 𝑣𝑚𝑎𝑥 𝜆𝑚𝑖𝑛 → 𝜆𝑚𝑖𝑛 = hence ℎ 𝑣𝑚𝑎𝑥 ℎ𝑐 𝜆𝑚𝑖𝑛 = , 𝜆𝑚𝑖𝑛 is the cutoff wavelength. 𝑘0 The cutoff wavelength is totally independent of the target material. However, the other characteristics of the spectrum depend on the target material. 17  Scattered Electrons Incident Electron ++ 3 2 1 2 3 Close interaction Moderate energy Impact with nucleus Maximum energy 1 Distant interaction Low energy Figure -8-: Production of bremsstrahlung The bremsstrahlung forms a continuous spectrum. The maximum photon energy (kiloelectronvolts) is equivalent to the. 18 5.2 Characteristic X-Ray Spectrum Projectile electrons interact with an inner-shell electron of the target rather than the outer shell electron. As depicted in figure 2.4, when a projectile electron from the filament collides with an electron in the K-shell of an atom, an electron will be ejected from the atom, provided that the energy of the bombarding electron is greater than the binding energy of the shell.. The hole so created in the K-shell is most likely to be filled by an electron falling in from the L- shell with the emission of a single X-ray photon of energy equal to the difference in the binding energies of the two shells, Ek − EL. The photon is referred to as k α radiation.. Alternatively, but less likely, the hole may be filled by an electron falling in from the M-shell with the emission of a single X-ray photon of energy , referred to as k𝛽 radiation. Electron + + ++ ejected ++ Incident Electron K-shell photon L-shell photon Characteristi M-shell N-shell photon N (n = 0 M (n = L (n = 2) Kα -10 Kβ -15 19 K (n = -20  Figure -9- : Energy levels diagram for Molybdenum and production ofcharacteristic Radiation. In the case of the usual target material, tungsten (Z=74), Ek = 70k e V EL = 12k e V EM = 2k e V Thus , the k α radiation photon energy; Ek − EL = 58 K𝑒V the k𝛽 radiation photon energy; Ek − EM = 68 K𝑒V There is also L-radiation, produced when a hole created in the L-shell is filled by an electron falling in from farther out. Even in the case of tungsten these photons have only 10KeV of energy, insufficient to leave the X-ray tube assembly, and so they play no part in radiology. Kα 3 Characteristic 2 Continuous x-rays Spectrum Kβ x-rays from a "Bremsstrahlung" 1 molybdenum target at 35 kV 30 40 50 60 70 80 90 Wavelength " λ" (10 -12 m) λmin Figure -10 - : Wavelength distribution of X-Ray production in a molybdenum target. The two peaks of Figure 2.5, labeled and , are part of what is called the Characteristic X- Ray Spectrum. The emission of characteristic X-Rays involves the following processes:- 20 1- The energetic electrons collide with an atom of the target knocking out one of the most internal electrons of the atom (n small) creating a hole in the atomic structure of the atom. 2-The hole is filled when an electron from a greater energy level from a middle shell of the atom (n mid value) jumps down to the lower energy shell emitting a high energy photon (characteristic X-Ray). The electron from the middle shell is subsequently replaced by and electron from an upper energy shell which in the transition emits a low energy photon. ………………………………………………………………………………………………… Lecture (6) 6.1 Controlling the X-Ray Spectrum (Voltage and Amperage) 1- Increasing the kV (a) Shifts the spectrum upward and to the right, (b) Increases the maximum energies (c) Increase the total number of X-ray photons. As shown in Fig -10- [Below a certain kV (70 kV for a tungsten target) the characteristic K- radiation is not produced]. 2- Increasing the mA does not affect the shape of the spectrum but increases the output of both bremsstrahlung and characteristic radiation in proportion. –The intensity of X-rays emitted is proportional to kV2 × mA. –The efficiency of X-ray production is the ratio Kα Continuous Spectrum "Bremsstrahlung" Characteristic Lines 120KV Relative numbers Kβ of photons 80KV 40KV 40 80 120 Photon energy (kVe) 21  Figure -11-: Effect of tube kilovoltage on X-ray spectra. The filament heating voltage (about 10 V) and current (about 10 A).. The accelerating voltage (typically 30-150 kV) between the anode and cathode This drives the current of electrons flowing between the anode and cathode.. KV𝑃 is a Kilovolt Peak and it’s the component that controls the quality of the x-ray beam produced. It is also controls the contrast or gray scale in the produced x-ray film.. The change in x-ray quantity is proportional to the square of the ratio of the ; if were doubled, the x-ray intensity would increase by a factor of four. Where and are the X-ray intensities at and , respectively. 6.2 Milliamperage Second (mA) :- is the product of [current in (mA) ×Time sec]. x-ray quantity is directly proportional to the mAs. When the mAs is doubled, the number of electrons striking the tube target is doubled, and therefore the number of x-rays emitted is doubled. 6.3 Interaction of X- Ray As a beam of X- or gamma rays passes through matter, three possible fates await each photon,as listed below: a- Penetrate (Transmitted): photon can pass through the section of matter without interacting. b-Absorbed: photon can interact with the matter and transferring to the matter all of their energy (the photon completely absorbed by depositing its energy) or some of it (partial absorption). c-Produce Scattered Radiation: photon can interact and diverted in a new direction, as scattered or defected from its original direction and deposited part of its energy. 22  Incident Transmitted X-ray beam Absorbed X-ray Scattered X-ray Figure -12-: Interactions of photons when an entering the human body; will either penetrate, be absorbed, or produce scattered radiation. 6.4 Compton Scattering The Compton scattering is the process whereby an X- or gamma ray interacts with a free or weakly bound electron and transfers part of its energy to the electron. Notice that :- - Electron leaves the atom and may act like a beta-particle - The x-ray photon leaves the site of the interaction in a direction different from that of the original photon. - The photon is be diverted in a new direction with reduced energy. As shown in figure-13-. Because of the change in photon direction, this type of interaction is classified as a scattering process sometimes called Compton Scattering. 23  - Compton electron Incident X-Ray Angle of deflection photon (θ) ++ Scattered + + ++ K X-Ray L M Figure -13-: A schematic representation of the Compton Scattering. This interaction involves the outer, least tightly bound electrons in the scattering atom. - The electron becomes a free electron with kinetic energy equal to the difference of the energy lost by the X-ray and the electron binding energy. - Because the electron binding energy is very small compared to the X-ray energy, the kinetic energy of the electron is very nearly equal to the energy lost by the X-ray: 𝐸𝑒 = 𝐸𝑥−𝑟𝑎𝑦 − 𝐸 ´ Where 𝐸𝑥−𝑟𝑎𝑦 = energy of incifent X − ray 𝐸 ´ = energy of scattered x-ray It was observed that when X-rays of a known wavelength interact with atoms, the X-rays are scattered through an angle 𝜃 and emerge at a different wavelength related to. 𝐸 ´ = 𝑚0 𝑐 2 /(1 − 𝑐𝑜𝑠𝜃 + 𝑚0 𝑐 2 /𝐸 ). Where 𝑚0 𝑐 2 = rest energy of electron = 511 K e V. 24  𝜃 = the angle between incident and scattered photon of x -ray. Since photons lose energy in a Compton interaction ,the wavelength always increases, and the relationship is be :- h [𝜆´ − 𝜆 = (1 − cosθ)] m0 c The quantity is known as the Compton wavelength of the electron; it is equal to2.43×10−12 m or 0.024 nm. Thus ∆𝝀 = 𝟎. 𝟎𝟐𝟒(𝟏 − 𝐜𝐨𝐬𝛉) Where is the initial wavelength, is the wavelength after scattering, is the Planck constant, is the electron rest mass, is the speed of light, is the scattering angle. The wavelength shift 𝜆´ − 𝜆 is at least zero (𝜃 = 0𝑜 ) and at most twice the Compton wavelength of the electron for (𝜃 = 180𝑜 ). 25  Recoil Electron Recoil electron Incident Incident Incident photon Recoil photon photon θ ≈ 0o Electron o θ= 90o θ ≈ 180 Forward- Back-scattered Side-scattered scattered photon photon photon Back-scattered photon Side-scattered photon Forward-scattered photon (θ = 180o) (θ = 90o) (θ = 0o) Figure -14- illustrates three different angles of Compton scattering. Example (1) :-Photon X- ray of wavelength (0.712 A0) are scattered in Compton collision from a target. Find the wavelength of x-ray photons which scattered at (900). h Solution :- [𝜆´ − 𝜆 = (1 − cosθ)] m0 c 𝜆´ = 𝜆 + 0.024 (1 − cosθ) 𝜆´ = 0.712 + 0.024 = 0.736 A0. ……………………………………………………………………………………………………………………….. 26