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Hungary-Croatia IPA Cross –border Co-operation Programme 2007-2013 Harmonization of Biotechnology BSc out-put with the Medical Biotechnology MSc in-put requirements at Osijek and Pecs Universities HUHR/1001/2.2.1/0010- BIOTECHEDU PHYSICS – OSIJEK INTRODUCTION TO SPECTROSCOPY Dario Faj, Hrvoje Brkić 1. Structure of atoms - hystory review 2. Structure and stability of atoms and moleculas 3. Radioactivity. EM vawes 4. Interaction EM vawes and matter 5. Introduction to spectroscopy 1. Structure of atoms - hystory review 1.1. Atomic structure The atom consists of a central nucleus around which electrons rotate in fixed orbits. The nucleus contains two kinds of particles, protons and neutrons, which together are called nucleons. Both particles have nearly the same mass but the proton carries a positive electric charge. Hence, the whole nucleus is positively charged. This charge is balanced by the negative charges of the orbital electrons, so from outside, the atom appears electrically neutral. Particle Symbol Mass (kg) Energy Charge (MeV) ---------------------------------------------------------Proton p 1.672*10-27 938.2 + Neutron n 1.675*10 -27 939.2 0 Electron e 0.911*10 -30 0.511 - The different natural elements ranging from hydrogen to uranium are built of increasing numbers of nucleons. The hydrogen nucleus has one proton and the uranium nucleus has 92 protons and 146 neutrons. It is the number of protons and hence the number of electrons that define the element and its chemical characteristics. The number of protons is called the atomic number (Z) and the total number of nucleons is called the mass number of the nucleus. All elements have different isotopes, which will have the same number of protons but different numbers of neutrons and thus different mass numbers. For instance, for the element carbon there exist eight different isotopes with mass numbers between 9 and 16. The atomic number for carbon is 6 so the number of neutrons ranges from 3 to 10. It should be stressed that an isotope of an element is not necessarily radioactive. Among the isotopes of carbon both carbon-12 and carbon-13 are stable nuclides and the others are unstable and hence are radioactive. Figure. Identification of isotopes Figure. Periodic table of elements. 1.2 Hystory review In fifth-century BC Greeks, Leucippus of Miletus and Democritus of Abdera gave the first atom theory we have any record of. Their theories were philosophical in origin. The basic idea was that if you could look at matter on smaller and smaller scales (which they of course couldn't) ultimately you would see individual atoms - objects that could not be divided further (that was the definition of atom). They believed that atoms were in constant motion, and always had been, at least in gases and liquids. Sometimes, however, as a result of their closelocking shapes, they joined in close-packed unions, forming materials such as rock or iron. Basically, Democritus and his followers thought all natural phenomena could in principle be understood in terms of interacting, usually moving, atoms. After, a little progress in atomic theory was made over the next two thousand years, mostly because Aristotle discredited it. The idea rose up again in the Renaissance period. Galileo believed in atoms, and later Newton gave a much more modern perspective on atoms and interatomic forces in the seventeenth century (Opticks, Book 3, Part 1): Quest. 31. Have not the small Particles of Bodies certain Powers, Virtues, or Forces, by which they act at a distance, not only upon the Rays of Light for reflecting, refracting and inflecting them, but also upon one another for producing a great Part of the Phenomena of Nature? For it's well known, that Bodies act upon one another by the Attractions of Gravity, Magnetism, and Electricity; and these Instances show the Tenor and Course of Nature, and make it not improbable that there be more attractive Powers than these… . For we must learn from the Phenomena of Nature what Bodies attract one another, and what are the Laws and Properties of the Attraction, before we enquire the Cause by which the attraction is perform'd. The Attractions of Gravity, Magnetism and Electricity, reach to very sensible distances, and so have been observed by vulgar eyes, and there may be others which reach to so small distances as hitherto escape Observation, and perhaps electrical Attraction may reach to such small distances, even without being excited by friction. In fact, although the forces binding atoms together in molecules cannot be properly understood without quantum mechanics, many of these forces are "short range" electrical forces - forces between bodies having overall electrical neutrality, but distorted charge distributions. These forces could definitely be categorized as "electrical Attraction reaching to small distances". Notice that Newton also leaves the door open for other short range forces, which were finally discovered in the 1930's! The first major step towards modern quantitative chemistry was taken by Lavoisier at the end of the eighteenth century. He discovered Oxygen and set the definition of the element. Before, there were no generally agreed on definitions of elements, principles or atoms, although a century earlier Boyle had suggested that element be reserved for substances that could not be further separated chemically. In his Elements of Chemistry (1789) Lavoisier writes: …if, by the term elements we mean to express those simple and indivisible atoms of which matter is composed, it is extremely probable that we know nothing about them; but if we apply the term elements, or principles of bodies, to express our idea of the last point which analysis is capable of reaching, we must admit as elements all the substances into which we are capable, by any means, to reduce bodies by decomposition. Not that we are entitled to affirm that these substances we consider as simple may not be compounded of two, or even of a greater number of principles; but since these principles cannot be separated, or rather since we have not hitherto discovered the means of separating them, they act with regard to us as simple substances, and we ought never to suppose them compounded until experiment and observation have proved them to be so. In sum, Lavoisier began the modern study of chemistry: he insisted on precise terminology and on precise measurement, and suggested as part of the agenda the classification of substances into elements and compounds. Once this program was truly underway, the atomic interpretation soon appeared. John Dalton (1766-1844) assumed that all atoms of an element were identical, and atoms of one element could not be changed into atoms of another element "by any power we can control". In 1811, the Italian physicist Amedeo Avogadro suggested that Dalton's picture of atoms and molecules could be reconciled with Gay-Lussac's results on volumes if one assumed that equal volumes of all gases, elements or compounds, contain equal numbers of molecules. Of course, he had no idea what the number might be, but the hypothesis made many predictions without knowing the number. In the year 1800, 31 elements were known. By 1860, that number had almost doubled, to 60, and the relative atomic weights, as well as many of the chemical properties, were known. In particular, in analyzing molecule formation, a valuable emerging concept was that of valence - the idea that each atom had a particular number of little hooks on it to attach itself to similar hooks on other atoms. A few years later, in 1872, the Russian physicist Mendeleev drew up his periodic Table of the Elements. First model of the atom was given by the J.J. Thomson in 1897. He experimentally proved existence of electron and afterwords E. Rutherford discovered atomic nuclei and gave solar system model of atom. In the late 19th century, it was found that the radiation from hydrogen, as well as other atoms, was emitted at specific quantized frequencies. It was the effort to explain this radiation that led to the first successful quantum theory of atomic structure, developed by Niels Bohr in 1913. He developed his theory of the hydrogenic (oneelectron) atom from four postulates: 1. An electron in an atom moves in a circular orbit about the nucleus under the influence of the Coulomb attraction between the electron and the nucleus, obeying the laws of classical mechanics. 2. Instead of the infinity of orbits which would be possible in classical mechanics, it is only possible for an electron to move in an orbit for which its orbital angular momentum L is and integral multiple of . 3. Despite the fact that it is constantly accelerating, an electron moving in such an allowed orbit does not radiate electromagnetic energy. Thus, its total energy E remains constant. 4. Electromagnetic radiation is emitted if an electron, initially moving in an orbit of total energy , discontinuously changes its motion so that it moves in an orbit of total energy . The frequency of the emitted radiation is equal to the quantity divided by h. Later, A.Sommerfeld introduced aditional quantum numbers (ℓ, m) to explain some experimental results. Figure. Early models of atom. The theory of atomic structure moved ahead with discovery of wave nature of electrons (L. de Broglie). Loui de Broglie showed that atomic particles have wave characteristics (diffraction) also and set the equation: h mv Further E. Schrödinger gave the equation of vawe function of electron ψ(r): 2 8 2 m ke2 E h r 0 • Solutions are energetic stations of electrons described with quantum numbers n, ℓ, m: • n - main: discrete energy of electrons in electric field of nuclei; energetic shells: K, L, M, N..; number of electrons in a shell is 2n2 • l - orbital: orbitals: s,p,d..; can be 0, 1, ... n-1 • m – magnetic: can be from – l to l • ms – spin can be +1/2 and -1/2 Figure. Model of atom today. 2. Structure and stability of atoms and moleculas 2.1. Structure and stability of atoms The electrons are bound to the nucleus by electrostatic forces. The binding energy of an electron is defined as the work necessary to release the electron from its orbit. The binding energy depends upon both the element and the position of the orbit. The different orbits or shells are named K, L, M, N, etc. where the K-shell is the shell closest to the nucleus. The electrostatic force is dependent on the distance between the charges which means that the binding energy will decrease from the inner shell outwards. The electrostatic force will also be dependent on the size of the charge, which means that the binding energy of electrons in a specified shell is higher in an element with a high atomic number than in an element with a low atomic number. For instance, the binding energy for an electron in the K-shell is 1.56 keV in aluminum (Z=13) and 88 keV in lead (Z=82). In an energetic stable atom the shells are filled by electrons from the inner shell and outwards. This structure can be changed by adding energy to the atom. The result will be either ionization or excitation. Ionization means that the energy added is high enough to release an orbital electron from the atom. Excitation means that an electron will be lifted to a shell further out. This results in a vacancy in the shell originally occupied by the electron, a vacancy which the atom tries to fill with an electron from an outer shell. When the vacancy is filled the released energy is emitted as electromagnetic radiation (characteristic X-rays) or is transferred to another electron which can then leave the atom (Auger electron). The electromagnetic radiation is called characteristic X-ray because its energy is characteristic for the element. This means that it is possible to identify an element by its characteristic X-rays. It is known that the nucleons, just like the electrons, can also occupy different energy levels and that the nucleus can be present in a ground state or in an excited state. Just as in the case of the atom, an excited state can be reached by adding energy to the nucleus. At deexcitation the nucleus will emit the excess of energy as electromagnetic radiation. In this case the electromagnetic radiation is called a gamma ray. The energy can also be transferred to one of the electrons in the inner shells of the atom, which then have high enough energy to leave the atom. This process is called internal conversion (IC). The energy of the gamma ray will be the difference in energies between the different energy levels in the nucleus. In a sense we can say that the energy of the gamma ray is characteristic for the nucleus and that the nucleus can be identified by its gamma rays in the same way as the characteristic X- ray identifies the atom. 2. 2. Quantum Numbers and electron configuration The Bohr model was a one-dimensional model that used one quantum number to describe the distribution of electrons in the atom. The only information that was important was the size of the orbit, which was described by the n quantum number. Schrödinger's model allowed the electron to occupy three-dimensional space. It therefore required three coordinates, or three quantum numbers, to describe the orbitals in which electrons can be found. The three coordinates that come from Schrödinger's wave equations are the principal (n), angular (l), and magnetic (m) quantum numbers. These quantum numbers describe the size, shape, and orientation in space of the orbitals on an atom. The principal quantum number (n) describes the size of the orbital. Orbitals for which n = 2 are larger than those for which n = 1, for example. Because they have opposite electrical charges, electrons are attracted to the nucleus of the atom. Energy must therefore be absorbed to excite an electron from an orbital in which the electron is close to the nucleus (n = 1) into an orbital in which it is further from the nucleus (n = 2). The principal quantum number therefore indirectly describes the energy of an orbital. The angular quantum number (l) describes the shape of the orbital. Orbitals have shapes that are best described as spherical (l = 0), polar (l = 1), or cloverleaf (l = 2). They can even take on more complex shapes as the value of the angular quantum number becomes larger. There is only one way in which a sphere (l = 0) can be oriented in space. Orbitals that have polar (l = 1) or cloverleaf (l = 2) shapes, however, can point in different directions. We therefore need a third quantum number, known as the magnetic quantum number (m), to describe the orientation in space of a particular orbital. (It is called the magnetic quantum number because the effect of different orientations of orbitals was first observed in the presence of a magnetic field.) Quantum Numbers and Electron Configurations give the distribution of electrons of an atom or molecule (or otherphysical structure) in atomic or molecular orbitals. An energy is associated with each electron configuration. Upon certain conditions, electrons are able to move from one orbital to another by emission or absorption of a quantum of energy, in the form of a electromagnetic wave (photon). Figure. Example of electron configuration. Rules Governing the Allowed Combinations of Quantum Numbers • The three quantum numbers (n, l, and m) that describe an orbital are integers: 0, 1, 2, 3, and so on. • The principal quantum number (n) cannot be zero. The allowed values of n are therefore 1, 2, 3, 4, and so on. • The angular quantum number (l) can be any integer between 0 and n - 1. If n = 3, for example, l can be either 0, 1, or 2. • The magnetic quantum number (m) can be any integer between -l and +l. If l = 2, m can be either -2, -1, 0, +1, or +2. Orbitals that have the same value of the principal quantum number form a shell. Orbitals within a shell are divided into subshells that have the same value of the angular quantum number. Chemists describe the shell and subshell in which an orbital belongs with a two-character code such as 2p or 4f. The first character indicates the shell (n = 2 or n = 4). The second character identifies the subshell. By convention, the following lowercase letters are used to indicate different subshells. s:l = 0; p:l = 1; d:l = 2; f:l = 3 The third rule limiting allowed combinations of the n, l, and m quantum numbers has an important consequence. It forces the number of subshells in a shell to be equal to the principal quantum number for the shell. The n = 3 shell, for example, contains three subshells: the 3s, 3p, and 3d orbitals. Before we can use these orbitals we need to know the number of electrons that can occupy an orbital and how they can be distinguished from one another. Experimental evidence suggests that an orbital can hold no more than two electrons. To distinguish between the two electrons in an orbital, we need a fourth quantum number. This is called the spin quantum number (s) because electrons behave as if they were spinning in either a clockwise or counterclockwise fashion. One of the electrons in an orbital is arbitrarily assigned an s quantum number of +1/2, the other is assigned an s quantum number of -1/2. Thus, it takes three quantum numbers to define an orbital but four quantum numbers to identify one of the electrons that can occupy the orbital. 2. 3. Structure and stability of molecules Molecules are stabile assotiations of atoms with structure tending to minimal potential energy. Molecular bonds are bonds of atoms within moleculas: • Energy of moleculas is always smaller than total energy of free atoms (principle of minimum energy). Energy change can be beetwen molecular orbitals, vibration stations and rotation stations. Vibrations of twotwo-atomatom-moleculas Vibration quantum number atom 1 E E 1 E E 1 h 1 2 2 2 k 2 M h atom 2 h 1 1 h 1 2 2 2 2 ~ 0.1 eV Energy difference between neighbour states is constant 3. Radioactivity. EM vawes. 3. 1. Radioactivity Not all combinations of protons and neutrons in the nucleus are stable. For light elements (mass number <20) stability is achieved if the number of protons and the number of neutrons are about the same. Because of the positive charge of the protons there is a repelling electrostatic force between them which is balanced by a different attractive short ranging nuclear force between the nucleons. In a heavy element the electrostatic force will be considerable due to the large number of protons. Thus, to reach stability, the number of neutrons must be relatively larger because the neutron increases the nuclear force without increasing the electrostatic force. If the relation between protons and neutrons is altered from the stable condition the equilibrium between the forces will be disturbed and the nucleus becomes energetically unstable. Such an unstable nucleus is called a radioactive nucleus or a radionuclide. In the transformation, which we generally call radioactive decay, the nucleus loses its excess of energy by fission or by emission of charged particles (alpha particles and beta particles). The result of the radioactive decay is a new nucleus with a different atomic number and in some cases a different mass number. The new nucleus will in many cases be excited and at deexcitation the energy emitted as one or several gamma rays. Fission is the process in which the unstable nucleus divides into two fragments of about equal size. This process is only possible in heavy nuclides. Radioactive decay by emission of an alpha () particle can also occur only in heavy elements because the alpha particle itself is a comparatively heavy particle consisting of two protons and two neutrons (a helium nucleus). In alpha decay the daughter nuclide will have an atomic number that is two units less and a mass number that is four units less. Examples of radionuclides with alpha decay are radium-226 and radon-222. The alpha particle energy from different radionuclides is usually in the range of 4-8 MeV. The medical use of alphaemitting radionuclides is very limited. Beta () decay can be one of three different kinds, -, + and electron capture (EC). The - particle is an electron which is released in the transformation of a neutron to a proton. In - decay the daughter nuclide will have an atomic number one unit greater than the mother nuclide but the same mass number. The + particle is an `electron' with a positive charge. It is called a positron and is released in the transformation of a proton to a neutron. In + decay the daughter nuclide will have an atomic number one unit less than the mother nuclide but the same mass number. Electron capture is an alternative to + decay. In the process one of the electrons in the inner shell of the atom is captured by the nucleus. No particle is emitted in the decay but due to the vacancy in the inner shell of the atom, a characteristic X-ray will be emitted. The transition energy released in beta-decay is divided between the beta particle and a particle called a neutrino. This means that the kinetic energy of the beta particles from a certain radionuclide will show a spectral distribution where the energies range from zero to a maximum which equals the transition energy. The mean energy of the particles is roughly 1/3 of the maximum energy. When considering a radioactive nucleus it can never be known when it is going to decay. It can only be stated that there is a certain probability that it decays within a certain period of time. For instance, a nucleus of iodine-131 has a probability of decaying of 0.086 (8.6 percent) per day. This is called the decay constant of the radionuclide which is different for different radionuclides. The number of decaying nuclei per unit time in a radioactive sample is called the activity of the radionuclide. The unit of activity is 1 Becquerel (Bq) which is the number of decaying nuclei per second. One Becquerel is a very small activity. The natural body content of potassium-40 is about 4000 Bq (4 kBq). In some nuclear medicine examinations the patients can receive 5001000 million Becquerel (500 MBq - 1 GBq) of technetium-99m. The activity of a sample containing a certain radionuclide will continuously decrease with a speed determined by the decay constant. Mathematically it is a monoexponential decrease. As an alternative to the decay constant the half-life of the radionuclide can be defined as the time needed to reduce the activity by 50 percent. 3. 2. Electromagnetic vawes During radioactive decay the unstable atom can release energy as a particle (α,β radiation) or in a form of electromagnetic (EM) vawes (γ radiation). EM spectra Energy of EM vawe E = h hc/ 4. Interaction EM vawes and matter The different types of radiation emitted in the radioactive decay are examples of ionizing radiation, which means that the kinetic energy of the single particle or photon is high enough to cause ionization, which is the process of removing an electron from the atom. The theoretical energy limit is of the order of 100 eV. If the energy transferred is less it will not cause ionization. Other types of ionizing radiation are charged particles from accelerators and cosmic radiation. Also X-rays are ionizing. Charged particles such as electrons, protons, alpha particles, etc. are called directly ionizing radiation while neutrons and photons are called indirectly ionizing radiation. This means that the ionization will take place in two steps, the first step being the release of a charged particle such as an electron which is then directly ionizing. When ionizing radiation passes through matter, it loses energy and will finally be absorbed completely. The energy lost by the radiation is absorbed by the material, e.g., the body. The processes involved are different for directly and indirectly ionizing radiation and also different for heavy and light charged particles as well as for photons. 4.1. Charged particles When a charged particle, such as an alpha particle, proton or electron, penetrates matter it will lose energy by interaction with orbital electrons. The mode of interaction is called collision although no true collision takes place between particles but rather collisions between the electric fields surrounding the particles involved. The energy transferred to the orbital electron in the process can be high enough for the electron to leave the atom. In fact, the kinetic energy of the ejected electron can be so high that it will act as an ionizing particle. It is then called a delta-particle. A heavy, charged particle such as the alpha particle, which has a mass about 7300 times the mass of the electron, will lose only a small fraction of its energy in each collision. Due to its mass it will not change direction in the collision with a light electron. Changes in direction can only happen in a collision with a heavy nucleus. On the one hand, such a collision is very rare because the volume of the nucleus is so much less than the volume of the atom, but on the other hand, due to its extensive electric field the heavy charged particle will literally strike every atom it passes. In conclusion, this means that the path of an alpha particle is straight and that the range in a material is quite small and well defined. A light, charged particle (electron or positron) can lose up to half its energy in each collision with an orbital electron. The possible high energy transfer in each collision means that more energetic delta-rays can be produced than in the case of heavy charged particles. In the collision, the incident particle will also change its direction which means that its path will be irregular and curved. Due to its small size, an electron can also pass several atoms without losing any energy or only a small fraction of its energy. Therefore, the electron has the ability to penetrate deeper into matter than a heavy charged particle. Because of the irregular path the range in matter will not be so well defined as that of a heavy particle. If the light particle is a positron it will annihilate when it stops. It will recombine with an electron and their masses will be transformed to energy and emitted as two photons in opposite directions, each having an energy of 511 keV. This annihilation radiation is the one used in positron emission tomography (PET), which means that the only radionuclides used in PET-studies are those decaying by +. When an electron comes close to the nucleus it will change direction due to the electrostatic forces acting upon it. In each such event of deflection the energy lost by the particle can be emitted as electromagnetic radiation called bremsstrahlung. The energy of the emitted photon can be between zero and the whole kinetic energy of the incident electron depending on the distance between the electron and the nucleus. The energy distribution of bremsstrahlung emitted in the process will continuously decrease from zero energy to the incident electron energy. The energy loss of a charged particle passing through matter is described by the mass stopping power which is the energy loss per unit length divided by the density of the absorber. The unit is thus MeV·cm2/g. Its value depends on the type of particle and the particle energy . The stopping power due to collisions is called non restricted linear energy transfer, LET. Heavy charged particles are usually called high LET radiation and light charged particles are called low LET radiation. 4. 2. Photons For photons (X-rays, gamma rays) there are three main types of interaction with matter: the photoelectric effect, the Compton process and pair production. In all three processes directly ionizing electrons or positrons are released or created. The photoelectric effect is that in which the incident photon transfers all its energy to a tightly bound orbital electron in one of the inner shells of the atom. This electron will leave the atom carrying kinetic energy which equals the photon energy minus the binding energy of the electron. The vacancy in the electron shell is filled and characteristic radiation is emitted as this occurs. In the Compton process, the incident photon collides with a loosely bound electron in the outer shell of the atom. In the collision, the incident photon transfers some of its energy to the electron which then leaves the atom. The photon changes its direction of movement after the collision so the result of the interaction will be a scattered photon with reduced energy and a recoil electron. Pair production only occurs if the incident photon has a very high energy. When the photon encounters the strong field around the nucleus it disappears and its energy transforms into an electron-positron pair. Since the sum of their masses is equivalent to an energy of 1022 keV, pair production is limited to photons whose energies equal or exceed 1022 keV. Theoretically, a photon can penetrate an absorber with no interactions at all. We can only define a probability that a photon will interact by some of the three described processes. This probability per unit length is called the linear attenuation coefficient. It is commonly divided by the density of the absorber. This gives the mass attenuation coefficient which has the unit cm2/g. The total mass attenuation coefficient is the sum of the single coefficients for each of the three modes of interactions. The dominating process depends on the energy of the photon and the atomic number of the absorber. Note that for human soft tissues with a mean atomic number of 7.8, the dominating interaction process is the Compton process for all photon energies used in medical applications (25 keV - 25 MeV). Thickness of an absorber necessary to reduce the transmission of radiation to 50 percent (HVL). Radiation quality HVL (mm) Concrete Lead 50 kV 4.3 0.06 100 kV 10.6 0.27 200 kV 25 0.52 500 kV 36 3.6 1 MV 44 7.9 2 MV 64 12.5 5 MV 96 16.5 10 MV 119 16.6 20 MV 137 16.3 4.3. Radiation quantities and units Absorbed dose The fundamental dosimetric quantity D, defined as: D= d dm where d is the mean energy imparted by ionizing radiation to matter in a volume element and dm is the mass of matter in the volume element. The energy can be averaged over any defined volume, the average dose being equal to the total energy imparted in the volume divided by the mass in the volume. The SI unit of absorbed dose is the joule per kilogram (J.kg-1), termed the gray (Gy). Equivalent dose The quantity H, defined as: H = DT . WR where DT is the absorbed dose delivered by radiation type R averaged over a tissue or organ T and WR is the radiation weighting factor for radiation type R. When the radiation field is composed of different radiation types with different values of WR, the equivalent dose is: H = WR . DT R The unit of equivalent dose is J.kg-1, termed the sievert (Sv). Effective dose The quantity E, defined as a summation of the tissue equivalent doses, each multiplied by the appropriate tissue weighting factor: E = WT . HT T where HT is the equivalent dose in tissue T and WT is the tissue weighting factor for tissue T. From the definition of equivalent dose, it follows that: E= WT WR DT,R = WR WT DT,R T R R T where WR is the radiation weighting factor for radiation R and DT,R the average absorbed dose in the organ or tissue T. The unit of effective dose is J.kg-1, termed the sievert (Sv). 4. 3. Radiation detectors As a detector of ionizing radiation any substance may be used that produces a measurable signal as a result of energy deposition in the material. The signal can be electrical charge, light, chemically changed molecules, etc. Some materials will emit the signal during the exposure to ionizing radiation, others can retain the changes and be measured a long time after the exposure. According to their uses detectors for ionizing radiation are divided into counters, dosimeters and spectrometers. A counter is a device that will only count the number of particles and photons interacting with the detector. It will not provide information about the type and energy of the radiation. This type of detector is generally used as a survey meter to determine if radiation is present or not and to check for contamination of radionuclides. A dosimeter is a device used to measure absorbed dose and absorbed dose rate, so the signal from such a detector must be proportional to the absorbed energy in the detector over a period of time. Dosimeters are important devices in medical applications and in radiation protection. Their uses range from measuring the radiation output from therapy machines to personnel monitoring. In a spectrometer the signal is proportional to the energy of the photon or particle interacting with the detector. This property is used in many applications in nuclear medicine. The gamma camera has spectrometric properties used to reduce the influence of scattered radiation on the image. The energy of the scattered photon is lower than that of the primary photon and thus it can be sorted out by special electronics. A spectrometer can also be used to identify radionuclides from the energy of the gamma-rays. Gas-filled detectors In the ionization process an ion-pair will be produced consisting of a negative electron and a positive atom (ion). If an electric field is applied between two electrodes then the electrons will move towards the positive electrode and the positive ions towards the negative electrode. A current will appear in the outer circuit which is proportional to the number of ion pairs produced per second. Depending on the strength of the electric field (high voltage) and the design of the detector the properties of the gas detector will be different. Luminescence detectors Upon deexcitation some organic molecules and inorganic crystals can emit visible light. This phenomenon is called radioluminescence. This property is used in scintillations detectors which are commonly used in medical applications. The number of light photons emitted upon absorption of a gamma-ray or a charged particle depends on the energy transferred to the detector. The light photons will be converted into an electrical signal in a device called a photomultiplier. The magnitude of this signal will depend on the number of light photons and thus the energy transferred to the detector by the photon or the particle. The size of the signal is electronically analyzed (pulse height analyzer). 5. Introduction to spectroscopy Spectroscopy studies interaction between matter and radiated energy. Basic knowledge needed to understand the spectroscopic phenomena is in atomic structure, electron states, spins, and nucleus structure. First spectroscopic measurements were done in visible region of electromagnetic spectra, but later on it expanded to ultraviolet and infrared regions. One of the first instruments in spectroscopy was optical prism because it’s famous “rainbow effect”. Important property of spectroscopy is that it has no chemical effects. The result of spectroscopy measurements is represented by spectra of atom or molecule, under investigation. A spectrum of atoms and molecules consists of series of lines, which represents energy states of atom or molecule. 5. 1. Classification of spectroscopy Usual classification of spectroscopy is by the nature of the interaction between the energy and the material. There we have: Emission spectroscopy, Absorption spectroscopy, Interferention spectroscopy Emission spectroscopy Light is electromagnetic wave like any other electromagnetic wave, and that means it consists of different wavelengths. When the substances under investigation are heated up, they emit energy in form of light (E=hν). With the help of some kind of spectroscope (which will be described later) this light can be distinguished and used in analysis. Because we study emitted lines, this part of spectroscopy is called emission spectroscopy. Usual spectrum observed in this kind of spectroscopy is shown in the figure. Absorption spectroscopy In absorption spectroscopy we measure the absorption of radiation, caused by its interaction with matter. Absorption of electromagnetic radiation can cause several effects in the atom, so the lines from the absorption spectroscopy are called by these effects, or vibration lines, translation lines, and their combination. The energy that causes the quantum mechanical change determines the frequency of the absorption line, but the frequency can be shifted by other types of interaction, like electric and magnetic fields. Lines received from absorption spectroscopy look like Diracks delta functions, but often there are widened by the instrument function, and more like Gaussians or Lorenzians. Interferention Interferention is more commonly used in some other parts of science, like precise measurement, optical testing, or measuring index of refraction, but it can also be used as a very good tool in Fourier Transform Spectroscopy. Devices that produce interferention are usually Michleson interferometer, and Faby-Perot interferometer, and both of them superimpose several light beams with each other (two for Michelson and tens, or hundreds for Faby Perot) Another classification of spectroscopy is according to the electromagnetic wave energy. There we have: Radiofrequent Microwave Infrared Visible and ultraviolet X-ray Radiofrequent spectroscopy deals with magnetic spin states. There are two most common methods in this kind of spectroscopy NMR(Nuclear Magnetic Resonance) and ESR(Electron Spin Resonance, also known as EPR – Electron Paramagnetic Resonance). As the name states, NMR deals with spins of atomic nuclei. Difference between spin states is shown when material of interest is under strong external magnetic field (in order of 1 T). Relaxation times are measured as a response to different electromagnetic pulses. EPR acts similar but it deals with spins of electron, and weaker external fields are used. Microwave spectroscopy is a very precise tool for the determination of molecular structure in gas phase molecules. It can be used to determine barriers of internal rotations such as are rotations of the CH3 group. This kind of spectroscopy has mayor role in determining weak interactions such as are hydrogen bonds, and van der Waals interactions. It is also very useful in astronomy when determining structure of interstellar media. Infrared spectroscopy as the name states deals in the infrared region of electromagnetic spectrum. It is usually connected with absorption spectroscopy. The infrared spectrum of a sample is recorded by passing a beam of infrared light through the sample. When the frequency of the infrared radiation is the same as the vibrational frequency of a bond, absorption occurs, and the absorption lines are recorded. Ultraviolet and visible spectroscopy refers to the wavelengths in ultraviolet and visible regions of electromagnetic spectra (10 -700 nm). Measurements in this part of spectroscopy are carried out in solutions, but they can be done with gases and solids also. Diagram of a single beam ultraviolet-visual spectrometer is shown in a figure. X - rays spectroscopy is divided in two main categories: Energy-Dispersive X-ray Spectroscopy (EDS) and Wavelength Dispersive X-ray Spectroscopy (WDS). In an energydispersive X-ray spectrometer we measure the energy of incoming photons by semiconductor detector. In a wavelength dispersive X-ray spectrometer the single crystal diffracts the photons which are collected by a detector. Without any motion there will be just one wavelength detected. 5. 2. Instruments in spectroscopy The schematic layout of a prism or grating spectrometer is shown in figure. Light from the slit is collimated by the lens L1 and dispersed by prism or grating and finally focused by the lens L2 in the plane P, where the spectral lines can be thought of as images of slit in light of different wavelengths. Although this schematic arrangement is normally adhered for prism instruments, the collimating and camera lenses are usually replaced by concave mirrors, to avoid problems of absorption and aberration problems. Prism instruments Conventional prism spectrograph is shown in the image below. Light from the slit S is collimated by the lens L1, refracted by the prism, and focused by the lens L2 in image plane P, which can be photographical plate, detector, or detector array. This setup is common for small and medium sized instruments, for which is not important to be monocromators. Two lenses have usually same focal length giving unit magnification, with usage of 60°prism. Modification of this basic device is possible depending on measurement purpose. Deviation and dispersion In the figure below there is throughput of ray through central part of prism with angle α.It can be seen from the geometry that deviation θ is given with θ=d1+d2 where d1=i1-r1 and d2=i2-r2, so it follows θ=i1+i2-α. Prism instruments are usually used near the minimum deviation position, for which can be shown that it passes prism simetrically. i1 is than equal to i2, and ray passes through prism parallel with base, so it follows θ=2i-α, and α=2r. Combining of this two equations with Snell law, sin i =n sin r, for relative refraction index it follows: sin i sin n sin 2 2 From this basic equation we can get expressions for angular dispersion: d 2 sin( / 2) dn 1 / 2 dn 1 n2 sin 2 / 2 d d 1 dn 1/ 2 2 d 1 (n / 2) d For standard prism (60°), this equation is simplified: dn/dλ is a dispersion, which depends on prism material, index of refraction, and wavelength. Rt Resolution of prism gratings is given by expression: dn d ,(where t is length of prism base) Typical value for dispersion dn/dλ in visible/ultraviolet region is 3*10-4 nm-1. If we take 100 mm as a practical upper limit for prism base, we get to 30 000 as rational limit for prism spectrometer resolution. Grating instruments Diffraction grating consists from a large number of narrow, very close, equidistant slits on plate, or concave grating. They can be setup on plane, or made by engraving, or holographic. Collimated light from array of very close slits is transmitted or reflected by the periodical structures formed on grooves, which act as coherent sources. For any given wavelength secondary waves interfere constructively at certain angles and destructively under others. Maximum of intensity is shown in the focal plane, under angles that correspond interferention maxima. Concave gratings differ from plane gratings, in fact that grooves are engraved in concave mirror, so grating acts as its own collimator. For the light of wavelength λ condition for constructive interferention is: m l d (sin sin ' ) d ' m Angular dispersion for grating is observed by differentiating upper equation: d d cos ' R For resolution we have three equivalent expressions: L Nm D d ' d Maximum resolving power for grating is 500 000. Interferometric spectrometers Both Micleson and Faby-Perot interferometer have division of amplitude, it means that interfering rays are produced by splitting of a input ray on partially reflecting surface. At Faby-Perot interferometer we have multiple reflections, and Michelson uses only one partially reflecting mirror, to get rays which are reflected back by mirrors. Scheme of Michelson interferometer is shown in figure. Light from extensive source behind entering aperture A is collimated by lens L1 before entering on a beam splitter B. Lens L2 makes image of aperture A as A' in plane P (Lenses are usually replaced by concave gratings to avoid chromatic problems). Usually two mirrors M1 and M2 setup that image M1' from M1 in partially reflecting mirror is parallel with M2 in distance t between them. Michelson interferometer has its extensive usage in Fourier Transform Spectroscopy (FTS). For monocromator input FTS gives interferogram that is clear sine function. By moving one of the mirrors, all the wavelengths are recorded, and interferogram is made from superposition of all lines from all wavelengths. This kind of measurement imposes characteristic modulation on all wavelengths, so we need to make inverse Fourier Transform on interferogram to get real spectral lines. Pair of Fourier Transforms is: I ( x) B( ) cos 2xd (W ) B( ) I ( x) cos 2xdx (W / cm 1 ) Where B(σ) is modificated function, and I(x) is interferogram 6. References 1. Bjorken, J. D., and Drell, S. D. Relativistic Quantum Mechanics. McGraw-Hill, Inc., 1964. 2. Eisberg, R. M., and Resnick, R. Quantum physics of atoms, molecules, solids, nuclei, and particles. 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