Medical Physics Lectures 8 & 9 PDF

Al- Safwa University College / Pharmacy Department The first stage / Medical Physics Lectures eight and nine : Radiation and Blackbody Radiation Laws : part One : Introduction : Physics of nuclear medicine It is the use of radioactive materials in medicine. It may be either diagnostic or the...

Al- Safwa University College / Pharmacy Department The first stage / Medical Physics Lectures eight and nine : Radiation and Blackbody Radiation Laws : part One : Introduction : Physics of nuclear medicine It is the use of radioactive materials in medicine. It may be either diagnostic or therapeutic ATOMIC STRUCTURE All matter is composed of atoms, Understanding the structure of atoms is critical to understanding the properties of matter HISTORY OF THE ATOM 1808 John Dalton suggested that all matter was made up of tiny spheres that were able to bounce around with perfect elasticity and called them ATOMS DALTONS ATOMIC THEORY 16 X + 8 Y 8 X2Y mass p = mass n = 1840 x mass e- Atomic Structure Atoms are composed of : protons – positively charged particles- neutrons – neutral particles- electrons – negatively charged particles- Protons and neutrons are located in the nucleus. Electrons are found in orbitals surrounding the nucleus. Every different atom has a characteristic number of protons in the nucleus. atomic number = number of protons Atoms with the same atomic number have the same chemical properties and belong to the same element. Each proton and neutron has a mass of approximately 1 dalton. The sum of protons and neutrons is the atom’s atomic mass. Mass number = number of protons + number of neutrons Where Z = Number of protons = atomic number. N = Number of neutrons. A = Mass number = number of protons + number of neutrons = Z+N According to Z, N, A, elements are classified to : 1- Isotopes---- Same Z, Different N, Different A Note: Isotopes are variants of a particular chemical element which differ in neutron number. They have the same symbol and same chemical and physical properties. 2- Isobars --------- Same A, different Z Note: Isobars are atoms (nuclides) of different chemical elements that have the same number of nucleons(P+N). They have different chemical and physical properties. 3- Isotones------Same N, different A and Z Note: Isotones are atoms (nuclides) of different chemical elements that have the same number of neutrons. They have different chemical and physical properties. 4- Isomeric state -------Same Z, N, and A, different energy levels Note: A nuclear isomer is a metastable state of an atomic nucleus caused by the excitation of one or more of its nucleons (protons or neutrons). Radioactivity A certain natural elements, heavy have unstable that disintegrate to emit various rays. Alpha (α), Beta (β) , and Gamma (𝛄 ) rays. Alpha(α ) Beta(β) Gamma(𝛄 ) 1- Positive charge Negative charge Without charge 2-Affected by Affected by magnetic& Doesn’t affected magnetic& electric field electric field  3-Stop in a few It is stopped in a few High energy photon centimeter of air (low meters of air and a few (high penetrating penetrating power) millimeters of a power). tissue(the penetrating power is more than α and less than ɣ 4-Is Helium atom High speed electron It is photon (2He4) 5-Has a fixed energy for Has spread of energy Has a fixed energy for a a given source up to max given source Isotpes Nuclei of a given element with different numbers of neutrons. There are two types: 1-Stable isotopes if they are not radioactive. Ex:(12C,13C( 2-Radioisotopes if they are radioactive. Ex: )11C,14C,15C) Radiation doses in nuclear medicine The dose to particular organ of the body depends on the physical characteristics of the radionuclide, what particles it emits and their energies, and the length of the time the radionuclide is in the organ : Two factors determine the length of time the radionuclide is in the organ , or the effective half-life (T½eff), the physical half-life (T½phy) and biological half-life (T½bio). The biological half-life of an element is the time needed for one half of the original atoms present in an organ to be removed from the organ. (T½bio) (T½phy) T½eff = (T½bio) + (T½phy) Example: 131 (a) What is the effective half-life of I in the thyroid if T½bio= 15 days and T½phy = 8 days? (15 days) (8 days) T½eff = = 5.2 days (15 days) + (8days) (b) What is the effective half-life of 131I hippuric acid if half of it excreted in 1-hr (e.g. T½bio = 1hr) (1-hr) (192-hr) T½eff = = 0.99-hr (1-hr) + (192-hr) 18 (c) What is the effective half-life of F in bone if T½bio = 7 days and T½phy = 110min (7 days ~ 104 min) (110min) (104 min) T½eff = = 109 min. (110 min) + (104 min)  Each element has specific number of protons in the nucleus carbon has 6 proton, nitrogen has 7 protons, O2 has 8 protons.  Nuclei of a given element with different numbers of neutrons called isotope of the element,   If they are not radioactive they are called stable isotope and if they are radioactive they are called radioisotopes: for example: carbon has two stable isotopes (C12, C13) and several radioisotopes (e.g. C11, C14, and C15).  Most elements do not have naturally radioisotopes, but radioisotopes of all elements can now be produced artificially.  The use of radioactivity in medicine was the development of nuclear reactor during World War II in the connection with the atomic bomb project.  The most useful radionuclides for nuclear medicine those that emit gamma rays, since gamma rays very penetrating.  The most common emission from radioactive elements is beta particles and gamma rays. Since beta particles are not very penetrating, they are easily absorbed in the body and are generally of little use for diagnosis. However some beta emitting radionuclides such as 3H and C14 play important role in medical research.  32 P is used for diagnosis of tumors in the eye because some of its beta particles have enough energy to emerge from the eye.  All gamma-emitting radionuclides of the common organic elements: carbon, nitrogen and oxygen are short lived, which makes their use in clinical medicine, difficult without an accelerator. A few medical centers for producing short lived elements.  Each radionuclide decays at fixed rate commonly indicated by the half-life (T½): the time needed for half of the radioactive nuclei to decay.  The basic equation describing radioactive decay is A = Ao e–λ t ……… (1) A : is the activity … Ao : is the initial activity ….. λ : is the decay constant ……t : is the time , since the activity was Ao. I t measured in (hr) , λ in ( hr-1). A= λ N ………….. (2) Where N is the number of radioactive atoms.  0.693 (T½) = ……………. (3) λ The unite of radioactivity, the curie Ci 10 Ci = 3.7*10 disintegration per second.  mci, Mci , nci, Picocurie pci *10-3 *10-6 *10-9 *10-12  SI unite for radioactivity is Becquerel (Bq) because it is so small KBq, MBq, GBq *103 *106 *109 disintegration per second The second part : Blackbody Radiation Laws All incident radiation is absorbed by an ideal blackbody, and none is reflected or transmitted. It’s a model that can be used to compare real-world radiation properties. The energy output of a blackbody is a function of its temperature and is not spread uniformly across all wavelengths. Theoretically, black bodies are surfaces that absorb all incident heat radiation. Mathematically, it is described by Stefan-Boltzmann law, Planck’s law, and Wein’s displacement law. Kirchhoff’s Law. When a body is heated above absolute zero, it emits radiation in all directions and at a wide variety of wavelengths. The amount of radiation energy radiated by a surface at a given wavelength is determined by the body’s composition, the condition of its surface, and the temperature of the surface. As a result, various bodies may produce varying amounts of radiation per unit of surface area. Despite the fact that they are at the same temperature. As a result, it’s only natural to wonder what the maximum amount of radiation a surface may produce at a particular temperature is. This curiosity necessitates the creation of an idealised body known as a blackbody that can be used to compare the radioactive features of real surfaces. Stefan-Boltzmann law The Stefan-Boltzmann law states that the total radiant heat output emitted from a surface is proportional to its absolute temperature to the fourth power. 4 E=eσAT Here, e= isthe emissivity of the body. E = is the radiant heat energy radiated from a unit area in one second T = is the absolute temperature (in kelvins) The Greek letter sigma indicates the Stefan-Boltzmann constant. The value of this constant is Only blackbodies, theoretical surfaces that absorb all incident heat radiation, are subject to the law. Planck’s law Max Planck derived the relation for the spectral blackbody emissive power in connection with his famous quantum theory in 1901, called Planck’s law. Planck made an assumption that radiation originates from oscillating atoms and that the energy to cause a vibration of each oscillator can never be in between but in a series of different values and can be expressed as, Here, is the absolute temperature of the surface, is the wavelength of the radiation that is emitted, and Boltzmann’s constant is. This relation is only true when the surface is in a vacuum or a gas. It must be modified for other mediums by substituting with , where n is the medium’s index of refraction. The term spectral denotes a wavelength-dependent relationship. Wein’s Displacement law The overall radiated energy increases as the temperature of a blackbody radiator rise, and the peak of the radiation curve shifts to shorter wavelengths. This relationship is known as Wien’s displacement law used to calculate the temperatures of hot radiant objects like stars, as well as any radiant object whose temperature is much higher than its surroundings. Wein’s displacement law for the spectral blackbody is mathematically expressed as, where, Blackbody radiation graph and observations This figure shows a plot of Wien’s displacement law, which is the locus of the radiation emission curves’ peaks, from which the following observations were made:  As the temperature rises, the curves shift to the left, toward the shorter wavelength region. As a result, at higher temperatures, a greater proportion of the radiation is emitted at shorter wavelengths. The peak of the curve in the given figure shifts toward shorter wavelengths as temperature rises. Wien’s displacement law gives the wavelength at which the peak occurs for a given temperature as Example 1 A black body emits radiation at 2000K. Calculate (a) monochromatic emissive power at wavelength (b) maximum emission wavelength and (c) the maximum emissive power. Solution: Given: To find: (a) By Planck’s law,  …..(1) (b) By Weins law, Now, substitute value of equation (2) in equation (1) (c) According to Stefan Boltzmann Law, ⸫The maximum emissive power is Applications of blackbody radiation The black bodies are used in applications such as lighting, heating, security, thermal imaging, and testing and measuring. Planck’s Law of Radiation can be used to determine the intensity of energy at any temperature and wavelength. For calibrating and testing radiation thermometers, a blackbody radiation source with a known temperature or whose temperature can be measured is commonly utilised. The Boltzmann distribution will be the spectrum of light coming out of the hole if the piece of metal is heated to a uniform temperature. Black bodies are useful for calibrating thermal cameras and other detectors by establishing consistent Boltzmann spectral distributions. Kirchhoff’s Law. Kirchhoff was able to succinctly summarize what was known in spectroscopy ‎at the time. These were called laws.‎ A sufficiently hot solid material produces light with a continuous ‎spectrum.‎ A sufficiently hot gas produces light with specific colors. These ‎correspond to a spectrum with lines at discrete wavelengths.‎ If the light from a hot glowing solid material passes through a gas ‎of a cooler temperature then the spectrum has the discrete wavelengths ‎characteristic of the gas deleted from the continuous spectrum of the ‎material.‎ These applied not just to visible light but to radiation in general. Kirchhoff ‎understanding that a gas absorbs light at the same wavelengths that it emits ‎enabled him to determine the composition of the Sun from the hitherto ‎mysterious Fraunhofer dark lines of the solar spectrum. Kirchhoff's work is an ‎example of the dictum