Medical Physics - Atomic Nature of Matter PDF

Course Packet LM03-FPHY 01 0425 Learning Module...

Course Packet LM03-FPHY 01 0425 Learning Module Medical Physics Course Packet 01 Atomic Nature of Matter y Knowledge Area Code : SCI sit r ive e of Course Code : FPHY0425 LE Un at ty St er Learning Module Code : LM-FPHY0425 a p SA ul ro Course Packet Code : LM-FPHY0425-01 ns p ni is a R Pe is FO an Th Learning Module: Medical Physics 3 T ta O Ba N  Course Packet 01 Atomic Nature of Matter Course Packet 01 Introduction (A comprehensive discussion of the course packet or topic as to what to expect by the learners, including activities included in this course packet as well as the scope and coverage.) Objectives 1. STATE the characteristics of the following atomic particles, including mass, charge, and location within the atom: 1. Proton 2. Neutron 3. Electron 2. DESCRIBE the Bohr model of an atom. 3. DEFINE the following terms: a. Nuclide b. Isotope c. Atomic number d. Mass number 4. Given the standard notation for a particular nuclide, Determine the following: a. Number of protons b. Number of neutrons c. Number of electrons 5. Describe the three forces that act on particles within the nucleus and affect the stability of the nucleus. 6. DEFINE the following terms: a. Enriched uranium b. Depleted uranium Learning Management System Learning Module: Medical Physics 4  Google Classroom. Duration (Specify the number of hours allotted for this course packet.) Course Packet 01 Topic 01: Atomic Nature of Matter = 9 hours (7 hours self-directed learning with practical exercises and 2 hours assessment) Delivery Mode online (synchronous or asynchronous)). Assessment with Rubrics (Discuss the assessment tool to be used along with the corresponding rubrics.) Requirement with Rubrics (Discuss the requirement along with the corresponding rubrics.) Readings: https://www.google.com.ph/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwiDs_D2lMXsA hXNUt4KHSMeBY84ChAWMAZ6BAgGEAI&url=https%3A%2F%2Fcourses.lumenlearning.com%2Fphy sics%2Fchapter%2F30-1-discovery-of-the-atom%2F&usg=AOvVaw15UtF84ZFsrM4M3CnUJNBt https://www.google.com.ph/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwiDs_D2lMXsAhX NUt4KHSMeBY84ChAWMAh6BAgJEAI&url=http%3A%2F%2Fabyss.uoregon.edu%2F~js%2Fast121%2Flect ures%2Flec07.html&usg=AOvVaw07OaurP6GRlh1qEmPMoewi https://www.google.com.ph/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwjv3aPRlcXsAhVU E4gKHT0FA484FBAWMAF6BAgFEAI&url=http%3A%2F%2Fweb.pdx.edu%2F~pmoeck%2Flectures%2Fmo dern%2FTRM-4.ppt&usg=AOvVaw2bpXgzUWz1nJ-WhxZPT8HO Introduction All matter is composed of atoms. The atom is the smallest amount of matter that retains the properties of an element. Atoms themselves are composed of smaller particles, but these smaller particles no longer have the same properties as the overall element. Lesson Proper: Structure of Matter Early Greek philosophers speculated that the earth was made up of different combinations of basic substances, or elements. They considered these basic elements to be earth, air, water, and fire. Modern science shows that the early Greeks held the correct concept that matter consists of a combination of basic elements, but they incorrectly identified the elements. Learning Module: Medical Physics 5  In 1661 the English chemist Robert Boyle published the modern criterion for an element. He defined an element to be a basic substance that cannot be broken down into any simpler substance after it is isolated from a compound, but can be combined with other elements to form compounds. To date, 105 different elements have been confirmed to exist, and researchers claim to have discovered three additional elements. Of the 105 confirmed elements, 90 exist in nature and 15 are man-made. Course Packet 01 Another basic concept of matter that the Greeks debated was whether matter was continuous or discrete. That is, whether matter could be continuously divided and subdivided into ever smaller particles or whether eventually an indivisible particle would be encountered. Democritus in about 450 B.C. argued that substances were ultimately composed of small, indivisible particles that he labeled atoms. He further suggested that different substances were composed of different atoms or combinations of atoms, and that one substance could be converted into another by rearranging the atoms. It was impossible to conclusively prove or disprove this proposal for more than 2000 years. The modern proof for the atomic nature of matter was first proposed by the English chemist John Dalton in 1803. Dalton stated that each chemical element possesses a particular kind of atom, and any quantity of the element is made up of identical atoms of this kind. What distinguishes one element from another element is the kind of atom of which it consists, and the basic physical difference between kinds of atoms is their weight. Subatomic Particles For almost 100 years after Dalton established the atomic nature of atoms, it was considered impossible to divide the atom into even smaller parts. All of the results of chemical experiments during this time indicated that the atom was indivisible. Eventually, experimentation into electricity and radioactivity indicated that particles of matter smaller than the atom did indeed exist. In 1906, J. J. Thompson won the Nobel Prize in physics for establishing the existence of electrons. Electrons are negatively- charged particles that have 1/1835 the mass of the hydrogen atom. Soon after the discovery of electrons, protons were discovered. Protons are relatively large particles that have almost the same mass as a hydrogen atom and a positive charge equal in magnitude (but opposite in sign) to that of the electron. The third subatomic particle to be discovered, the neutron, was not found until 1932. The neutron has almost the same mass as the proton, but it is electrically neutral. Bohr Model of the Atom The British physicist Ernest Rutherford postulated that the positive charge in an atom is concentrated in a small region called a nucleus at the center of the atom with electrons existing in orbits around it. Niels Bohr, coupling Rutherford's postulation with the quantum theory introduced by Max Planck, proposed that the atom consists of a dense nucleus of protons surrounded by electrons traveling in discrete orbits at fixed distances from the nucleus. An electron in one of these orbits or shells has a specific or discrete quantity of energy (quantum). When an electron moves from one allowed orbit to another allowed orbit, the energy difference between the two states is emitted or absorbed in the form of a single quantum of radiant energy called a photon. Figure 1 is Bohr's model of the hydrogen atom showing an electron as having just dropped from the third shell to the first shell with the emission of a photon that has an energy = hv. (h = Planck's -34 constant = 6.63 x 10 J-s and v = frequency of the photon.) Bohr's theory was the first to successfully account for the discrete energy levels of this radiation as measured in the laboratory. Although Bohr's atomic model is designed specifically to explain the hydrogen atom, his theories apply generally to the structure of all atoms. Additional information on electron shell theory can be found in the Chemistry Fundamentals Handbook. Learning Module: Medical Physics 6 Course Packet 01 Figure 1 Bohr's Model of the Hydrogen Atom Properties of the three subatomic particles are listed in Table 1. Measuring Units on the Atomic Scale The size and mass of atoms are so small that the use of normal measuring units, while possible, is often inconvenient. Units of measure have been defined for mass and energy on the atomic scale to make measurements more convenient to express. The unit of measure for mass is the atomic mass unit (amu). One -24 atomic mass unit is equal to 1.66 x 10 grams. The reason for this particular value for the atomic mass unit will be discussed in a later chapter. Note from Table 1 that the mass of a neutron and a proton are both about 1 amu. The unit for energy is the electron volt (eV). The electron volt is the amount of energy acquired by a single electron when it falls through a potential difference of one volt. One electron volt is equivalent to 1.602 -19 -19 x 10 joules or 1.18 x 10 foot-pounds. Nuclides The total number of protons in the nucleus of an atom is called the atomic number of the atom and is given the symbol Z. The number of electrons in an electrically-neutral atom is the same as the number of protons in Learning Module: Medical Physics 7  the nucleus. The number of neutrons in a nucleus is known as the neutron number and is given the symbol N. The mass number of the nucleus is the total number of nucleons, that is, protons and neutrons in the nucleus. The mass number is given the symbol A and can be found by the equation Z + N = A. Each of the chemical elements has a unique atomic number because the atoms of different elements contain a Course Packet 01 different number of protons. The atomic number of an atom identifies the particular element. Each type of atom that contains a unique combination of protons and neutrons is called a nuclide. Not all combinations of numbers of protons and neutrons are possible, but about 2500 specific nuclides with unique combinations of neutrons and protons have been identified. Each nuclide is denoted by the chemical symbol of the element with the atomic number written as a subscript and the mass number written as a superscript, as shown in Figure 2. Because each element has a unique name, chemical symbol, and atomic number, only one of the three is necessary to identify the element. For this reason nuclides can also be identified by either the chemical name or the chemical symbol followed by the mass number (for example, U-235 or uranium- 235). Another common format is to use the abbreviation of the chemical element with the mass number superscripted (for example,235U). In this handbook the format used in the text will usually be the element's name followed by the mass number. In equations and tables, the format in Figure 2 will usually be used. Figure 2. Nomenclature for Identifying Nuclides Example: State the name of the element and the number of protons, electrons, and neutrons in the nuclides listed below. Solution: The name of the element can be found from the Periodic Table (refer to Chemistry Fundamentals Handbook) or the Chart of the Nuclides (to be discussed later). The number of protons and electrons are equal to Z. The number of neutrons is equal to Z - A. Learning Module: Medical Physics 8 Course Packet 01 Isotopes Isotopes are nuclides that have the same atomic number and are therefore the same element, but differ in the number of neutrons. Most elements have a few stable isotopes and several unstable, radioactive isotopes. For example, oxygen has three stable isotopes that can be found in nature (oxygen-16, oxygen-17, and oxygen-18) and eight radioactive isotopes. Another example is hydrogen, which has two stable isotopes (hydrogen-1 and hydrogen-2) and a single radioactive isotope (hydrogen-3). The isotopes of hydrogen are unique in that they are each commonly referred to by a unique name instead of the common chemical element name. Hydrogen-1 is almost always referred to as hydrogen, but the term protium is infrequently used also. Hydrogen-2 is commonly called deuterium and symbolized D. Hydrogen- 2 3 3 is commonly called tritium and symbolized T. This text will normally use the symbology 1H and 11-1 for deuterium and tritium, respectively. Atomic and Nuclear Radii The size of an atom is difficult to define exactly due to the fact that the electron cloud, formed by the electrons moving in their various orbitals, does not have a distinct outer edge. A reasonable measure of atomic size is given by the average distance of the outermost electron from the nucleus. Except for a few of the lightest atoms, the average atomic radii are approximately the same for all atoms, about 2 x 10 cm. Like the atom the nucleus does not have a sharp outer boundary. Experiments have shown that the nucleus is shaped like a sphere with a radius that depends on the atomic mass number of the atom. The relationship between the atomic mass number and the radius of the nucleus is shown in the following equation. -13 1/3 r = (1.25 x 10 cm) A where: r = radius of the nucleus (cm) A = atomic mass number (dimensionless) The values of the nuclear radii for some light, intermediate, and heavy nuclides are shown in Table 2. Learning Module: Medical Physics 9 Course Packet 01 -8 From the table, it is clear that the radius of a typical atom (e.g. 2 x 10 cm) is more than 25,000 times larger than the radius of the largest nucleus. Nuclear Forces In the Bohr model of the atom, the nucleus consists of positively-charged protons and electrically-neutral neutrons. Since both protons and neutrons exist in the nucleus, they are both referred to as nucleons. One problem that the Bohr model of the atom presented was accounting for an attractive force to overcome the repulsive force between protons. Two forces present in the nucleus are (1) electrostatic forces between charged particles and (2) gravitational forces between any two objects that have mass. It is possible to calculate the magnitude of the gravitational force and electrostatic force based upon principles from classical physics. Newton stated that the gravitational force between two bodies is directly proportional to the masses of the two bodies and inversely proportional to the square of the distance between the bodies. This relationship is shown in the equation below. where: Fg = gravitational force (newtons) m1 = mass of first body (kilograms) m2 = mass of second body (kilograms) -11 2 2 G=gravitational constant (6.67 x 10 N-m /kg ) r= distance between particles (meters) The equation illustrates that the larger the masses of the objects or the smaller the distance between the objects, the greater the gravitational force. So even though the masses of nucleons are very small, the fact that the distance between nucleons is extremely short may make the gravitational force significant. It is necessary to Learning Module: Medical Physics 10  calculate the value for the gravitational force and compare it to the value for other forces to determine the significance of the gravitational force in the nucleus. The gravitational force between two protons that are -20 -24 separated by a distance of 10 meters is about 10 newtons. Coulomb's Law can be used to calculate the force between two protons. The electrostatic force is directly Course Packet 01 proportional to the electrical charges of the two particles and inversely proportional to the square of the distance between the particles. Coulomb's Law is stated as the following equation. where: Fe = electrostatic force (newtons) 9 2 2 K = electrostatic constant (9.0 x 10 N-m /C ) Q1 = charge of first particle (coulombs) Q2 = charge of second particle (coulombs) r = distance between particles (meters) -20 Using this equation, the electrostatic force between two protons that are separated by a distance of 10 12 -24 meters is about 10 newtons. Comparing this result with the calculation of the gravitational force (10 newtons) shows that the gravitational force is so small that it can be neglected. If only the electrostatic and gravitational forces existed in the nucleus, then it would be impossible to have stable nuclei composed of protons and neutrons. The gravitational forces are much too small to hold the nucleons together compared to the electrostatic forces repelling the protons. Since stable atoms of neutrons and protons do exist, there must be another attractive force acting within the nucleus. This force is called the nuclear force. The nuclear force is a strong attractive force that is independent of charge. It acts equally only between pairs of neutrons, pairs of protons, or a neutron and a proton. The nuclear force has a very short range; it acts only -13 over distances approximately equal to the diameter of the nucleus (10 cm). The attractive nuclear force between all nucleons drops off with distance much faster than the repulsive electrostatic force between protons. In stable atoms, the attractive and repulsive forces in the nucleus balance. If the forces do not balance, the atom cannot be stable, and the nucleus will emit radiation in an attempt to achieve a more stable configuration. Chart of the Nuclides A tabulated chart called the Chart of the Nuclides lists the stable and unstable nuclides in addition to pertinent information about each one. Figure 3 shows a small portion of a typical chart. This chart plots a box for each individual nuclide, with the number of protons (Z) on the vertical axis and the number of neutrons (N = A - Z) on the horizontal axis. Learning Module: Medical Physics 11  The completely gray squares indicate stable isotopes. Those in white squares are artificially radioactive, meaning that they are produced by artificial techniques and do not occur naturally. By consulting a complete chart, other types of isotopes can be found, such as naturally occurring radioactive types (but none are found in the region of the chart that is illustrated in Figure 3). Course Packet 01 Located in the box on the far left of each horizontal row is general information about the element. The box contains the chemical symbol of the element in addition to the average atomic weight of the naturally occurring substance and the average thermal neutron absorption cross section, which will be discussed in a later module. The known isotopes (elements with the same atomic number Z but different mass number A) of each element are listed to the right. Figure 3: Nuclide Chart for Atomic Numbers 1 to 6 Information for Stable Nuclides For the stable isotopes, in addition to the symbol and the atomic mass number, the number percentage of each isotope in the naturally occurring element is listed, as well as the thermal neutron activation cross section and the mass in atomic mass units (amu). A typical block for a stable nuclide from the Chart of the Nuclides is shown in Figure 4. Figure 4 Stable Nuclides Information for Unstable Nuclides Learning Module: Medical Physics 12  - For unstable isotopes the additional information includes the half life, the mode of decay (for example,ẞ , α), the total disintegration energy in MeV (million electron volts), and the mass in amu when available. A typical block for an unstable nuclide from the Chart of the Nuclides is shown in Figure 5. Course Packet 01 Figure 5: Unstable Nuclides Neutron - Proton Ratios Figure 6 shows the distribution of the stable nuclides plotted on the same axes as the Chart of the Nuclides. As the mass numbers become higher, the ratio of neutrons to protons in the nucleus becomes larger. For helium-4 (2 protons and 2 neutrons) and oxygen-16 (8 protons and 8 neutrons) this ratio is unity. For indium-115 (49 protons and 66 neutrons) the ratio of neutrons to protons has increased to 1.35, and for uranium-238 (92 protons and 146 neutrons) the neutron-to-proton ratio is 1.59. If a heavy nucleus were to split into two fragments, each fragment would form a nucleus that would have approximately the same neutron-to-proton ratio as the heavy nucleus. This high neutron-to-proton ratio places the fragments below and to the right of the stability curve displayed by Figure 6. The instability caused by this excess of neutrons is generally rectified by successive beta emissions, each of which converts a neutron to a proton and moves the nucleus toward a more stable neutron-to-proton ratio. Figure 6: Neutron - Proton Plot of the Stable Nuclides Natural Abundance of Isotopes The relative abundance of an isotope in nature compared to other isotopes of the same element is relatively constant. The Chart of the Nuclides presents the relative abundance of the naturally occurring isotopes of an Learning Module: Medical Physics 13  element in units of atom percent. Atom percent is the percentage of the atoms of an element that are of a 24 particular isotope. Atom percent is abbreviated as a/o. For example, if a cup of water contains 8.23 x 10 22 atoms of oxygen, and the isotopic abundance of oxygen-18 is 0.20%, then there are 1.65 x 10 atoms of oxygen- 18 in the cup. Course Packet 01 The atomic weight for an element is defined as the average atomic weight of the isotopes of the element. The atomic weight for an element can be calculated by summing the products of the isotopic abundance of the isotope with the atomic mass of the isotope. Example: Calculate the atomic weight for the element lithium. Lithium-6 has an atom percent abundance of 7.5% and an atomic mass of 6.015122 amu. Lithium-7 has an atomic abundance of 92.5% and an atomic mass of 7.016003 amu. Solution: Atomic Mass Lithium = (0.075) (6.015122 amu) + (0.925) (7.016003 amu) = 6.9409 amu The other common measurement of isotopic abundance is weight percent (w/o). Weight percent is the percent weight of an element that is a particular isotope. For example, if a sample of material contained 100 kg of uranium that was 28 w/o uranium-235, then 28 kg of uranium-235 was present in the sample. Enriched and Depleted Uranium Natural uranium mined from the earth contains the isotopes uranium-238, uranium-235 and uranium-234. The majority (99.2745%) of all the atoms in natural uranium are uranium-238. Most of the remaining atoms (0.72%) are uranium-235, and a slight trace (0.0055%) are uranium-234. Although all isotopes of uranium have similar chemical properties, each of the isotopes has significantly different nuclear properties. For reasons that will be discussed in later modules, the isotope uranium-235 is usually the desired material for use in reactors. A vast amount of equipment and energy are expended in processes that separate the isotopes of uranium (and other elements). The details of these processes are beyond the scope of this module. These processes are called enrichment processes because they selectively increase the proportion of a particular isotope. The enrichment process typically starts with feed material that has the proportion of isotopes that occur naturally. The process results in two types of the same element; one with a higher than natural proportion of one isotope and one with a lower than natural proportion. In the case of uranium, the natural uranium ore is 0.72 a/o uranium-235. The desired outcome of the enrichment process is to produce enriched uranium. Enriched uranium is defined as uranium in which the isotope uranium-235 has a concentration greater than its natural value. The enrichment process will also result in the byproduct of depleted uranium. Depleted uranium is defined as uranium in which the isotope uranium- 235 has a concentration less than its natural value. Although depleted uranium is referred to as a by-product of the enrichment process, it does have uses in the nuclear field and in commercial and defense industries. Atomic Nature of Matter Summary Learning Module: Medical Physics 14  Atoms consist of three basic subatomic particles. These particles are the proton, the neutron, and the electron. Protons are particles that have a positive charge, have about the same mass as a hydrogen atom, and exist in the nucleus of an atom. Course Packet 01 Neutrons are particles that have no electrical charge, have about the same mass as a hydrogen atom, and exist in the nucleus of an atom. Electrons are particles that have a negative charge, have a mass about eighteen hundred times smaller than the mass of a hydrogen atom, and exist in orbital shells around the nucleus of an atom. The Bohr model of the atom consists of a dense nucleus of protons and neutrons (nucleons) surrounded by electrons traveling in discrete orbits at fixed distances from the nucleus. Nuclides are atoms that contain a particular number of protons and neutrons. Isotopes are nuclides that have the same atomic number and are therefore the same element, but differ in the number of neutrons. The atomic number of an atom is the number of protons in the nucleus. The mass number of an atom is the total number of nucleons (protons and neutrons) in the nucleus. The notation is used to identify a specific nuclide. "Z" represents the atomic number, which is equal to the number of protons. "A" represents the mass number, which is equal to the number of nucleons. "X" represents the chemical symbol of the element. Number of protons = Z Number of electrons =Z Number of neutrons = A-Z The stability of a nucleus is determined by the different forces interacting within it. The electrostatic force is a relatively long-range, strong, repulsive force that acts between the positively charged protons. The nuclear force is a relatively short-range attractive force between all nucleons. The gravitational force the long range, relatively weak attraction between masses, is negligible compared to the other forces. Enriched uranium is uranium in which the isotope uranium-235 has a concentration greater than its natural value of 0.7%. Depleted uranium is uranium in which the isotope uranium-235 has a concentration less than its natural value of 0.7%. Application: https://www.youtube.com/watch?v=4BRL7UcUZhY Learning Module: Medical Physics 15  https://www.youtube.com/watch?v=1iVUysdimRo Videos to watch: Course Packet 01 Enhancement Activity: 1. Name the three particles of the atom and their respective charges are: a. b. c. 2. The number of protons in one atom of an element determines the atom’s , and the number of electrons determines of an element. 3. The atomic number tells you the number of in one atom of an element. It also tells you the number of in a neutral atom of that element. The atomic number gives the “identity “of an element as well as its location on the Periodic Table. No two different elements will have the atomic number. 4. The of an element is the average mass of an element’s naturally occurring atoms, or isotopes, taking into account the of each isotope. 5. The of an element is the total number of protons and neutrons in the of the atom. 6. The mass number is used to calculate the number of in one atom of an element. In order to calculate the number of neutrons you must subtract the from the. 7. Give the symbol and number of protons in one atom of: Lithium Bromine Iron Copper Learning Module: Medical Physics 16  Oxygen Mercury Arsenic Helium 8. Give the symbol and number of electrons in a neutral atom of: Course Packet 01 Uranium Chlorine Boron Iodine Antimony Argon 9. Give the isotope symbol and number of neutrons in one atom of the following elements. Show your calculations. Barium – 138 Sulfur – 32 Carbon – 12 Hydrogen – 1 _______ Fluorine – 19 Magnesium – 24 Silicon - 28 Mercury – 202 _______ 10. Name the element which has the following numbers of particles. Be specific. (Include charges and mass numbers where possible.) 26 electrons, 29 neutrons, 26 protons 53 protons, 74 neutrons ______ 2 electrons (neutral atom) _______ 20 protons 86 electrons, 125 neutrons, 82 protons (charged atom) 0 neutrons 11. If you know ONLY the following information can you always determine what the element is? (Yes/No). number of protons number of neutrons number of electrons in a neutral atom number of electrons Learning Module: Medical Physics 17 Part l: Label the parts of this atom (nucleus, protons, electrons, neutrons) Part 2: Answer these: 1. The subatomic particle with no electrical charge is the __________________ 2. The subatomic particle with a positive charge is the ____________________ 3. The subatomic particle with a negative charge is the ____________________ 4. There are the same number of these two particles in an atom 5. The atomic number is the same as the number of ________________________ 6. Where is most of the mass of an atom located?/ 7. Which particles account for the mass of the atom? _________________________________(Atomic mass or mass number) and ____________________ 8.Complete the following table Symbol Atomic Number Number of Number of Number of Mass Protons Neutrons Electrons 9 9. The atomic number is the number of in one atom of an element. It is also the number of in a neutral atom of that element. The atomic number gives the "identity "of an element. No two different elements will have the atomic number. 10. The/of an element is the average mass of an element 's naturally occurring atoms, or isotopes, taking into account the of each isotope. Learning Module: Medical Physics 18 11. In order to calculate the number of neutrons you must subtract the ________________________from the_____________________. 12. Give the symbol and number of protons in one atom of: // Lithium Mercury Iron 13. Complete the table below. Symbol Atomic Mass Number Number of Number of Number of Number Protons Electrons Neutrons 23 39 19 38 38 50 20 40 Ions +2 -1 Isotopes 110 47 36S 26M 14. Draw a Bohr model for the following: Argon (18) Magnesium (12) Learning Module: Medical Physics 19 15. Complete the following with the terms "new element", ion, isotope, or molecule. Learning Module: Medical Physics 20