MME211 Science of Materials Lectures 2023 PDF

MME211 – SCIENCE OF MATERIALS Lecturers: Prof. David Esezobor Dr. Ademola Agbeleye Metallurgical and Materials Engineering Dept Email: [email protected] SESSION TOPIC Course Outline Course Outline, Laboratory...

MME211 – SCIENCE OF MATERIALS Lecturers: Prof. David Esezobor Dr. Ademola Agbeleye Metallurgical and Materials Engineering Dept Email: [email protected] SESSION TOPIC Course Outline Course Outline, Laboratory Experiments, WEEK 1 Types of Materials Atomic Structure – Mass Number – Isotopy Physical Model of the Atom WEEK 2 - Quantum Numbers - Hund’s Rule  Valency Model of the Atom Valency and Inertness WEEK 3 Excitation and Ionization Energy Atomic Theory/Structure and Properties of Atomic Nuclei WEEK 4 - Dalton’s - Thomson - Bohr’s Rutherford’s Radioactivity  Inter Atomic Bonding WEEK 5 Crystal Structure Stacking Sequence and Stacking Faults Miller Indices WEEK 7 Interplanar Distance Crystal Imperfections  Atomic Movements Phase Equilibrium Diagrams and Alloys WEEK 8 WEEK 9 TEST 1 WEEK 10 Solid State Transformations Survey of Occurrence and Extraction of Metals Non Crystalline Solids - Polymers - Ceramics  Composites Ceramics Polymers WEEK 11 Thermoplastics and Thermosets WEEK 12 Materials Selection WEEK 13 Review WEEK 14 Review /TUTORIAL WEEK 15 FINAL EXAM LABORATORY PROGRAMS Laboratory 1: Introduction to Laboratory Experiments Laboratory 2: Rockwell and Brinell Hardness Tests Laboratory 3: Annealing Laboratory 4: Phase Diagram of Binary Alloys Laboratory 5: Jominy End Quench Test Materials Selection Laboratory 6: Non-destructive Testing Methods Review / Tutorial FINAL EXAM  Grading Test 20 % Final Exam 60 % Lab reports 20 %  REFERENCES 1. C. A. Loto. A Textbook of Materials Science & Engineering 2. James P. Schaffer et al,. The Science and Design of Engineering Materials. 2nd Edition, McGraw-Hill, 1999 3. J.C. Anderson et al. Materials Science. 2nd Edition, E.L.B.S., 1974 4. John, Introduction to Engineering Materials. Macmillan 5. D.J. Davies, L.A. Oelmann. The Structure, Properties and Heat Treatment of Metals. Pitman, 1983 6. Atkins, Physical Chemistry 7. Khanna O.P. Materials Science & Metallurgy. Dhanpat Rai Pub. Ltd. New Delhi, 2008 8. Rajput R.K. Materials Science & Engineering. S. K. Kataria & Sons. Delhi, 2007  Science of Materials The importance of Science of Materials has evolved during the last 40 years as different classes of materials became more and more competitive with one another. The four primary general classes of materials are metals, ceramics, polymers and composites. What makes these classes of materials unique is their composition, bonding and structure. Additionally, these distinct characteristics govern the applications for using each class of material  Why Science of Materials? All classes of material collectively account for all tangible objects on Earth. The field of material science enables the understanding and improvement of existing and new materials with the potential to catapult humanity to new frontiers. The wealth of information in this lesson is adequate to intrigue students to consider pursuing paths of study in material science. The introductory presentation introduces the general classes of materials, terminology and applications.  Types of Materials Metals: good electrical and thermal conductivity, high strength, high stiffness, and have good ductility. Some metals, such as Fe, Co and Ni are magnetic. At extremely low temperatures, some metals and intermetallic compounds become superconductors. (5 categories of Engineering Materials): Metals, Polymers, Ceramics, Semi-conductors & Composites.  Pure metals: Pure metals are elements which come from a particular area of the periodic table. Examples of pure metals include copper in electrical wires and aluminum in cooking foil and beverage cans. Metal Alloys: Metal Alloys contain more than one metallic element. Their properties can be changed by changing the elements present in the alloy. Examples of metal alloys include stainless steel which is an alloy of iron, nickel, and chromium; and gold jewelry which usually contains an alloy of gold and nickel.  The most important properties of metals include density, fracture toughness, strength and plastic deformation. The atomic bonding of metals also affects their properties. In metals, the outer valence electrons are shared among all atoms, and are free to travel everywhere. Since electrons conduct heat and electricity, metals make good cooking pans and electrical wires. Many metals and alloys have high densities and are used in applications which require a high mass-to-volume ratio. Some metal alloys, such as those based on Aluminum, have low densities and are used in aerospace applications for fuel economy. Many metal alloys also have high fracture toughness, which means they can withstand impact and are durable.  POLYMERS Polymers are long – chain molecules composed of many mers bonded together. The most common commercial polymer is POLYETHYLENE –(C2H4)n- where n can range from approximately 100 to 1000. An alternative name for this category is PLASTICS, which describes the extensive formability of many polymers during fabrication. A polymer has a repeating structure, usually based on a carbon backbone. The repeating structure results in large chainlike molecules. The “mer” in a polymer is a single hydrocarbon molecule such as ethylene (C2H4). Polymers are contained within animal (wool, leather), insect (silk) and vegetable (wood, cotton) products.  Polymers are useful because they are lightweight, are corrosion resistant, are easy to process at low temperatures, and are generally inexpensive. One of the distinct properties of polymers is that they are poor conductors of electricity and heat, which makes them good insulators. TYPES OF POLYMER There are 2 types of polymers: thermoplastics and the thermosets. Rubber or elastomers form another group of polymeric materials.  Thermoplastic polymers, in which the long molecular chains are not rigidly connected, have good ductility and formability; thermosetting polymers are stronger but more brittle because the molecular chains are tightly linked.  CERAMICS Ceramics are compounds formed between metallic and nonmetallic elements; they are most frequently oxides, nitrides, and carbides. The wide range of materials that falls within this classification includes ceramics that are composed of clay minerals, cement, and glass. These materials are typically insulative to the passage of electricity and heat, and are more resistant to high temperatures and harsh environments than metals and polymers. With regard to mechanical behavior, ceramics are hard but very brittle.  Composites Composites are formed from two or more types of materials. Examples include polymer/ceramic and metal/ceramic composites. Composites are used because overall properties of the composites are superior to those of the individual components. For example: polymer/ceramic composites have a greater modulus than the polymer component, but aren't as brittle as ceramics. Three types of composites are: Particle-reinforced composites Fiber-reinforced (continuous & random)composites Structural (laminate & sandwich panels) composites  SEMICONDUCTORS Semiconductors have electrical properties that are intermediate between the electrical conductors and insulators. Furthermore, the electrical characteristics of these materials are extremely sensitive to the presence of minute concentrations of impurity atoms, which concentrations may be controlled over very small spatial regions. The semiconductors have made possible the advent of integrated circuitry that has totally revolutionized the electronics and computer industries (not to mention our lives) over the past two decades.  BIOMATERIALS Biomaterials are employed in components implanted into the human body for replacement of diseased or damaged body parts. These materials must not produce toxic substances and must be compatible with body tissues (i.e., must not cause adverse biological reactions). All of the above materials—metals, ceramics, polymers, composites, and semiconductors—may be used as biomaterials.  Material Structure All matter is considered to be composed of unit substances known as chemical elements. These are the smallest units that are distinguishable on the basis of their chemical activity and physical properties. The elements are composed of atoms which have distinct structure characteristic of each element. Element: The smallest part of a substance that retains the same properties of that substance and can not be broken down any further. Elements are composed of atoms which have a distinct structure characteristic of each element. Atom: The smallest particle of an element which retains the distinct structure characteristic of an element.  Atomic Structure: The free atom is composed of electrons, protons, and neutrons. Almost the entire mass of the atom is concentrated in the nucleus, which contains the protons (positive charges) and neutrons (electrically neutral particles). The electrical charge q carried by each e and p is 1.60x10-19 coulombs. An atom consists of a minute positively charged nucleus surrounded by a sufficient number of electrons (negative charges) to keep the atom as a whole neutral. The nucleus is 10-14m in diameter. Since the electron and proton have equal but opposite electrical charge, the neutral atom must contain an equal number of electrons and protons. Figure 1. Atomic Model  Atomic Mass Number: Atomic Mass Number, A = Number of electrons, e + Number of neutrons, N or it can be equal to Number of Protons, p + Number of Neutrons, N i.e. A = e + N or A = p + N The mass of each proton and neutron is about 1.67x10-24 g which is referred to a.m.u, but the mass of each electron is 9.11x10-28g which makes a negligible contribute to the atomic mass of the element. Mp is greater than Me by 1876 Mass Number has a mass very close to the atomic mass unit. The mass number of an atom approximately expresses its ATOMIC MASS. Mass Number is the mass of Avogadro number, NA= 6.02x1023 mol-1 is the number of atoms or molecule in a g mole. The unit of atomic mass is g/g mole or a.m.u, which is the mass of carbon 12. Atomic Number: Atomic Number, Z = Number of electrons = Number of protons Z = e = p. The number of p in the nucleus of an atom is the characteristic of the element in which that atom belongs and is called the ATOMIC NUMBER of that element.  Proton Neutron Electron Symbol p N e Mass , kg 1.67x10-27 1.67x10-27 9.11x10-31 Charge, C 1.6x10-19 0 1.6x10-19 Mass relative to e 1876 1876 1 Charge relative to p +1 0 -1 The electrons, spinning on their own axes as they rotate around the nucleus, are arranged in definite shells. The maximum number of electrons that can fit in each shell is 2n2 where n is the shell number. The maximum number of electrons that can fit in the first shell (K) is two, the second shell (L) eight, the third shell (M) eighteen, the fourth shell (N) thirty two, etc.  ISOTOPES From the Greek words “isos” which means same and “topes” – place. Atoms having an identical charge of their nucleus (and, consequently, identical chemical properties) , but a different numbers of neutron and (and, therefore, a different mass number) are known as isotopes. Atomic mass = average (means) of the proportion (abundances) isotopes. Cl +17 35 37 17 Cl =17 35.43 Cl i.e 75.53% of 35 + 2.43% of 37 All the elements in the periodic table exhibit isotopic character except Be, Fe, Na, Al, P, Sc, Mn, Co, As, Y, Nb, Rh, I Cs, Pr, Ts, Ho, Tm, Au. The chemical properties of isotopes are identical. This means that if there does exist a certain difference between isotopes with respect to their chemical properties, it is so small that it is virtually not detected, only those involving mass effects would be noticed. An exception is the hydrogen isotopes 1H and 2H. Owing to the enormous relative difference in their atomic masses (the mass of an atom of one isotope is double that of an atom of the other isotope) the properties of these isotopes differ quite appreciable. The 2H is called Deuterium (D). The deuterium content in ordinary hydrogen is about 0.015%.  PHYSICAL MODEL OF THE ATOM (ELECTRONIC STRUCTURE) I. An e has the lowest energy when it is in the orbit closest to the nucleus (i.e. normal or ground state of an atom) II. The energy of an e can take on only definite “allowed” values, in other words it is quantized i.e. electron occupy discrete energy levels within the atom. Each e possesses a particular energy, with no more than 2 e in each atom having the same energy. III. The energy level to which each e belongs is determined by the 4 quantum numbers. IV. The number of POSSIBLE ENERGY levels is determined by the 1st 3 quantum number FIRST (PRINCIPAL) QUANTUM number, n The possible energy states of an electron in an atom are determined by the volume of the principal quantum number, n that can take 1,2,3…., etc. An e has the smallest energy at n=1. It grows with n increases. At n=1, e is the 1st or ground energy level, at n=2, it is at 2nd level etc. n determines the dimension of the electron cloud. A greater value of n corresponds to greater dimensions of the dimensions of the electron cloud (layers or shells). A DISCRETE number of e is situated in every level and is equal to N = 2n2 where N – total number of e 1st level N = 2x12 =2 electrons 2nd level N = 2x22 = 8 electrons 3rd level N = 2x32 = 18 electrons and etc. Principal quantum number, n 1 2 3 4 5 6 7 Designation of energy level K L M N O P Q  2nd (ORBITAL) or AZIMUTHAL Quantum number, l The shape of the e cloud is determined l K Shell that can take the value of o to (n-1). It determines (n=1) 2e the value of ORBITAL ANGULAR MOMENTUM of an electron. L Shell (n=2) N= 8:8e l=O when n=1 does not mean an electron at rest, but a motion M Shell that does not give rise to a resultant angular momentum, L (n=3) L=mvr m is the mass of the particle, v is the velocity and r is the position vector connecting the center of revolution to the particle. Figure 1. The atomic structure of sodium 23 11 Na The angular momentum of the electron L h r Lm = ( q ( q + 1) (1) mv 2n h-plank’s constant = 6.626x10-34Js q – the charge of the electron.  The azimuthal quantum numbers are customarily called the ENERGY SUBLEVELS OR SUBSHELLS of an electron in an atom. They are designated by lowercase letters Orbital q. no 0 1 2 3 4 5 6 7 Designation of energy level s p d f g h i j s-sharp, p-principal, d-diffuse, f-fundamental. when n=2 we have either 0 or -1 i.e. 2 sublevels In general, in the nth level, there will be n sublevels with equals to 0, 1, 2, 3,…, n-1  THIRD (MAGNETIC) QUANTUM number, ml indicates the orientation of an electron. It gives the number of energy levels or orbital for each azimuthal quantum number. The total of ml for each is 2l+1. The values of ml are given by whole numbers between n – e and +e. for example 3 different values of (-1, 0, +1) are possible for p electron (=1) and s for M, (-2,-1,0,+1,+2) for d electron (=2) which is 2(2) +1=5. ml is called magnetic because of the interact of the magnetic field set up by an electron with which the external magnetic field depends on its value. All orbitals of equal in a given sublevel are energy (they degenerate). In the presence of a magnetic field their different orientations cause them to have different energies. Three quantum numbers (n, l, and ml) are required to specify a particular orbital.  SHAPE AND ARRANGEMENTOF ELECTRONS IN SPACE Electron clouds of 1s, 2p and 3d electrons i) Since ml = (0) =1 for “s” state ii) p orbital l = 1; ml (-1, 0, 1) = 3, accordingly l =0, then any possible they can be arranged in space in 3 ways arrangement of an S electron cloud in space are identical Z Y Z Z Y Y 1S 2px 2py X X X Z The 3 p electron clouds are oriented along mutually Y perpendicular direction, which are conventionally taken 2pz as the direction of the coordinate axes (x, y or z); the X corresponding states of the electrons are designated px, py, and pz iii) For d orbital l = 5; ml = (-2,-1,0,+1,+2) = 5 values of the magnetic quantum number are possible and accordingly, 5 different orientations of the d electron clouds in space. p - orbitals  d - orbitals 3dxy 3dyz 3dz² 3dxz 3dx² - y² f ORBITALS At the fourth and higher levels, there are seven f orbitals in addition to the 4s, 4p, and 4d orbitals.  FOURTH QUANTUM NUMBER, (SPIN QUANTUM NUMBER) ms or simply the spin is used to determine the INTRINSIC state of an electron. Unlike n, l , and ml, ms is not associated with motion of the electron about the nucleus. It can be loosely associated with the spin of the electron about its own axis. This can have only 2 values + ½ or –½ depending on the direction of rotation of the electron about its axis (ms = +½ or - ½ ). Two electrons in the same orbital having values of +½ and -½ are said to be paired; both of them would have the same amount of energy. NOTE: The possible values of the spin quantum number differ by UNITY. Four quantum numbers (n, l, ml, and ms) are required to specify a particular electron. PAULI EXCLUSION PRINCIPLE It specifies that no more than 2 electrons, each with oppositely electronic spins, may be present in each orbital. The spin quantum number is assigned values + ½ to reflect the different spins.  Summary Table 1.2 Maximum number of electrons in atom energy levels and sublevels Energy Energy Possible Values Number of Number of Level, n sublevel, of Magnetic orbitals electrons l (n-1) Quantum In In In In Number, sublevel level sublevel level ml (2l+ 1) K (n=1) s(l=O) 0 1 1 2 2 L (n=2) s(l=O) 0 1 2 p(l=1) -1, 0, +1 3 6 8 4 M (n=3) s(l=0) 0 1 2 p(l=1) -1, 0, +1 3 6 18 9 d(l=2) 5 10 -2,-1,0,+1,+2 N=(n=4) s(l=0) 0 1 2 p(l=1) -1, 0, +1 3 16 6 d(l=2) -2,-1,0,+1,+2 5 10 32 f(l=3) -3,-2,-1,0,+1,+2,+3 7 14  CONCLUSION Each principal level of quantum number, n contains a total n sublevels Each sublevel of quantum No, l contains a total 2l + 1 orbitals Each orbital can hold two electrons The maximum number of e in each energy level is 2n2 The shorthand notation frequently used to donate the electronic structure of an atom combines the numerical value of the principal quantum No, n, the lowercase letter rotation for the azimuthal quantum No and a superscript showing the number of electrons in each orbital. Thus, the shorthand notation for the electronic structure of bromine which has an atomic number of 35 is 1s2, 2s2, 2p6, 3s2, 3p6, 3d10, 4s2 4p5 The four quantum numbers: n = 1, 2, 3, … l = 0, 1, 2, 3, …. (n-1) ml = 0, ±1, ±2, ±3, … ±l ms = +1/2 or -1/2 NOTE The energy state of the electrons depends not only on the principal quantum number n, but also on the orbital quantum number. This is associated with the circumstance that an electron in an atom is not only attracted by the nucleus, but is also repelled by the electrons between the given electron and the nucleus. The internal electron layers form a peculiar shield that weakens the attraction to the nucleus  ORBITAL DIAGRAMS HUND’S RULE An atomic orbital diagram shows the electron distribution in an atom by means of a diagram which accounts for the distribution by all four quantum numbers. An orbital is shown by a box, circle or line. An electron is shown by an arrow. The arrows also show the spin of the electron so that when two electrons are in the same orbital, the arrows point in opposite directions to represent their opposing spins. Sublevels are shown by a designation under the appropriate orbitals Orbital diagram indicates the number of electrons in each orbital and their respective spins: 1s2 2s2 2p1 Electron configuration of boron B  Definition (Hund’s Rule) In an atom in which orbitals of equal energy are to be filled by electrons, the order of filling is such that as many electrons remain unpaired as possible I: Ms are the same, while their spin are I C antiparallel 2p II: 2p electrons occupy different orbitals (i.e. have different Ms and their spins II C are opposite) III Different orbits correspond to the 2 III C s p electrons while their spins are parallel 2s Among the 3 diagrams, the third is correct and it corresponds to the greatest value of the total spin of an atom. (In I & II the sum of the spin of all electrons is zero while, for the third diagram it is unity.  Therefore Hund’s rule states that the maximum value of the total spin of an atom corresponds to the stable i.e. unexcited state in which the atom has the smallest possible energy; at any other distribution of the electrons, the energy of the atom will be higher, so that it will be in an excited, unstable state. In other words the distribution of the electrons within the limits of an energy sublevel at which the absolute value of the total spin of the atom is maximum corresponds to the stable state of an atom. 1st Rule The sequence of filling of the atomic electron orbitals depends on the values of the principal and orbital quantum number. And the energy of an electron rises as the sum of these 2 quantum number increases, i.e. with increasing n+l. With an increase in the charge of the nucleus of an atom, the electron orbitals are filled consecutively from orbitals with a smaller value of the sum of the principal and orbital quantum (n + l) to orbitals with a greater value of this sum. 2nd Rule At identical values of the sum n+l the orbital are filled consecutively in the direction of the growth in the value of the principal quantum number, n  Note: The chemical properties of the elements are determined first of all by the structure of the outer electron layer of their atom and depend only to a smaller extent on the content of the structure of the preceding (inner) electron layers. All the d (transition) elements are METALS whereas the filling of the outer P sublevel result in a transit from a metal to a typical non-metal and finally, to a noble gas. The outer orbitals of d metals are filled in order of energy stability and an increased energy stability is a property of electrons configurations with exactly a HALF-FILLED or TOTAL-FILLED sublevel (e.g. structures containing 3 electrons in the outer layer, five d electrons in the layer preceding the outer one, or seven f electrons in a still deeper layer).  Violation The violations of the “normal” sequence of filling the energy states in (lanthanum (Z =57) (the appearances of a 5d instead of a 4f electron) and cesium (the simultaneous appearance of two 4f election). This can be explained as follows: upon an increase in the charge of the nucleus the electrostatic attraction to it of an electron in a given energy sublevel becomes stronger and the energy of the electron diminishes. The energy of the electron in different sublevels changes differently because the charge of the nucleus is increased to a different extent with respect to these electrons. In particular, the energy of 4f of electrons diminishes with a growth in the charge of the nucleus more sharply than the energy of the 5d electrons. E 4f 5d Z 57 58 Dependence of the energy of the 4f and 5d electrons on the nuclear charge.  Consequently in La (Z =57), the energy of the 5d electrons is found to be lower and in cesium (Z=58) higher than that of the 4f electrons. Accordingly, the electron that in La is in the sublevel 5d in cesium passes to the sublevel 4f 57La 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d10 5s2 5p6 5d1 6s2 58Ce 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d10 4f2 5s2 5p6 6s2 The most stable state of an electron in an atom corresponds to the minimum possible value of its energy  Tutorial Questions Why does the ns orbital go before the (n−1)d orbital when writing transition metal electron configurations? The valence shell of the element X contains 2 electrons in a 5s subshell. Element X also has a partially filled 4d subshell. What type of element is X? How many electrons does H2SO4 have? How many atoms does each element have? Oxygen reacts with fluorine to form only OF2, but sulphur which is in the same group 16 as oxygen, reacts with fluorine to form SF2, SF4 and SF6. Explain?  Los Alamos National Laboratory's Chemistry Division Group** Periodic Table of the Elements Period 1 18 IA VIIIA 1A 8A 1 2 13 14 15 16 17 2 1 H IIA IIIA IVA VA VIA VIIA He 1.008 2A 3A 4A 5A 6A 7A 4.003 3 4 5 6 7 8 9 10 2 Li Be B C N O F Ne 6.941 9.012 10.81 12.01 14.01 16.00 19.00 20.18 11 12 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 3 Na Mg IIIB IVB VB VIB VIIB ------- VIII ------- IB IIB Al Si P S Cl Ar 22.99 24.31 3B 4B 5B 6B 7B ------- 8 ------- 1B 2B 26.98 28.09 30.97 32.07 35.45 39.95 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 4 K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr 39.10 40.08 44.96 47.88 50.94 52.00 54.94 55.85 58.47 58.69 63.55 65.39 69.72 72.59 74.92 78.96 79.90 83.80 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 5 Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe 85.47 87.62 88.91 91.22 92.91 95.94 (98) 101.1 102.9 106.4 107.9 112.4 114.8 118.7 121.8 127.6 126.9 131.3 55 56 57 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 6 Cs Ba La* Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn 132.9 137.3 138.9 178.5 180.9 183.9 186.2 190.2 190.2 195.1 197.0 200.5 204.4 207.2 209.0 (210) (210) (222) 87 88 89 104 105 106 107 108 109 110 111 112 114 116 118 7 Fr Ra Ac~ Rf Db Sg Bh Hs Mt --- --- --- --- --- --- (223) (226) (227) (257) (260) (263) (262) (265) (266) () () () () () () 58 59 60 61 62 63 64 65 66 67 68 69 70 71 Lanthanide Series* Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu 140.1 140.9 144.2 (147) 150.4 152.0 157.3 158.9 162.5 164.9 167.3 168.9 173.0 175.0 90 91 92 93 94 95 96 97 98 99 100 101 102 103 Actinide Series~ Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr 232.0 (231) (238) (237) (242) (243) (247) (247) (249) (254) (253) (256) (254) (257)  Periodic Table VALENCE: The valence of an atom is the ability of the atom to enter into chemical combination with other elements and is often determined by the number of electron in the outer most combined s p level. O2-referred valence and H2-referred valence Mg- 2; Al- 3; Ge- 4; Na- 1; P- 3, 5; Mn- 2, 3, 4, 6, 7 ELECTRONEGATIVITY: Describes the tendency of an atom to gain an electron. Atoms with almost completely filled outer energy level, like Chlorine is strongly electronegative and readily accepts electron.  EXCITATION, IONIZATION AND IONIZATION ENERGIES: When atoms are exposed to high energy high temperature or exposed to fast-moving electrons from nearly any source, they tend to become excited and to give off energy in the form of radiation. The nature of the radiation emitted depends on the excitation which is used. When atoms through collisions, absorb energy and become excited, they move in the process to higher allowed electronic energy levels. Once excited the atoms will be unstable and will tend to return to lower electronic energy levels, ultimately reaching the lower energy level, the ground state of the atom. Under excitation the atom will quickly reach a state of dynamic equilibrium in which some atoms are releasing energy at the same rate that it is being absorbed by other.  In a process in which an excited atom makes a transition to a lower energy level, a photon of light may be emitted (A ray of light can be considered to consist of photons which appear to have some properties characteristic of particles). The wavelength of the photon is related to the magnitude of the change in energy (ΔE) of the atom by hc DEatom = E Photon = (2)  where h is a physical constant, called = Planck’s constant 6.626 x 10-34 J.S, c is the speed of light = 2.998 x 108 m/s and  the wavelength of the photon in meters.  IONIZATION ENERGY and AFFINITY ELECRON The amount of energy needed to detach an electron from an atom with conversion of the latter into a positive ion is called ionization energy. The smallest voltage of the field at which the speed of the electrons becomes sufficient for ionization of the atoms is the ionization potential of the atoms and is expressed in volts. The energy of an electron is often expressed in electron volts (eV) 1eV is the energy acquired by an electron in an accelerating electric field with a potential difference of one volt 1eV = 1.6x10-19J = 96.5KJ/mol (1 kJ·mol−1 is equal to 0.239 kcal·mol−1 or 1.04×10−2 eV per particle) The ionization energy expressed in electron-volts numerically equals the ionization potential expressed in volts. The first ionization energy, of an atom is the energy change of the formation of positive ion from the gaseous atom; X(g) = X+(g) +e 1st E-ionization energy  The magnitude of the E, can be a measure of the greater as smaller “metallicity” of an element the smaller the E, the easier it is to detach an electron from the atom and the stronger should the metallic properties of the element be expressed. An increase in the atomic number of element is attended by diminishing of the ionization energy in the groups. This fronts to an increase in the metallic properties and accordingly, a decrease in the non-metallic properties of the relevant element. This regularity is associated with the growth in the atomic radii. - the smaller the atom, the more tightly its electrons are held to the nucleus and the more difficulty they are to be removed. In addition, an increase in the number of intermediate electron layers between the nucleus of an atom and the outer electrons leads to greater screaming of the nucleus, i.e. diminishing its effective charge. Both these factors (the growing of its effective charge) lead to weakening of the bond of the outer electrons with the nucleus and consequently, to lowering of the ionization energy. Large atoms such as those of the alkali metals have relatively low ionization energies because the outer electrons are far away from the positive charge of the nucleus.  Summary The properties of an atom are determined by the following factors: – The atomic number that corresponds to the number of electrons or protons in a neutral atom – The mass of the atom – The spatial distribution of the electrons in orbits around the nucleus – The energy of the electrons in the atom and – The ease of adding or removing one or more electrons from the atom to create a charged ion.  Tutorial Determine the electron configuration for a sulfur atom, a selenium atom and a tellurium atom. Explain why these three elements display similar characteristics? Explain how an “inert gas” like xenon (Xe) can react with fluorine to form a stable compound. Why does it not react with nitrogen? Calculate the wavelength of radiation emitted when an electron in the hydrogen atom jumps from an excited n = 2 state to the n = 1.  Atomic Theory John Dalton (1808) According to British chemist Dalton’s atomic theory, all matter, whether an element, a compound or a mixture is composed of small particles called atoms. The postulates of this theory may be stated as follows: All matter is made of very tiny particles called atoms. Atoms are indivisible particles, which cannot be created or destroyed in a chemical reaction. Atoms of a given element are identical in mass and chemical properties  Atoms of different elements have different masses and chemical properties. Atoms combine in the ratio of small whole numbers to form compounds The relative number and kinds of atoms are constant in a given compound. Dalton was the first scientist to use the symbols for elements in a very specific sense. When he used a symbol for an element he also meant a definite quantity of that element, that is, one atom of that element.  Berzilius suggested that the symbols of elements be made from 1 or 2 letters of the name of the element. In the beginning, the names of elements were derived from the name of the place where they were found for the first time. For example, the name copper was taken from Cyprus. Some names were taken from specific colors. Eg, gold was taken from the English word meaning yellow. Now-a-days, IUPAC (International Union Of Pure And Applied Chemistry) approves names of elements. Many of the symbols are the first one or two letters of the element’s name in English. The first letter of a symbol is always written as a capital letter (uppercase) and the second letter as a small letter (lowercase).  Thomson’s Theory The idea of an atom as indivisible particles proposed by Dalton continued until the year 1897 when British Physicist J.J. Thomson discovered negatively charged particles which were later named electrons. Thomson’s Atomic Model- Postulates (1904) According to the postulates of Thomson’s atomic model, an atom resembles a sphere of positive charge with electrons (negatively charged particles) present inside the sphere. The positive and negative charge is equal in magnitude and therefore an atom has no charge as a whole and is electrically neutral. Thomson’s atomic model resembles a spherical plum pudding as well as a watermelon. It resembles a plum pudding because the electrons in the model look like the dry fruits embedded in a sphere of positive charge just like a spherical plum pudding.  The model has also been compared to a watermelon because the red edible part of a watermelon was compared to the sphere having a positive charge and the black seeds filling the watermelon looked similar to the electrons inside the sphere. Limitations of Thomson’s Atomic Model Thomson’s atomic model failed to explain how the positive charge holds on the electrons inside the atom. It also failed to explain an atom’s stability. The theory did not mention anything about the nucleus of an atom. It was unable to explain the scattering experiment of Rutherford.  The energy lost by the electron in the abrupt transition is precisely the same as the energy of the quantum of emitted light. An electron jumping from orbit n=3 to orbit n=2, emitting a photon of red light with an energy of 1.89 eV. In the Bohr model of the atom, electrons travel in defined circular orbits around the nucleus. The orbits are labeled by an integer, the quantum number n. Electrons can jump from one orbit to another by emitting or absorbing energy.  Limitations of Bohr’s Model of an Atom Bohr’s model of an atom failed to explain the Zeeman Effect (effect of magnetic field on the spectra of atoms). It also failed to explain the Stark effect (effect of electric field on the spectra of atoms). It violates the Heisenberg Uncertainty Principle (dual nature of matter and waves) It could not explain the spectra obtained from larger atoms. STRUCTURE AND PROPERTIES OF ATOMIC NUCLEI. RADIOACTIVITY Radioactivity: This is a phenomenon of the emission of radiation by certain element capable of penetrating through a substance, ionizing air, and of causing photographic plates to darkened. Radioactivity defined as the spontaneous emission of particles (alpha, beta, neutron) or radiation (gamma, K capture), or both at the same time, from the decay of certain nuclides that these particles are, due to an adjustment of their internal structure. Radioactive decay (also known as nuclear decay or radioactivity) is the process by which an unstable atomic nucleus loses energy (in terms of mass in its rest frame) by emitting particles or radiation, or both. Radioactivity can be natural or artificial. In natural radioactivity, the substance already has radioactivity in the natural state. In artificial radioactivity, the radioactivity has been induced by irradiation  STRUCTURE AND PROPERTIES OF ATOMIC NUCLEI. RADIOACTIVITY This phenomenon (Radioactivity) was first discovered in uranium compounds by the French physicist A. BECQUEREL. Investigation of the Curies (Pierre) and of the British physicist RUTHERFORD showed that radioactive radiation is not homogeneous: a magnetic field causes it to divide into three beams, one of which does not change its original direction, while the other 2 deviate in opposite directions. The rays that do no deviate in a magnetic field and, consequently, have no electric charge, were called GRAMMA RAYS. They are electromagnetic radiation similar to X-rays and having a very high penetrability. The deflection of the other outer 2 teams under the action of magnetic field indicates that these beams consist of electrically charged particles. The opposite direction of the observed deflecting witness that one beam contains negatively charged particles (BETA RAYS), while the other (ALPHA RAYS) CONTAINS POSITIVELY CHARGED PARTICLES. The beta rays were found to be a stream of rapidly moving electrons. The positively charged alpha rays were found to consist of particles whose mass equals that of a helium atom and whose charge is absolute value is double that of an electron.  Rutherford proved by direct experiments that these particles are charged helium atoms. The results of the experiment proved that Radium atoms in the process of radioactive mission disintegrate (decay), transforming into atom of other elements, particularly into helium atoms  4 226 88 Ra ⎯ ⎯→ 2 He + 222 86 Rn NUCLEAR MODEL OF THE ATOM According to the model proposed in 1903/1904 by J.J Thomson, an atom consists of a positive charge uniformly distributed over the entire volume of the atom and electron migrating inside this charge. To verify Thomson’s hypothesis and establish more accurately the internal structure of an atom, E-Rutherford performed series of experiments involving scattering of alpha particles by thin metal plates (gold foil) in 1911  A M S Se C F Thin gold foil Set-up of alpha particle scattering experiment Source S of alpha rays was placed in lead capsule C with a borehole drilled in it in order to obtain a pencil of alpha particles flying in a definite direction. Upon reaching screen being coated with zinc sulphide, the alpha particles cause to grow the gold foil F placed between the radiation source and the screen. The flashes on the screen allowed the experimentalist to assess the deflection of the particles from the original direction, although the thickness of the foil was hundredths of thousands of atomic diameters. But a certain fraction of the particles was nevertheless deflected through small angles while from time to time the particles sharply changed the direction of their motion, and some of them even rebounded from the foil as if they had encountered a massive obstacle. If followed from these results that the predominating part of the space occupied by an atom of a metal contains no heavy particles only electrons can be there. And the mass of main alpha particles is almost 7,500 times greater than that of an electron, so that a collision with the latter cannot virtually affect the direction of the motion. Cases of where deflection and even rebounding of the alpha particles however signify that an atom contains heavy particles in which the predominating part of the entire mass of the atom is concentrated. This nucleus occupies a very small volume and must have a positive charge. This is why that nucleus repels the positively charged alpha particles.  On the basis of these considerations, Rutherford in 1911 proposed the following model of the structure of an atom which is known as the structure of an atom also regarded as the nuclear model of the atom. An atom consists of a positively charged nucleus in which the predominating part of the atom’s mass is concentrated, and of electrons orbiting around it. The positive charged of the nucleus is neutralized by the total negative charge of the electrons, so that the atom as a whole is electrically neutral. The centrifugal force produced owing to rotation of the electrons around the nucleus is balanced by the force or electrostatic attraction of the electrons to the oppositively charged nucleus. The size of the nucleus is very small in comparison with that of an atom is of the order of 10-8cm, whereas the diameter of the nucleus is of the order of 10-13 to 10-12 cm. This experiment made it possible not only to detect an atomic nucleus, but also to determine its charge. It followed that the charge of a nucleus (expressed in units of electron charge) numerically equals the atomic number) of the element in the periodic table.  The physical meaning of the atomic number of an element in the periodic table was found to be a very important constant of an element expressing the positive charge of its atom’s nucleus. It can be seen that from their electrons orbiting about the nucleus also equal to the atomic number of the element. This discovery eliminated an apparent contradiction in the periodic table the position of some of the elements with a greater atomic mass ahead of elements with a smaller atomic mass (127.6 52 Fe − and −126 53.9 I ,..39.9 18 Ar − and − 39 19 K ,..58.9 27 Co − and − 58.7 28 Ni ) There is no contradiction here because the placement of an element in the table is determined by the charge of the atomic nucleus. The charge of a Fe atom is 52, and that of an iodine atom 53-established experimentally. Thus, the charge of the atomic nucleus is the basic quantity determining the properties of an element and its position in the periodic table. The determination of the atomic number of the element according to the charges of the nuclei of their atoms made it possible to establish the total number of position in the periodic table.  CONTRADICTIONS IN RUTHERFORD’S THEORY The theory could not explain the stability of the atom. An electron orbiting about a positively charged nucleus ought to emit electromagnetic energy in the form of high waves. And by so doing, the electron lose part of its energy which would result in the violation of equilibrium between the centrifugal force associated with the rotation of the electron and the force of electrostatic attraction of the electron to the nucleus. To restore equilibrium, the electron must move closer to the nucleus. Thus, an electron continuously emitting electromagnetic energy and moving along spiral will approach the nucleus. After exhausting all its energy, it should “fall” onto the nucleus, and the atom will stop existing. This conclusion contradicts the real properties of atomic, without decay for an exceedingly long time. The model led to improper conclusions on the nature of atomic spectra. The radiation of a glowing solid or liquid body consists of electromagnetic waves of every possible frequency continuous spectrum. An appreciable step in the development of the atomic structure concept was made by NEILS BOHR who proposed a theory combining the nuclear model of the atom with the quantum theory of light.  QUANTUM THEORY OF LIGHT MAX PLANCK showed that radiant energy is emitted and absorbed by bodies not continuously, but discretely i.e. in separate portions (quanta). Frequency of the energy emitted or absorbed, ϑ is given by the Einstein equation (Planck) ΔE = E2 – E1 = hϑ.--------------------------- (3) The proportionality constant h-the Planck constant, E2 -the final energy of the atom after the jump, E1 - the initial energy of the atom before the jump, a negative Δ E means that energy is emitted. EINSTEIN concluded that electromagnetic (radiant) energy exists only in the form of quanta and that consequently radiation is a stream of indivisible material “particles” (photons) whose energy is determined by the Planck equation. It follows from the quantum theory of light that a photon behaves like a particle i.e. displays corpuscular properties. It however, also has wave properties. It has wave - particle duality Bohr theory failed to predict properly the energy levels of some other simple systems such as vibrating or rotating diatomic molecules.  WAVE MECHANICS QUANTUM MECHANICS AND WAVE FUNCTION The particle properties of the photon are expressed by the Planck equation E = hϑ ------------------------(4) according to which the photon is indivisible and exists as a discrete formation. The wave properties of the photon, on the other hand are expressed in the equation. λϑ = c -------------------------(5) Relating the wavelength of electromagnetic oscillation to its frequency ϑ and the speed of propagation, c Thus hc E = -----------------------(6)   But a photon having the energy, E also possesses a certain mass in accordance with the Einstein equation E = mc2 -------------------------------------------(7) but hc mc 2 =  Whence h  = mc The product mc is called the momentum of the body h -----------------------------------------(8) = p Eq. 8 was first derived by de Broglie by assuming that a photon has both wave and particle properties. He assumed that wave-particle duality is a property of electrons in addition to photons. Consequently, an electron must display wave properties and like a photon, it must obey the last equation, which is often called de BROGLIE EQUATION The fact that an electron has a wavelength does not necessarily mean that it is a wave; it does mean that the motion of the electron is governed by the same differential equations that describe wave motion d 2 s 4 2 + 2 s = 0 ----------------------(9) dx 2  Eq 9 Schrodinger standing waves equation. Where s is the max. transverse displacement, or amplitude, of a segment of string dx, x is the distance along the string, and λ is the wavelength.  WAVE FUNCTION Based on the concept of Schrödinger that the state of an electron moving in an atom must be described by the equation of a standing electromagnetic wave. By substituting the wave function ψ for the amplitude s, the de Broglie wavelength, h/(mv) = h/p, for λ, and E-V for the kinetic energy ½ mv2. The result is d 2 8 2 m 2 + 2 ( E − V ) = 0 -------------------------------(10) dx h where E-represents total energy and V represents potential energy. The three - dimensional form will be d 2 d 2 d 2 8 2 m 2 + 2 + 2 + 2 ( E − V ) = 0 -----------------------------(11) dx dy dz h wave functions are sinusoidal for the particle in the given system. The wave function ψ is of special significance for characterizing the state of an electron. Like the amplitude of any wave process, it can take on both positive and negative values. The quantity ψ2 however, is always positive. The higher the values ψ2 in a given region, the greater is the probability of an electron displaying its action here i.e. if its existence being detected in a physical process. To be more precisely, the probability of detecting an electron in a certain small volume is expressed by ψ2 ΔV. Thus, the quantity ψ2 itself expresses the DENSITY OF THE PROBABILITY of finding an electron in the corresponding region of space The density of an electron cloud is proportional to the square of the wave function. From the properties of waves, the latter can have finite amplitudes only inside the system, the amplitude at the walls must the zero.  Antinodes – maximum amplitude Nodes n – amplitude of the oscillation vanishes If the length of a one-dimensional atom (the distance λ1 =2d =2d/1 between the walls is d and n is an integer equal to 1,2,3,… A The wavelength, λ of the allowed waves n=1 2d n n  = --------------(12) A λ2 =d =2d/2 n By combining de Broglie’s equation n n n n=2 h 2d nh -A = = or mv = λ4=d =2d/4 mv n 2d n n Energy, E to certain allowed values 1 1 n=4 E =  mv2 = (mv)2 2 2 d 2 1  nh  h2 E=   = n 2 ----(13) 2m  2d  8md 2 Some wave functions of a particle in one-dimensional box  This equation tells us that a particle, of any kind confined to move in a region of any length will have only certain energies allowed to it. Those energies (from Eq. 13) depend on the mass, m of the particle, the interval d through which it can move, and the quantum number, n. Implications of de Broglie relation 1. A confined particle cannot have zero energy since n cannot be zero if a wave is to be present. Since n can equal 1,2,3.. the particles may take on many energies, the lowest value will be when n=l 2. The lowest energy available to a particle depends markedly on its mass and on the size of the space to which it is confined. This energy varies inversely with the mass every time the mass is decreased by a factor of 2 the energy is doubled. The minimum energy also varies inversely with the square of the length through which the particle can move.  RADIOACTIVE ISOTOPES Radioactive hydrogen isotope 3H-Tritium (T) (with half-life of about 12 years) prepared only artificially. Tritium is unstable. The elements of higher Z contain at least as many neutrons as protons, but because of the shielding effect of the innermost electrons this does not affect the material properties. In the atoms of higher Z, the number of neutrons considerable exceeds the number of protons, and these elements are often referred to as the heavy elements. E.g. of natural uranium which is artificially produced by neutron bombardment of thorium. The nucleus itself eventually becomes unstable and the addition of a further neutron may cause nuclear “fission”. The atom then disintegrates with the production of two new atoms and a debris of elementary particles and radiations. U − 99% 238 92 235 233 0.7% 92U and 92U  ISOTOPIC INDICATIORS (TRACERS) Isotopic indicators or “labeled atoms” (tracer atom) are widely used in studying the mechanism of chemical and biological processes. This use is based on the possibility of tracing the ways of transition of an element in chemical transformation by measuring the concentration of one of its isotopes in one of the substances taken for a reaction. Since all the isotopes of the same element behave virtually identically in chemical reactions, by determining the change in the composition of the isotopes of a given element in the various products, we can trace its path. For example, the use of the heavy oxygen isotope 18O in studying how carbon dioxide is assimilated by plants. (Carbon dioxide and water enriched with 18O were used for the experiments) showed that the process occurs according to the following reaction, in which the isotope 18O is marked with an asterisk. 6CO2 + 12H2O* = C6H12O6 + 6H2O + 6O2* 6CO2* + 12H2O = C6H12O6* + 6H2O* + 6O2 It was thus established that the oxygen returned by plants to the atmosphere is taken completely from water and not from carbon dioxide. 18O a stable isotope which is quite rare in nature (abundance = 0.20%). This isotope is readily detected by using a mass spectrometer. Carbon-14 can be used also. In Medicine: The high-energy radiation given off by Radium is used in the treatment of cancer.  ISOTOPIC INDICATIORS (TRACERS) Tracing food sources and diets The quantities of the different isotopes can be measured by mass spectrometry and compared to a standard; the result (e.g. the delta of the 13C = δ13C) is expressed as parts per thousand (‰): Stable carbon isotopes in carbon dioxide are utilized differentially by plants during photosynthesis.  RADIOACTIVITY NUCLEAR REACTIONS Nuclear reactions differ form ordinary chemical reactions. 1. In ordinary reactions, the different isotopes of an element show virtually identical chemical properties; in nuclear reactions they behave quite differently. 12 The chemical properties of 6 C and 146C are very similar but the 126C nucleus is extremely stable while the 146Cnucleus decomposes spontaneously. 2. The nuclear reactivity of an element is essentially independent of its state of chemical combination. E.g. Ra2+ ion in RaCl2 and elementary Radium behave similarly from a nuclear stand point. In ordinary chemical reaction on the other hand, the radium atom and the Ra2+ ion behave quite differently since they have different outer electronic structures. 3. Nuclear reaction frequently involve the conversion of one element to another (with a change in the number of protons in the nucleus. Elements in ordinary chemical reaction retain their identity.  226 88Ra ⎯ ⎯→ He + 4 2 222 Rn 86 4. Nuclear reactions are accompanied by energy changes which exceed by several orders of magnitude, those associated with ordinary chemical reaction. The energy evolved when a gram of radium undergo radioactive decay is about 500,000 times as great as that given off when an equal amount of radium reacts with chlorine to form radium chloride.  RADIOACTIVITY By radioactivity is meant the spontaneous transformation of an unstable isotope of one chemical element into an isotope of another element attended by the emission of elementary particles or nuclei (for instance alpha particles). The rate of radioactive transformations is characterized by the radioactive decay constant which shows part of the total number of atom of a radioactive isotopes decays in one second. The greater the radioactive decays, the more rapidly does an isotope decay. The number of atoms of a radioactive isotope decaying in unit time is propositional to the total number of atom of this isotope present at the given moment. The time needed for half of the original amount of a radioactive element to decay is called the HALF-LIFE. This quantity characterizes the lifetime of an element. It ranges from fraction of a second to hundreds of millions of years. E.g., the half-life of Radon is 3.85 days, of Radium is 1620 years, of Carbon 5,700 years, of uranium 4500 million years. The main kinds of radioactive radiation include alpha, beta and gamma radiation.  Beta particles Positively negatively charge charged plate Radioactive sample Gamma particles No charge Alpha particles Negatively positive charge charge plate 2He +2e  Alpha Radiation which consists of a stream of positively charge particles (alpha particles) that carry a charge of +2 and have a mass of 4 on the atomic mass scale. In alpha decay, the nucleus of an atom emits 2 protons and 2 neutrons bound in a nucleus of the helium atom 42He. The result is lowering of the charge of the initial radioactive nucleus by 2, and of its mass number by 4. Thus alpha decay results in the formation of an atom of an element having an atomic number two less than the original isotope. 238 92 U = He +4 2 234 90 Th Beta Radiation (decay) which is made up of a stream of negatively charged particles (beta particles) that have all the properties of electrons. (mass charge ≈-1) Beta particles results from the transformation of a neutron (mass =l charge =o) at the surface of the nucleus into a proton (mass=l, charge = +1). Consequently beta-emission leaves the mass number unchanged but increases the atomic number by one unit 234 90Th= −1 e+0 234 91 Pa The process of beta decay can be written as neutron →proton + electron or n → P+e-. The electron appearing in this transformation flies out of the nucleus, and the positive charge of the latter grows by unity. A proton may also transform into a neutron as: Protons → neutron +Positron or P → n+e+ A positron, whose symbol is e+, is an elementary particle with a mass equal to that of an electron, but carrying a positive electric charge. The charges of an electron and a positron are identical in absolute value. A proton may transform into a neutron with the formation of a positron when the instability of the nucleus is due to an excess content of protons in it. One of the protons in the nucleus transforms into a neutron, the positron that appears flies out of the nucleus, and the charge of the nucleus diminishes by unity. This kind of radioactive decay is called POSITRON BETA DECAY (+ decay) in contrast to the previously considered ELECTRON BETA DECAY (- decay). As a result of beta decay the atom is transformed into a new element whose atomic number is one greater (with - decay) or one less (with + decay) than that of the original isotope. 30 15 P → 30 14 Si + 0 1e (+ decay) 28 13 Al → 28 14 Si + 0 −1 e (- decay) 11 6 C → 11 5 B + 0 1e (+ decay) 6 14 C →14N + 0e 7 −1 (- decay)  GAMMA Radiation, electromagnetic radiation of very short wavelength (λ=0.0005 to 0.1nm) i.e. high –energy photons. The emission of gamma radiation accompanies virtually all nuclear reaction as the result of an energy change within the nucleus, whereby an unstable, excited nucleus remitting form alpha – or beta-emission given off a photon and drop to a lower more stable energy state (no mass change, no change in Z). INTERACTION OF RADIATION The commonly instrument used to detect and measure radiation is the Scintillation counter. We have also Geiger Muller counter. The harmful effect of radiation upon human beings is caused by its ability to ionize and ultimately destroy the organic molecules of which body cells are composed. The extent of damage depends upon 1. the energy and the 2. types of radiation. The former is expressed in GRAYS. A gray corresponds to the absorption of one joule per kilogram of tissue. The total biological effect of radiation is expressed in rems. Number of Rems = n x (number of grays) where n is 100 for , , and x radiation and 1000 for  radiation or high –energy neutrons. Effect of exposure to a single dose of radiation Dose (Rems) Probable effect 0 to 25 No observable effect 25 to 50 Small decrease in white blood cell count 50 to 100 Lesions, marked decrease in white blood cells 100 to 200 Nausea, vomiting, loss of hair 200 to 500 Hemorrhaging, ulcers, possible death 5000 + Fatal. Radiation can produce mutations in plants and animals by bringing about changes in chromosomes. Federal research council has set an upper limit of 0.17 per year above background as the max. dosage to which major population group can be exposed.  USE FULNESS In Medicine Treatment of cancer to destroy or arrest the growth of malignant tissue (Radium). Even cheaper cobalt-60. Sodium iodine containing radioactive iodine (131I or 126I) used to destroy the malignant cells (cancer of the thyroid) in human beings. RATE OF RADIOACTIVE DECAY FIRST ORDER RATE LAW The first order equation reaction X- products; rate = − Dconc.x =k(conc. X) − Dconc.x Dt = − kDt conc.x log10 conc. X = log10 (conc. X)o – Kt / 2.30 (ΔConc x = conc of x at t – conc of x at t = zero; conc x – (conc x)0 (Δt = t – 0 = t) where (conc. X)o is the initial concentration and t is the elapsed time (Xo is the amount of radioactive substance at zero time (when the counting process starts ) and X is the amount remaining after time t. The first order rate constant K, is the characteristic of the isotope undergoing radioactive decay. (conc.x ) o kt log 10 = ----------------------------------(14) Conc.x ) 2.30  Derivation of Eq. 14 is as follows: dx Rate = − = kx dt dx = − kdt x x t dx Integrating from t = 0 to t and from x0 to x  x0 x = − K  dt 0 ln x – ln x0 = - Kt and ln X = 2.30 log10X Kt log 10 x − log 10 x0 = − 2.30 x0 Kt 2.30 x0 Since X = X0/2; log 10 = or log 10 =t X0 = 2X; x 2.30 K x X0/X = 2 2.30 0.693 t 0.5 = log 10 2 = -----------(15) K K PROBLEM 1. The radioactive radium-192, which has a half life period of 74.4 days, is used as a source of material for industrial radiography. Determine the source intensity, as a percentage of the initial intensity, after i) 25 days ii) 50 days and iii) 100 days 2.The radioactive isotope of Cobalt, Co–60, has a half – life period of 5.62 years. Calculate the rate of constant for the isotope decay How long will it take for Co–60 to reduce to 85 % of its original value? If a hospital purchases 20 mg of this isotope, how much will remain after 10 years? 3. The common radioactive isotope of radium has a half – life of 1620 years. Calculate i) The first order rate constant for the decay of radium – 226 ii The fraction of a sample of this isotope which will remain after 100 years. iii) Use your results to comment on the global attempt to protect the environment  ATOMIC BONDING There are two types of bonds: Primary Secondary Primary Bonds: Primary bonds are the strongest bonds which hold atoms together. The three types of primary bonds are: Ionic Bonds Covalent Bonds Metallic Bonds bonding is achieved when atoms fill their outer s and p levels.  Bonding Energies and Melting Temperatures for Various Substances  Bonding Models Bonding holds atoms together to form solids materials In solids, atoms are held at preferred distances from each other (equilibrium distances) Distances larger or smaller than equilibrium distances are not preferred. Equilibrium spacing r0 is approximately 0.3nm Consequently, as atomic bonds are stretched, atoms tend to attract each other, and as the bonds are compressed, atoms repel each other. Simple bonding models assume that the total bonding results from the sum of two forces: an attractive force (FA ) and a repulsive (FR). The net force F N = F A + F R The repulsive force dominates at small distances, and the attractive force dominates at larger distances. At equilibrium they are just equal  Bonding Forces and Energies It is convenient to work with energy than forces. Bonding energy (also called interaction energy or potential energy) between two isolated atoms at separation r is related to the force by The total energy has a minimum at the point of equilibrium separation. Bonding energy E0 corresponds to the energy at ro– the energy that would be required to separate these two atoms to an infinite separation. Interpretation: holding one atom at the origin, a second atom would repel that atom at separation r < ro and attract it when ro< r.  Bonding energy between two atoms The interaction energy at equilibrium is called the bonding energy between the two atoms. To break the bond, this energy must be supplied from outside. Breaking the bond means that the two atoms become infinitely separated. In real materials, containing many atoms, bonding is studied by expressing the bonding energy of the entire materials in terms of the separation distances between all atoms.  THE IONIC BOND Lost and gain of electrons Ionic bond is created between 2 unlike atoms with different electronegativities i.e. one atom donate its valence electrons to a different atom. Both atoms now have filled (or empty) outer energy levels but both have acquired an electrical charge and as ions. The donor of the electron is left with a positive charge and is a cation while the electron accepter acquires a net negative charge and is an anion. The oppositely charged ions are then attracted to one another to produce the ionic bond. THE IONIC BOND  Ionic Bonding Energy – minimum energy most stable – Energy balance of attractive and repulsive terms A B EN = EA + ER = − + r rn Repulsive energy ER Interatomic separation r Net energy EN Adapted from Fig. 2.8(b), Callister & Rethwisch 8e. Attractive energy EA 102  Examples: Ionic Bonding Predominant bonding in Ceramics NaCl MgO CaF 2 CsCl Give up electrons Acquire electrons Adapted from Fig. 2.7, Callister & Rethwisch 8e. (Fig. 2.7 is adapted from Linus Pauling, The Nature of the Chemical Bond, 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by Cornell University. 103  The ionic bond is non-directional. A positively charged Na+ Cl- Na+ Cl- will attract any adjacent Cl- equally in all directions. The more electropositive the metal and the more Na+ Cl- Na+ electronegative the non-metal, the greater the ionic contribution to bonding. LiFl is almost completely ionic MgO has a little covalent character in its bond sand Cl- Na + Cl- SiO2 is about half conic half covalent. The non-directional of ionic bond is due to the spherically symmetry of the electric field of an iron, i.e. The ionic bond between diminishes with the distance according to the same Na and Cl way regardless of directions. When a force is applied to NaCl crystal the electrical balance between the ions is upset. Partly for this reason, ionically bonded materials behave in a brittle manner. Electrical conductivity is also poor; when a voltage is applied the electrical charge is transferred by the movement of entire ion which does not move as easily as electrons. Ionic bond does not have saturability. The oppositely attracted charge ions retain their ability to interact electrostatically with other ions. The forces of attraction of oppositely charged ions must predominate over the force of mutual repulsion exerted between ions of the same sign. The absence of directionality and saturability in an ionic bond is the reason why ionic molecules tends to associate i.e. to combine with one another.  COVALENT BOND Covalent bonding requires that electron be shared between atoms in such a way that each atom has its outer sp orbital filled. For example, a silicon atom, which has a valence of 4 obtains 8 electrons in its outer energy shell by sharing its electrons with 4 surrounding silicon atoms. Therefore in Si 4 covalent bonds must be formed. In order for the covalent bonds to occur the Si atoms must be arranged as the bonds have a fixed DIRECTIONAL relationship with one another. In Si, C the arrangement produces a tetrahedron with angles of about 109o between the covalent  Si Si Si Si o o o Si Si Si 1090 o o o In Si, C a tetrahedral structure is formed with angles of about 109o required between ach covalent bond. A covalent chemical bond is formed by 2 electrons with anti parallel spins , this electron pair belonging to 2 atoms. The strength of a covalent bond grows with an increasing degree of overlapping of the interaction electron clouds. The ability of atoms to participate in the formation of a restricted number of covalent bonds is called SATURABILITY of covalent bond. The formation of a covalent bond is a result of overlapping of the valence electron clouds of the interaction atoms. But such overlapping is possible only with a definite mutual orientation of the electron cloud; here the overlap region is arranged in a definite direction with respect to the interacting atoms. In other words, a covalent bond is DIRECTIONAL.  DIRECTION OF A COVALENT BOND The properties of a molecule, its ability to enter into chemical reactions with other molecules (its reactivity) depend not only on the strength of the chemical bonds in the molecule, but to a considerable extent on its dimensional structure too. In a hydrogen molecule, the atomic S-electron clouds overlaps near the imaginary straight line joining the nuclei of the interacting atoms (i.e. the bond axis). A covalent bond formed in such a way is known as a  (sigma) bonds. overlapping of atomic electron clouds in a hydrogen molecule. If p-electron clouds are oriented along the bond axis, they can also participate in the formation of a sigma bond. Overlapping of the 2p-electron cloud of the fluorine atom and the Is-electron cloud of the hydrogen atom in the formation of a sigma bond in the molecule HF Note: In the formation of a chemical bond energy is always evolved as a result of the decrease in the potential energy of the system of interacting electrons and nuclei this is why the potential energy of a particle formed a (a molecule or crystal) is always less than the total potential energy of the initial free atom. The chemical bond in the molecule F2 is also sigma bond, it is formed by the 2p- electron clouds of the F atoms. Overlapping of the 2p-electron cloud of the fluorine atom and the Is-electron cloud of the hydrogen atom in the formation of a sigma bond in the molecule HF  When P- electron clouds oriented perpendicularly to the bond axis interact, two overlaps regions are formed at both rides of this axis instead of a single region. Such a covalent bond is called a π (pi) (Bond) z  - Bond + (b) x - - z z y + + π - Bond π - Bond - - y y Overlapping of the 2p-electron clouds in the molecule N2 a – sigma bond and 2-pi bonds  HYBRIDIZATION OF ATOMIC ELECTRON ORBITALS The method of hybridization of atomic orbital proceeds from the assumption that in the formation of a molecule, instead of the initial atomic s-, p-, and d-electron clouds, equivalent “blended” or hybrid electron clouds are formed that are stretched out in a direction towards the neighboring atoms, the result being their more complete overlapping with the electron clouds of these atoms. The more complete overlapping of the valence electron clouds the stronger the chemical bond formed and consequently to additional gain in energy. If this gain in energy is sufficient to more than compensate the expenditure of energy for the deformation of initial atomic electron clouds, such hybridization in the long run leads to diminishing of potential energy of the molecule formed and consequently to an increase in its stability.  sp-hybridization – Hybridization of 1s and 2p - + + orbital leading to the formation of two sp orbital BeF2 linear orientation F 2p Be Overlapping of the 2p electron clouds of the fluorine atoms with the 2s and 2p electron clouds of Beryllium atom. - + + - F Be F BeF2 straight line 180o F sp3-hybridization B F F equilateral triangle 120o BF3 CH4 Tetrahedron 109.5o i) 4 pairs of electrons around the central atom are all shared, the molecule is tetrahedral ii) when one pair is unshared, the structure is that of a pyramid with an equilateral triangle as large iii) 2 unshared pairs lead to a bent.  METALLIC BOND The metallic bond involves sharing of delocalized electron given a non-directional bond high electrical conductivity. The metallic bond forms when atom give up their valence electron, which then form an electron sea (or gas) leaving behind a core consisting of the nucleus and inner electron and the core becomes an ion with a positive charge. The positively charge atom cores are bonded by mutual attraction to the negatively charged electron. Metallic bonds are non directional; the electron holding he atoms together are not fixed in one position. This properly permit metals to have good ductility and to be deformed into useful shapes since when the former is bent and the atoms attempt to change their relationships to one another, the direction of the bond merely shifts rather then the bond breaking. Since the electrons are free to move, they lead to good thermal and electrical conductivity. Metallic bond. Metallic bond and electron cloud  Secondary Bonds: Secondary bonds are much weaker than primary bonds. They often provide a "weak link" for deformation or fracture. Example for secondary bonds are: Hydrogen Bonds and Van der Waals Bonds Hydrogen Bonds Hydrogen bonds are common in covalently bonded molecules which contain hydrogen, such as water (H2O). Since the bonds are primarily covalent, the electrons are shared between the hydrogen and oxygen atoms. However, the electrons tend to spend more time around the oxygen atom. This leads to a small positive charge around the hydrogen atoms, and a negative charge around the oxygen atom. When other molecules with this type of charge Hydrogen bonds. transfer are nearby, the negatively charged end of one molecule will be weakly attracted to the positively charged end of the other molecule. The attraction is weak because the charge transfer is small.  Van der Waals Bonds Van der Waals bonds are very weak compared to other types of bonds. These bonds are especially important in noble gases which are cooled to very low temperatures. The electrons surrounding an atom are always moving. At any given point in time, the electrons may be slightly shifted to one side of an atom, giving that side a very small negative charge. This may cause an attraction to a slightly positively charged atom nearby, creating a very weak bond. At most temperatures, thermal energy overwhelms the effects of Van der Waals bonds. Van Der Waals bonding is a secondary bonding, which exists between virtually all atoms or molecules, but its presence may be obscured if any of the three primary bonding types is present. Secondary bonding forces arise from atomic or molecular dipoles. In essence, an electron dipole exists whenever there is some separation of positive and negative portions of an atom or molecule. When an electron cloud density occurs at one side of an atom or molecule during the electron flight about the nucleus, Van Der Waals forces are generated. This creates a dipole wherein one side of the atom becomes electrically charged and the other side has deficiency of electrons and is considerably charged positive. 120 121  Crystal Lattice Structures Atoms are the building blocks of all materials. They are bonded or "held together" by cohesive forces in a manner characteristic of a particular material. In a liquid state the atoms of metal are of random arrangement, having short-range order. At times several unlike atoms will arrange themselves in the characteristic pattern of a particular metal. There is the phenomenon of random grouping, scattering, and regrouping for short periods of time is characteristic of the liquid state. As the random grouping mechanism becomes less frequent and the atomic movement of unlike atoms become more agitated, the material may become a gas. As the energy input decreases, the random movement of the unlike atoms becomes less frequent, the bonding becomes stronger, and ordered arrays of atoms form lattices. A crystal is a repeating array. In describing this structure we must distinguish between the pattern of repetition (the lattice type) and what is repeated (the unit cell). The most fundamental property of a crystal lattice is its symmetry. In three-dimensions, unit cells stack like boxes, filling the space, making the crystal. A Crystal: A repetitive, three dimensional arrangement of atoms or ions in a solid. It possess a periodicity that produces long-range order i.e. the local atomic (ionic) arrangement is repeated at regular intervals millions of times in the 3 dimensions of space.  The most stable arrangement of atoms in a crystal will be that which minimizes the energy per unit volume or in other words, the one that – Preserves electrical neutrality – Satisfies the directionality and discreteness of all covalent bonds – Minimizes strong ion-ion repulsion – Packs the atoms as closely as possible consistent with (1), (2) and (3)  Orientation of the unit cells in a lattice. Cubic Lattice Structure Hexagonal Lattice Structure Unit Cell: When a solid has a crystalline structure, the atoms are arranged in repeating structures called unit cells, which are the smallest units that show the full symmetry of a crystal. Lattice: The three dimensional array formed by the unit cells of a crystal is called lattice. Face-centered cubic (F.C.C.) Body-centered cubic (B.C.C. Hexagonal-close-packed (H.C.P.)  Crystal Systems 7 systems (7 unique unit cell shapes) to describe crystal structures. Lattice pts can be arranged in only 14 different arrays called Bravais lattices Lattice pt: The vertices of the unit cell Lattice parameter: The length of the unit cell edges The angles and lengths within the repeat unit determine the class to which the lattice cell belongs Basis: “group of things” located on a lattice Lattice + Basis = Crystal Structure  Cl-1 Cl-1 Cl-1 Cl-1 Simple Cubic (S.C) c c Cs+1 CN = 8 a b Cl-1 α b Cl-1 a Cl-1 Cl-1 Brass – SC r/R >0.73 CaTiO3 – SC Body Centered Cubic (B.C.C) Lattice Structure aSC = 2(rCs+ +RCl-)/√3 Face Centered Cubic (F.C.C) Lattice Structure Closed Packed Hexagonal (C.P.H) Lattice Structure  Relationship between the radius, r and lattice parameters a0√3 c a0√3 Cd c a CN=8 C Zn 2 b Mg α b 4r Co a0( BCC ) = a 3 Zr a0√2 Ti Fe-α, V, Cr, Mo, Na, W, SiF4, Mg(OH)2 Be a0√2 CN=12 Al2O3, 4r ZnS, a0( FCC ) = NiAs, c 2 CdI2 c a b CN=12 α b a a0√2 4 MgO, CH4 c=( )a0( HCP ) = 1.633a0 = 3.266r Al, Ni, Ag, Fe-ɣ, Cu, Au, CH4, NaCl, LiF 6  Miller Indices Indices of Directions – Determine the coordinates of 2 pts that lie in the direction of interest – h1, k1, l1 and h2, k2, l2 – Subtract the coordinates of the 2nd pt from those of the 1st pt: h’ = h2 - h1, k’ = k2 - k1 and l’ = l2 - l1, – Clear fractions from the differences – h’, k’ and l’ – to give indices in lowest integer values, h, k, l – Write the indices in square brackets without commas: [h k l] – If h < 0, we write [ĥ k l] z Directions Indices [h k l ] To determine the angle between directions OA [1 0 0] OB [1 1 0] If A = ui + vj + wk and B = F u’I + v’j +w’k, then, C OC [1 1 1] D A. B = A B cos φ where OD [2 0 1] E y φ is the angle between 0 OE [0 1 0] the 2 vectors A x B OF [1 1 2]  uu 1 + vv1 + ww1   = cos  2 2 2 1 12 12 12 1  −1 CB [0 0 1]  (u + v + w ) (u + v + w )  2 2 Indices of Planes Identify the coordinates intercepts of the plane. If the plane is parallel to one of the axes, the intercept is taken as infinity Take the reciprocal of the intercepts Clear fractions, but do not reduce to lowest integers Cite planes in parentheses – (h k l). A Plane Intercepts Indices A ∞,∞,1 (0 0 1) B B 1,1,1 (1 1 1) C 1,1,∞ (1 1 0) C D ½,⅔,1 (3 4 6) D  Linear density, ρL is the ratio of the C number of atoms centered along direction within one unit to the length of the line contained within one unit Plana