Chapter 5 Electronic Structure And Periodic Properties Of Elements PDF

Chapter 5 Electronic Structure and Periodic Properties of Elements 1 5.1. Electromagnetic energy  Visible light, x-rays, 𝛾 − 𝑟𝑎𝑦 and microwaves are some of the types of electromagnetic radiation (also called electromagnetic...

Chapter 5 Electronic Structure and Periodic Properties of Elements 1 5.1. Electromagnetic energy  Visible light, x-rays, 𝛾 − 𝑟𝑎𝑦 and microwaves are some of the types of electromagnetic radiation (also called electromagnetic energy or radiant energy).  All electromagnetic radiation consists of energy propagated by electric and magnetic fields that increase and decrease in intensity as they move through space.  This classical wave model explains why rainbows form, how magnifying glasses work, and many other familiar observations. 2 5.1.1. Characteristics of Light The Wave Nature of Light  The wave properties of electromagnetic radiation are described by three variables and one constant.  Frequency (v, Greek nu): The frequency of a wave is the number of cycles it undergoes per second, expressed by the unit 1/second [s-1; also called a hertz (Hz)].  Wavelength (λ, Greek lambda) The wavelength is the distance between any point on a wave and the corresponding point on the next crest (or trough) of the wave, that is, the distance the wave travels during one cycle.  Wavelength has units of meters or, for very short wavelengths, nanometers (nm, 10-9 m), picometers (pm= 10-12 m), or the non-SI unit angstroms (Å= 10-10 m). 3 Cont…  Speed: The speed of a wave is the distance it moves per unit time (meters per second), the product of its frequency (cycles per second) and wavelength (meters per cycle):  In a vacuum, electromagnetic radiation moves at 2.997924583X108 m/s (3.00 X 108 m/s to three significant figures), a physical constant called the speed of light (c): C = v x λ……………………..5.1  Since the product of v and λ is a constant, they have a reciprocal relationship radiation with a high frequency has a short wavelength, and vice versa. 4 Cont… 5 Cont…  Amplitude: The amplitude of a wave is the height of the crest (or depth of the trough).  For an electromagnetic wave, the amplitude is related to the intensity of the radiation, or its brightness in the case of visible light.  Light of a particular color has a specific frequency (and thus, wavelength) (lower amplitude, less intense) or brighter (higher amplitude, more intense). 6 The Electromagnetic Spectrum  Visible light represents a small region of the electromagnetic spectrum.  All waves in the spectrum travel at the same speed through a vacuum but differ in frequency and, therefore, wavelength.  The spectrum is a continuum of radiant energy, so each region meets the next.  For instance, the infrared (IR) region meets the microwave region on one end and the visible region on the other.  We perceive different wavelengths (or frequencies) of visible light as colors, from red (λ< 750 nm) to violet (λ < 400 nm).  Light of a single wavelength is called monochromatic (Greek, ―one color‖), whereas light of many wavelengths is polychromatic. White light is polychromatic. 7 Cont…  The region adjacent to visible light on the short-wavelength end consists of ultraviolet (UV) radiation (also called ultraviolet light).  Still shorter wavelengths (higher frequencies) make up the x-ray and gamma (g) ray regions.  Some types of electromagnetic radiation are utilized by familiar devices; for example, long-wavelength, low-frequency radiation is used by microwave ovens, radios and cell phones. 8 Cont… Regions of the electromagnetic spectrum. 9 Cont… For example: A dental hygienist uses x-rays (λ = 1.00 Å) to take a series of dental radiographs while the patient listens to a radio station (λ = 325 cm) and looks out the window at the blue sky (λ = 473 nm). What is the frequency (in s-1) of the electromagnetic radiation from each source? (Assume that the radiation travels at the speed of light, 3.00 X 108 m/s.) Solution 10 The Particle Nature of Light  Three observations involving matter and light confounded physicists at the turn of the 20th century: blackbody radiation, the photoelectric effect and atomic spectra.  Explaining these phenomena required a radically new picture of energy. Blackbody Radiation and the Quantum Theory of Energy  The light given off by an object being heated  The quantum theory. In 1900, the German physicist Max Planck  He proposed that a hot, glowing object could emit (or absorb) only certain quantities of energy: E = nhv where E is the energy of the radiation, v is its frequency, n is a positive integer (1, 2, 3, and so on) called a quantum number, and h is Planck’s constant. (h = 6.626 X 10-34J.s). 11 Cont…  The energy of an atom is quantized energy packet is called a quantum (―fixed quantity‖; plural, quanta).  A quantum of energy is equal to hv.  An atom changes its energy state by emitting or absorbing one or more quanta, and the energy of the emitted (or absorbed) radiation is equal to the difference in the atom’s energy states: ∆𝑛 = 1 12 The Photoelectric Effect and the Photon Theory of Light  When monochromatic light of sufficient frequency shines on a metal plate, a current flows  For current to flow, the light shining on the metal must have a minimum, or threshold, frequency, 13 Cont…  The photon theory. Building on Planck’s ideas, Albert Einstein proposed in 1905 that light itself is particulate, quantized into tiny ―bundles‖ of energy, later called photons.  One ―particle‖ of light, whose energy is related to its frequency, not its amplitude: Example: A student uses a microwave oven to heat a meal. The wavelength of the radiation is 1.20 cm. What is the energy of one photon of this microwave radiation? 14 Atomic Spectra Line Spectra and the Rydberg Equation  Instead, it creates a line spectrum, a series of fine lines at specific frequencies separated by black spaces.  The Rydberg equation, that predicted the position and wavelength of any line in a given series: 15 5.2. The Bohr Model of the Hydrogen Atom  Two years after the nuclear model was proposed, Niels Bohr (1885– 1962), a young Danish physicist working in Rutherford’s laboratory, suggested a model for the H atom that did predict the existence of line spectra. 16 Cont… 17 Features of the Model  Quantum numbers and electron orbit.  The quantum number n is a positive integer (1, 2, 3,...) associated with the radius of an electron orbit, which is directly related to the electron’s energy: the lower the n value, the smaller the radius of the orbit, and the lower the energy level.  Ground state: When the electron is in the first orbit (n = 1), it is closest to the nucleus, and the H atom is in its lowest (first) energy level, called the ground state.  Excited states: If the electron is in any orbit farther from the nucleus, the atom is in an excited state.  Absorption: If an H atom absorbs a photon whose energy equals the difference between lower and higher energy levels, the electron moves to the outer (higher energy) orbit. 18 Cont…  Emission: If an H atom in a higher energy level (electron in farther orbit) returns to a lower energy level (electron in closer orbit), the atom emits a photon whose energy equals the difference between the two levels. Limitations of the Model  Despite its great success in predicting the spectral lines of H, the Bohr model failed with every other atom. The reason is that it is a one electron model.  Electrons do not move in fixed, defined orbits.  the energy of an atom occurs in discrete levels, and an atom changes energy by absorbing or emitting a photon of specific energy. 19 The Energy Levels of the Hydrogen Atom 20 Cont… Finding the wavelength of a spectral line. with Planck’s expression for the change in energy of an atom Example: A hydrogen atom absorbs a photon of UV light and its electron enters the n = 4 energy level. Calculate (a) the change in energy of the atom and (b) the wavelength (in nm) of the photon. solution 21 Spectral Analysis in the Laboratory Analysis of the spectrum of the H atom led to the Bohr model, the first step toward our current model of the atom. The terms spectroscopy, spectrophotometry, and spectrometry refer to a large group of instrumental techniques that obtain spectra that correspond to a substance’s atomic or molecular energy levels. The two types of spectra most often obtained are emission and absorption spectra: An emission spectrum is produced when atoms in an excited state emit photons characteristic of the element as they return to lower energy states. An absorption spectrum is produced when atoms absorb photons of certain wavelengths and become excited from lower to higher energy states. 22 5.3. Development of Quantum theory The Wave-Particle Duality of Matter and Energy  The early proponents of quantum theory demonstrated that energy is particle-like and matter is wavelike properties. The Wave Nature of Electrons  Attempting to explain why an atom has fixed energy levels, a French physics student, Louis de Broglie, considered other systems such as the vibrations of a plucked guitar string.  de Broglie proposed that if energy is particle-like, perhaps matter is wavelike.  He reasoned that if electrons have wavelike motion in orbits of fixed radii, they would have only certain allowable frequencies and energies. 23 de Broglie Equation  famous equation for mass-energy equivalence E = mc2  Equation for the energy of a photon ℎ𝑐 E = hv = λ  de Broglie derived an equation for the wavelength of any particle of mass m—whether planet, baseball, or electron—moving at speed u: 24 The Particle Nature of Photons  If electrons have properties of energy, do photons have properties of matter? The de Broglie equation suggests that we can calculate the momentum (p), the product of mass and speed, for a photon.  Wave-Particle Duality Classical experiments had shown matter to be particle- like and energy to be wavelike.  But results on the atomic scale show electrons moving in waves and photons having momentum.  Thus, every property of matter was also a property of energy.  The truth is that both matter and energy show both behaviors:  This dual character of matter and energy is known as the wave-particle duality 25 Heisenberg’s Uncertainty Principle  1927, the German physicist Werner Heisenberg postulated the uncertainty principle, which states that it is impossible to know simultaneously the position and momentum (mass times speed) of a particle.  For a particle with constant mass m, the principle is expressed mathematically as  where ∆x is the uncertainty in position, ∆u is the uncertainty in speed, and h is Planck’s constant.  The more accurately we know the position of the particle (smaller ∆x), the less accurately we know its speed (larger ∆u) and vice versa. 26 The Quantum-Mechanical Model of the Atom  Acceptance of the dual nature of matter and energy and of the uncertainty principle culminated in the field of quantum mechanics, which examines the wave nature of objects on the atomic scale.  In 1926, Erwin Schrödinger derived an equation that is the basis for the quantum-mechanical model of the H atom.  The model describes an atom with specific quantities of energy that result from allowed frequencies of its electron’s wavelike motion.  The electron’s position can only be known within a certain probability.  The electron’s matter wave occupies the space near the nucleus and is continuously influenced by it. 27 Cont…  ―orbital‖ in the quantum-mechanical model bears no resemblance to an ―orbit‖ in the Bohr model: an orbit is an electron’s actual path around the nucleus, whereas an orbital is a mathematical function that describes the electron’s matter-wave but has no physical meaning. Quantum Numbers of an Atomic Orbital  An atomic orbital is specified by four quantum numbers that are part of the solution of the Schrödinger equation and indicate the size, shape, orientation and direction in space of the orbital. 1. The principal quantum number (n) is a positive integer (1, 2, 3, and so forth). It indicates the relative size of the orbital. 28 Cont…  The principal quantum number specifies the energy level of the H atom:  the higher the n value, the higher the energy level. When the electron occupies an orbital with n = 1, the H atom is in its ground state and has its lowest energy. When the electron occupies an orbital with n = 2 (first excited state), the atom has more energy. 2. The angular momentum quantum number (l)  is an integer from 0 to n - 1. It is related to the shape of the orbital. Note that the principal quantum number sets a limit on the angular momentum quantum number:  n limits l. For an orbital with n = 1, l can have only one value, 0. For orbitals with n = 2, l can have two values, 0 or 1. For orbitals with n = 3, l can have three values, 0, 1, or 2; and so forth. Thus, the number of possible l values equals the value of n. 29 The magnetic quantum number (ml)  is an integer from -l through 0 to +l. It prescribes the three- dimensional orientation of the orbital in the space around the nucleus.  The angular momentum quantum number sets a limit on the magnetic quantum number:  l limits ml An orbital with l = 0 can have only ml = 0.  However, an orbital with l = 1 can have one of three ml values, -1, 0, or +1; that is, there are three possible orbitals with l = 1, each with its own orientation.  Note that the number of ml values equals 2l+1, which is the number of orbitals for a given l.  The total number of ml values, that is, the total number of orbitals, for a given n value is n2 30 Example: What values of the angular momentum (l) and magnetic (ml) quantum numbers are allowed for a principal quantum number (n) of 3? How many orbitals are allowed? Solution n Determining l values: for n = 3, l = 0, 1, 2. Determining ml for each l value: For l = 0, ml = 0, For l = 1, ml = -1, 0, +1, For l = 2, ml = -2, -1, 0, +1, +2 There are nine ml values, so there are nine orbitals with n = 3.  As we saw, the total number of orbitals for a given n value is n2, and for n = 3, n2 = 9.  Exercise: What are the possible l and ml values for n = 4? 31 The Hierarchy of Quantum Numbers for Atomic Orbitals 32 Summary of quantum numbers of electrons in atoms 33 Quantum Numbers and Energy Levels  The energy states and orbitals of the atom are described with specific terms and are associated with one or more quantum numbers:  1. Level. The atom’s energy levels, or shells, are given by the n value: the smaller the n value, the lower the energy level and the greater the probability that the electron is closer to the nucleus.  2. Sublevel. The atom’s levels are divided into sublevels, or subshells, that are given by the l value. Each designates the orbital shape with a letter:  l = 0 is an s sublevel.  l = 1 is a p sublevel.  l = 2 is a d sublevel.  l = 3 is an f sublevel. 34 Cont…  (The letters derive from names of spectroscopic lines: sharp, principal, diffuse and fundamental.) Sublevels with l values greater than 3 are designated by consecutive letters after f: g sublevel, h sublevel, and so on.  A sublevel is named with its n value and letter designation; for example, the sublevel (subshell) with n = 2 and l = 0 is called 2s.  3. Orbital. Each combination of n, l, and ml specifies the size (energy), shape, and spatial orientation of one of the atom’s orbitals. We know the quantum numbers of the orbitals in a sublevel from the sublevel name and the quantum-number hierarchy. 35 Cont…  For example, any orbital in the 2s sublevel has n = 2 and l =0, and given that l value, it can have only ml = 0; thus, the 2s sublevel has only one orbital.  Any orbital in the 3p sublevel has n = 3 and l = 1, and given that l value, one orbital has ml = -1, another has ml = 0, and a third has ml = +1; thus, the 3p sublevel has three orbitals. 36 Shapes of Atomic Orbitals The s Orbital: An orbital with l 5 0 has a spherical shape with the nucleus at its center and is called an s orbital. Because a sphere has only one orientation, an s orbital has only one ml value: for any s orbital, ml = 0  node, where the probability of finding the electron drops to zero  The p Orbital An orbital with l = 1 is called a p orbital and has two regions (lobes) of high probability, one on either side of the nucleus. The nucleus lies at the nodal plane of this dumbbell-shaped orbital.  The d Orbital An orbital with l = 2 is called a d orbital. There are five possible ml values for l = 2: -2, -1, 0, +1, and +2. Thus, a d orbital has any one of five orientations. 37 Orbitals with Higher l Values Orbitals with l = 3 are f orbitals and have a principal quantum number of at least n=4. Figure shows one of the seven f orbitals (2l + 1 = 7); each f orbital has a complex, multi lobed shape with several nodal planes. 38 5.4. Electronic structure of atoms The Exclusion Principle and Orbital Occupancy  no two electrons in the same atom can have the same four quantum numbers. Therefore, the second He electron occupies the same orbital as the first but has an opposite spin:  An atomic orbital can hold a maximum of two electrons and they must have opposing spins. 5.4.2. The Aufbau principle (German aufbauen, ―to build up‖) We start at the beginning of the periodic table and add one proton to the nucleus and one electron to the lowest energy sublevel available. 39 5.4.3. Electronic configuration and the periodic table  There are two common ways to indicate the distribution of electrons:  The electron configuration: This shorthand notation consists of the principal energy level (n value), the letter designation of the sublevel (l value), and the number of electrons (#) in the sublevel, written as a superscript: nl#.  The orbital diagram: An orbital diagram consists of a box (or circle, or just a line) for each orbital in a given energy level, grouped by sublevel (with nl designation shown beneath), with an arrow representing an electron and its spin: ↑ is +1/2 and ↓ is -1/2. 40 Cont… Building Up Period 1 Building Up Period 2 Lithium, Beryllium, Boron, Carbon, Nitrogen, Oxygen, Fluorine, Neon 41 42 Hund’s rule  When orbitals of equal energy are available, the electron configuration of lowest energy has the maximum number of unpaired electrons with parallel spins. Building Up Period 3 Partial orbital diagrams show only the sublevels being filled, here the 3s and 3p. Condensed electron configurations (rightmost column) have the element symbol of the previous noble gas in brackets, to stand for its configuration, followed by the electron configuration of filled inner sublevels and the energy level being filled. 43 Partial orbital diagrams and electronic configuration for the elements in period 3 44 General Principles of Electron Configurations  The partial (highest energy sublevels being filled) ground-state electron configurations of the known elements.  Similar Outer Electron Configurations Within a Group Among the main-group elements (A groups)—the s-block and p-block elements—outer electron configurations within a group are identical.  Some variations in the transition elements (B groups, d block) and inner transition elements ( f block) occur  Orbital Filling Order: When the elements are ―built up‖ by filling levels and sublevels in order of increasing energy, we obtain the sequence in the periodic table 45 46 47 Cont… Categories of Electrons We can describe three categories of electrons: 1) Inner (core) electrons: are those an atom has in common with the previous noble gas and any completed transition series. They fill all the lower energy levels of an atom. 2) Outer electrons are those in the highest energy level (highest n value). They spend most of their time farthest from the nucleus. 3) Valence electrons are those involved in forming compounds: For main-group elements, the valence electrons are the outer electrons. For transition elements, in addition to the outer ns electrons, the (n - 1)d electrons are also valence electrons, though the metals Fe (Z = 26) through Zn (Z = 30) may use only a few, if any, of their d electrons in bonding. 48 Group and Period Numbers Among the main-group elements (A groups), the A number equals the number of outer electrons (those with the highest n); thus, chlorine (Cl; Group 7A) has 7 outer electrons, and so forth. The period number is the n value of the highest energy level. For an energy level, the n value squared (n2) is the number of orbitals, and 2n2 is the maximum number of electrons (or elements).  For example, consider the n = 3 level. The number of orbitals is n2 = 9: one 3s, three 3p, and five 3d.  The number of electrons is 2n2 = 18: two 3s and six 3p electrons for the eight elements of Period 3, and ten 3d electrons for the ten transition elements of Period 4 49 Transition and Inner Transition Elements The d block and f block occur between the main-group s and p blocks 1) Transition series: Periods 4, 5, 6, and 7 incorporate the 3d, 4d, 5d, and 6d sublevels, respectively 2) Inner Transition: Period 6 holds the first of two series of inner transition elements, those in which f orbitals are being filled. The two inner transition series  The Period 6 inner transition series, called the lanthanides (or rare earths), occurs after lanthanum (La; Z = 57), and the 4f orbitals are filled.  The Period 7 inner transition series, called the actinides, occurs after actinium (Ac; Z = 89), and the 5f orbitals are filled. 3) Irregular filling patterns: Irregularities in the filling pattern, such as those for Cr and Cu in Period 4, occur in the d and f blocks because the sublevel energies in these larger atoms differ very little. 50  Cont… 24Cr = and 29Cu = Exercise Using the periodic table and assuming a regular filling pattern, give the full and condensed electron configurations, partial orbital diagrams showing valence electrons only, and number of inner electrons for the following elements: (a) Potassium (K; Z = 19) (b) Technetium (Tc; Z = 43) (c) Lead (Pb; Z = 82), d) Ni (Z = 28) e) Sr (Z = 38) f) Po (Z = 84) 51 5.5. Periodic variation in element properties  In this section, we focus on three atomic properties that reflect the central importance of electron configuration and effective nuclear charge: atomic size, ionization energy, and electron affinity.  Most notably, these properties are periodic, which means they generally exhibit consistent changes, or trends, within a group or period. Trends in Atomic Size  Atomic size (the extent of the contour) in terms of how closely one atom lies next to another.  We measure the distance between atomic nuclei in a sample of an element and divide that distance in half. The size of an atom in a compound depends somewhat on the atoms near it.  In other words, an element’s atomic size varies slightly from substance to substance. 52 Cont… 1) Metallic radius: Used mostly for metals, it is one-half the shortest distance between nuclei of adjacent, individual atoms in a crystal of the element. 2) Covalent radius: Used for elements occurring as molecules, mostly non metals, it is one-half the shortest distance between nuclei of bonded atoms.  Radii measured for some elements are used to determine the radii of other elements from distances between atoms in compounds.  For instance, in a carbon-chlorine compound, the distance between nuclei in a C—Cl bond is 177 pm.  Using the known covalent radius of Cl (100 pm), we find the covalent radius of C (177 pm - 100 pm = 77 pm) 53 Cont…  As the principal quantum number (n) increases, the probability that outer electrons spend most of their time farther from the nucleus increases as well; thus, atomic size increases.  As the effective nuclear charge (Zeff) increases, outer electrons are pulled closer to the nucleus ; thus, atomic size decreases.  The net effect of these influences depends on how effectively the inner electrons shield the increasing nuclear charge: – Atomic radius generally increases down a group. Because As we move down a main group, each member has one more level of inner electrons that shield the outer electrons very effectively. – Atomic radius generally decreases across a period. Because greater electron repulsions, outer electrons shield each other only slightly, so Zeff rises significantly, and the outer electrons are pulled closer to the nucleus: 54 Transition Elements 1. Down a transition group, n increases, but shielding by an additional level of inner electrons results in only a small size increase from Period 4 to 5 and none from 5 to 6. 2. Across a transition series, atomic size shrinks through the first two or three elements because of the increasing nuclear charge. 3. A transition series affects atomic size in neighbouring main groups. Shielding by d electrons causes a major size decrease from Group 2A(2) to Group 3A(13) in Periods 4 through 6. Example: Using only the periodic table rank each set of main-group elements in order of decreasing atomic size: (a) Ca, Mg, Sr (b) K, Ga, Ca (c) Br, Rb, Kr (d) Sr, Ca, Rb 55 Example: Using only the periodic table rank each set of main-group elements in order of decreasing atomic size: (a) Ca, Mg, Sr (b) K, Ga, Ca (c) Br, Rb, Kr (d) Sr, Ca, Rb Solution (a) Sr > Ca > Mg. These three elements are in Group 2A(2), and size decreases up the group. (b) K > Ca > Ga. These three elements are in Period 4, and size decreases across a period. (c) Rb > Br > Kr > Rb is largest because it has one more energy level (Period 5) and is farthest to the left. Kr is smaller than Br because Kr is farther to the right in Period 4. (d) Rb > Sr > Ca> Ca is smallest because it has one fewer energy level. Sr is smaller than Rb because it is farther to the right. 56 Trends in Ionization Energy  The ionization energy (IE) is the energy required for the complete removal of 1 mol of electrons from 1 mol of gaseous atoms or ions.  Pulling an electron away from a nucleus requires energy to overcome their electrostatic attraction. Because energy flows into the system, the ionization energy is always positive (like ∆H of an endothermic reaction). Atoms with a low IE tend to form cations during reactions. Atoms with a high IE (except the noble gases) tend to form anions.  Ionization energy generally decreases down a group.  Ionization energy generally increases across a period. 57 Example: Using the periodic table only, rank the elements in each set in order of decreasing IE1: (a) Kr, He, Ar; (b) Sb, Te, Sn; (c) K, Ca, Rb; (d) I, Xe, Cs. Solution (a) He > Ar> Kr. These are in Group 8A(18), and IE1 decreases down a group. (b) Te > Sb > Sn. These are in Period 5, and IE1 increases across a period. (c) Ca > K > Rb. IE1 of K is larger than IE1 of Rb because K is higher in Group 1A(1). IE1 of Ca is larger than IE1 of K because Ca is farther to the right in Period 4. (d) Xe > I > Cs. IE1 of I is smaller than IE1 of Xe because I is farther to the left. IE1 of I is larger than IE1 of Cs because I is farther to the right and in the previous period. 58 Trends in Electron Affinity  The electron affinity (EA) is the energy change (kJ/mol) accompanying the addition of 1 mol of electrons to 1 mol of gaseous atoms or ions.  The first electron affinity (EA1) refers to the formation of 1 mol of monovalent (1-) gaseous anions: 59 Cont…  We might expect a smooth decrease (smaller negative number) down a group because size increases, and the nucleus is farther away from an electron being added.  We might expect a regular increase (larger negative number) across a period because size decreases, and higher Zeff should attract the electron being added more strongly. There is an overall left-to-right increase, but it is not at all regular. 60