The Wave Nature of Light. Chapter Seven: Electromagnetic Waves. c = λν. λ and ν are inversely related

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1 The Wave Nature of Light Chapter Seven: ATOMIC STRUCTURE & PERIODICITY Electromagnetic radiation is energy propagated by vibrating electric and magnetic fields. Electromagnetic radiation forms a whole electromagnetic spectrum, depending on frequency. It can be though of as waves or streams of photons Radiation carries energy through space. Electromagnetic Waves Electromagnetic Radiation Exhibits Wave Properties and Particulate Properties All matter exhibits both particulate and wave properties. Large pieces of matter exhibit predominately particulate properties; whereas very small bits of matter, such as photons, show both. Waves have three primary characteristics Wavelength, λ (lambda) the distance between two consecutive peaks or troughs in a wave Frequency, ν (nu) The number of waves or cycles per second that pass a given point in space. Units of frequency are Hertz (1/s = s -1 = Hz) Speed of light, c in a vacuum 3.0 x 10 8 m/s 3.0 x cm/s c = λν c = λν λ and ν are inversely related 1

2 Classification of Electromagnetic Radiation Quantized Energy and Photons Some phenomena can t be explained using a wave model of light: Blackbody radiation is the emission of light from hot objects. The photoelectric effect is the emission of electrons from metal surfaces on which light shines. All electromagnetic Visible waves radiation have has characteristic wavelengths wavelengths between and frequencies. The electromagnetic 400 nm (violet) spectrum and 750 nm here (red). displaces various types of electromagnetic radiation arranged in order of increasing wavelength. Example 7.1 A-B Emission spectra are the emissions of light from electronically excited gas atoms. Hot Objects and the Quantization of Energy Heated solid emits radiation (black body radiation). The wavelength distribution depends on the temperature i.e., red hot objects are cooler than white hot objects. Planck s Constant Studying radiation profiles emitted by solid bodies heated to incandescence, Max Planck found that matter could absorb or emit energy only in whole-number multiples of the quantity hv. Planck s constant, h = x J s Energy is quantized; it can occur only in discrete units of hv called quanta. E = hν Energy of a Photon A system can transfer energy only in whole quanta. Thus energy seems to have particulate properties. Albert Einstein proposed that electromagnetic radiation is itself quantized. He suggested that electromagnetic radiation can be viewed as a stream of particles called photons. In the photoelectric effect, metals eject electrons called photoelectrons when light shines on them. The alkali metals are particularly subject to the effect. Red light (ν = 4.3 x s -1 ), for example, will not cause the ejection of photoelectrons from potassium, no matter how intense the light. Yet even a very weak yellow light (v = 5.1 x s -1 ) shinning on potassium begins the effect. 2

3 The photoelectric effect provides evidence for the particle nature of light and for quantization. Einstein derived the famous equation: E = mc 2 hc E = hv = photon λ For the photoelectric effect, you need the proper intensity of radiation to liberate electrons from the surface of a metal. Below the threshold frequency no e are ejected. Above the threshold frequency, the excess energy appears as the kinetic energy of the ejected e. The greater the intensity means more photons are available to release electrons. E hc/λ h c c λc E = mc2 m = = = 2 2 h h m = λ = λc mv Example 7.2 A-C a) Diffraction occurs when electromagnetic radiation is scattered from a regular array of objects, such as the ions in a crystal of NaCl. b) Bright spots in the diffraction pattern result from constructive interference of waves (waves are in phase). c) Dark areas result from destructive interference of waves (waves are out of phase) NaCl Line Spectra Radiation composed of only one wavelength is called monochromatic. Radiation that spans a whole array of different wavelengths is called continuous. When radiation from a light source, such as a light bulb, is separated into its different wavelength components, a spectrum is produced. KCl pattern for NaCl pattern for DNA White light can be separated into a continuous spectrum of colors. A rainbow is a continuous spectrum of light produced by the dispersal of sunlight by raindrops or mist. On continuous spectrum there are no dark spots which would correspond to different lines. Not all radiation is continuous. A gas placed in a partially evacuated tube and subjected to a high voltage produces single colors of light. The spectrum that we see contains radiation of only specific wavelengths; this is called a line spectrum. absorption/emission spectrum The emission spectra of elements are quite different from the spectrum of white light. While white light gives a continuous spectrum, atomic emission spectra consist of relatively few lines and are called line spectra or discontinuous spectra. Each line in an emission spectrum corresponds to one exact frequency of light emitted by the atom. Therefore each line corresponds to a specific amount of energy being emitted. The figure above shows the visible portion of the emission spectrum of hydrogen. 3

4 Bohr s Model Rutherford assumed that electrons orbited the nucleus analogous to planets orbiting the sun. However a charged particle moving in a circular path should lose energy. This means that the atom should be unstable according to Rutherford s theory. Bohr noted the line spectrum of certain elements and assumed that electrons were confined to specific energy states. These were called orbits. Bohr s model is based on three postulates: Only orbits of specific radii, corresponding to certain definite energies, are permitted for e in an atom. An e has a specific energy and is an allowed energy state. Energy is only emitted or absorbed by an e as it moves from one allowed energy state to another (E is gained or lost as a photon). The Energy States of Hydrogen Atom A change between two discrete energy levels emits a photon of light. Colors from excited gases arise because e move between energy states in the atom. Since the energy states are quantized, the light emitted from excited atoms must be quantized and appear as a line spectra. n = principal quantum number (i.e. n = 1, 2, 3,... ) n = 1 is closest to nucleus; the ground state is lowest in E. An e in a higher energy state is said to be in an excited state. Electronic Transitions in the Bohr Model for the Hydrogen Atom What color of light is emitted when an excited electron in the hydrogen atom falls from: a) n = 5 to n = 2 b) n = 4 to n = 2 c) n = 3 to n = 2 Limitations of the Bohr Model The Bohr Model has several limitations: It cannot explain the spectra of atoms other than hydrogen. Electrons do not move about the nucleus in circular orbits. However, the model introduces two important ideas: The energy of an electron is quantized: electrons exist only in certain energy levels described by quantum numbers. Energy gain or loss is involved in moving an electron from one energy level to another. Bohr s model paved the way for later theories Explain the hydrogen emission spectrum. Why is it significant that the color emitted is not white? How does the emission spectrum support the idea of quantized energy levels? Example 7.4 A-C 4

5 The Uncertainty Principle Heisenberg s Uncertainty Principle: we cannot determine the exact position, direction of motion, and speed of subatomic particles simultaneously. For electrons: we cannot determine their momentum and position simultaneously. Quantum Mechanics and Atomic Orbitals Schrödinger proposed an equation containing both wave and particle terms. Solving the equation leads to wave functions, Ψ The wave function describes the electron s matter wave. The square of the wave function, gives the probability of finding the electron. That is, gives the electron density or probability density for the atom. Electron density is another way of expressing probability. A region of high electron density is one where there is a high probability of finding an electron. Orbitals and Quantum Numbers If we solve the Schrödinger equation, we get wave functions and energies for the wave functions. A specific wave function is called an orbitals. Schrödinger s equation requires three quantum numbers: Principal quantum number, n (n = 1, 2, 3...) Angular momentum number, l (0 to n 1) Magnetic quantum number, m l ( l to +l) They equated the electron motion around the nucleus to a standing wave. Only certain circular orbits have a circumference into which a whole number of wavelengths of the standing electron wave will fit. Other orbits would produce destructive interference. Schrödinger used complicated math to solve three dimensional wave functions. The specific wave function is called an atomic orbital. In the quantum mechanical model, an atomic orbital is not like Bohr s orbital. Probability Distribution for the 1s Wave Function Radial Probability Distribution Heisenberg Uncertainty Principle There is a fundamental limitation to just how precisely we can know both the position and momentum of a particle at a give time. Probability Distribution is represented by regions of shading; the more intense the color, the more likely an electron is to be located there. Notice that the probability of finding the electron at a particular position is greatest close to the nucleus and drops off rapidly as the distance from the nucleus increases. For a hydrogen atom, imagine the space around the hydrogen nucleus is made up of a series of thin spherical shells, when the total probability of finding the electron in each spherical shell is plotted versus the distance from the nucleus, the plot above is obtained, the graph is called the radial probability distribution 5

6 Each atomic orbital is characterized by a series of numbers called quantum numbers The principal quantum number (n) Integral values: 1, 2, 3... Describe the size and energy level of the orbital The angular momentum number (l) Integral values from 0 to n 1 for each value of n Describes the shape of the atomic orbital Sometimes called a subshell The magnetic quantum number (m l ) Integral values between l and - l, including zero. Relates to the orientation of the orbital in space relative to the other orbitals in the atom. The electron spin quantum number (m s ) Represents the spin; orbital w/ 2 e - must have opposite spins Quantum Numbers Play Quantum Numbers video Quantum Numbers Two Representations of the Hydrogen 1s, 2s, and 3s Orbitals Note that 2s and 3s orbitals contain areas of high probability separated by areas of zero probability. These latter areas are called nodal surfaces or nodes. The number of nodes increases as n increases. Example 7.6 A-B By definition, the size of the orbital relates to the surface that contains 90% of the total electron probability. p orbitals d Orbitals Cross section of the electron probability distribution of a 3p orbital (showing notes) 6

7 f Orbitals Representation of Orbitals In a many-electron atom, for a given value of n, the energy of an orbital increases with increasing value of l. Orbitals of the same energy are said to be degenerate. 2p x, 2p y, 2p z Answer 7.7 Questions Pauli Exclusion Principle In a give atom, no two electrons can have the same set of four quantum numbers (n,l, m l, and m s ).. This is known as Pauli Exclusion Principle An orbital can hold only two electrons, and they must have opposite spins. This accounts for the electron arrangements of the atoms in the periodic table. Since electron spin is quantized, we define m s (spin magnetic quantum number) as +1/2 or -1/2 Example 7.8 A-B Polyelectronic Atoms Polyelectronic atoms are atoms with more than one electron. For atoms with more than one electron, we must deal with repulsive forces between electrons. Electrons experiencing repulsion from other electrons are not as tightly bound near the nucleus and we say the electron is screened or shielded. Penetration effects cause electrons in 2s orbital to be attracted to the nucleus more strongly than an electron in a 2p orbital. The same thing happens in other orbitals. 7.9 Questions in Notes 1. What are the three energy contributions that must be considered when describing the helium atom? 2. What does your textbook mean by the electron correlation problem? How do we deal with the problem? 3. Why does it take more energy to remove an electron from Al + than from Al? 7

8 7.9 Questions in Notes 4. Why do electrons prefer to fill s, p, d, and then f within a particular quantum level? 7.9 Questions in Notes 6. Why does the 3d orbital have a higher energy than 3p even though it has its maximum probability closer to the nucleus than the 3p? 5. What it the penetration effect, and why is it important? Electrons in Atoms The electronic structure of an atom refers to the arrangement of electrons. The chemical behavior of an atom is entirely defined by its electronic structure. History of Periodic Table Early Periodic Table published in 1872 Dmitri Mendeleev Conceived independently by Meyer and Mendeleev Mendeleev get s most of the credit because he explained how it could be used to predict unknown elements First table listed elements by mass Modern table lists them by atomic number Electron Configurations and the Periodic Table The periodic table can be used as a guide for electron configurations. The periodic number is the value of n. The s-block and p-block of the periodic table contain the representative, or main-group, elements. Group 3B-2B have their d orbital being filled. The lanthanide and actinides have their f orbitals being filled. ACS Periodic Table 8

9 Electron Configuration Rules Aufbau Principle Electrons fill lowest energy orbitals first Hund s Rule The lowest energy configuration for an atom is the one having the maximum number of unpaired electrons allowed by Paul Principle in a particular set of degenerate orbitals Electron Configurations Valence Electrons electrons on the outermost principal quantum level of an atom Core Electrons inner electrons Exceptional Electron Configurations Chromium & Molybdenum Copper, Silver & Gold Determine the expected electron configurations for each of the following: 1. S 2. Ba 3. Ni Ag + 1s 2 2s 2 2p 6 3s 2 3p 4 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 4d 10 5s 2 5p 6 6s 2 1s 2 2s 2 2p 6 3s 2 3p 6 3d 6 4s 2 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 4d 10 Examples 7.11 A-D Periodic Properties Lithium Beryllium Oxygen Fluorine Neon Position on the periodic table and electron configurations can be used to highlight periodic properties. Elements in the same column contain the same number of outter-shell electrons or valence electrons. 3p + & 3e - 1s 2 2s 1 Sodium 4p + & 4e - 1s 2 2s 2 8p + & 8e - 1s 2 2s 2 2p 4 Sulfur 9p + & 9e - 1s 2 2s 2 2p 5 10p + & 10e - 1s 2 2s 2 2p 6 Argon Effective Nuclear Charge (Z eff ) is the charge experienced by an electron on a many-electron atom. The electron is attracted to the nucleus, but repelled by electrons that shield or screen it from the full nuclear charge. The attraction an electron has to the nucleus depends on its distance from the nucleus and the number of electrons in the spherical volume out to the electron in question. 11p + & 11e - 1s 2 2s 2 2p 6 3s 1 16p + & 16e - 1s 2 2s 2 2p 6 3s 2 3p 4 18p + & 18e - 1s 2 2s 2 2p 6 3s 2 3p 6 Moving left to right, electrons experience increasing nuclear attraction and become more tightly bound to the nucleus electrons. Electrons occupying the higher energy levels are shielded from the pull of the nucleus 9

10 Ionization Energy Trends in Ionization Energies (kj/mol) for the Representative Elements The ionization energy of an atom is the minimum energy required to remove an electron from the ground state of the isolated gaseous atom or ion. First Ionization Energy is energy required to remove the highest energy electron of a gaseous atom. Second Ionization Energy is energy required to remove the second highest energy electron of a gaseous atom. Al(g) Al + (g) + e - Al + (g) Al 2+ (g) + e - Al 2+ (g) Al 3+ (g) + e - Al 3+ (g) Al 4+ (g) + e - I 1 = 580 kj/mol I 2 = 1815 kj/mol I 3 = 2740 kj/mol I 4 = 11,600 kj/mol Left to right IE increases because Z eff increases Going down IE decreases because shielding of outter e increases The Values of First Ionization Energy for the Elements in the First Six Periods The Values of First Ionization Energy for the Elements in the First Six Periods Notice the positive IE value means that the process requires energy (endothermic). Is trend always consistent across a period? The s electrons are more effective at shielding than p electrons so forming s 2 p 0 is more favorable. When second electron is placed in a p orbital, the electron-electron repulsions increases. When this electron is removed, the resulting s 2 p 3 is more stable. Successive Ionization Energies (kj/mole) for the Elements in Period 3 Ionization energies for an element increase in magnitude as successive electrons are removed because more energy is required to pull an electron away from an increasingly positive ion. A sharp increase in ionization energy occurs when an inner-shell electron is removed. The ionization energy of the magnesium atom requires 735 kj/mol. Which of the following is the most correct statement concerning the second ionization energy of Mg? I. It is less than 735 kj/mol because Mg wants to lose the second electron to have the same electron configuration as Ne. II. It is equal to 735 kj/mol because both electrons are being taken from the 3s orbital. III. It is greater than 735 kj/mol because the second electron is being taken from a positive ion. IV. Energy is released when the second electron comes off because the Mg atom wants to lose second electron to have the same electron configuration as Ne. 10

11 1800 Relative Ionization Energies for Elements X Y First Second Third Fourth First Ionization Energy (kj/mol) Na Mg Al Si Na Mg Al Si Element P S Cl Ar K Identify specific discontinuities in ionization in going across this period. What accounts for this? P S Cl Ar K Identify the elements. Why is there more than one answer? First Ionization Energy (kj/mol) Na Mg Al Si P S Cl Ar K First Ionization Energy (kj/mol) Na Mg Al Si P S Cl Ar K 0 0 Na Mg Al Si Element P S Cl Ar K Na Mg Al Si Element P S Cl Ar K Identify specific discontinuities in ionization in going across this period. What accounts for this? Explain why argon has the highest ionization energy. First Ionization Energy (kj/mol) Na Mg Al Si Na Mg Al Si Element P S Cl Ar K Explain the ionization energy difference between sodium and potassium P S Cl Ar K Electron Affinities Electron affinity is the energy change when a gaseous atom gains an electron to form a gaseous ion. Electron affinity and ionization energy measure the energy changes of opposite processes. Electron affinity Cl(g) + e Cl (g) E = 349 kj/mol Ionization Energy Cl(g) Cl + (g) + e E = 1251 kj/mol Electron affinity can be either exothermic or endothermic. Look at electron configurations to determine whether electron affinity is positive or negative. An extra electron in Ar needs to be placed in the 4s orbital which is significantly higher in energy than 3p orbital (endothermic). The added e to Cl is placed in 3p to form a stable 3p 6 (exo). Electron affinities do not change greatly down a group. 11

12 Sizes in Atoms The apparent radius is determined by half of the closest distance separating the nuclei when they undergo a collision. Atomic size varies consistently through the periodic table. As we move down, atoms become larger. As principal quantum number, n, increases down a group, the distance of the outermost electrons from the nucleus becomes larger. As we move across a period, they become smaller. As we move across the periodic table, the number of core electrons remains constant; however, the nuclear charge increases. Therefore, there is an increased attraction between the nucleus and the outermost electrons. The attraction causes the atomic radius to decrease. Atomic Radius Obtained by measuring the distances between atoms in chemical compounds. Trends: Decrease left to right due to increase in effective nuclear charge. Increase going down due to increase in orbital size. Periodic Trends in Ionic Radius Ionic size is important in predicting lattice energy and in determining the way in which ions pack in a solid. Just as atomic size is periodic, ionic size is also. In general: Cations are smaller than their parent ions because electrons have been removed and Z eff is increased pulling remaining electrons in closer. Anions are larger than their parent ions because electrons have been added increasing electron-electron repulsions and decreasing the Z eff which cannot pull as much on the added electrons. Isoelectronic Series All members of an isoelectronic series have the same number of electrons and hence the same electron configurations. As nuclear charge increases in an isoelectronic series, the ions become smaller. O 2- > F - > Na + > Mg 2+ > Al 3+ Information in Periodic Table Arrange the elements oxygen, fluorine, and sulfur according to increasing Ionization energy Atomic size Examples 7.12 A-B 1. It is the number and type of valence electrons that primarily determine an atom s chemistry. 2. Need to understand how to figure out electron configurations from table 3. Need to memorize names of groups of atoms 4. Need to understand trends such as metals have low ionizations energies and lose electrons 5. The division of metals and nonmetals approximate many elements along division exhibit both properties 12

13 Metals Metallic character Increases down a group Decreases left to right Characteristics: Metals are lustrous, malleable and ductile. Metals are solid at room temperature (except Hg, Ga, & Cs) and have high melting temperatures. Metals tend to have low ionization energies and tend to form cations easily. Metals tend to be oxidized when they react. Compounds of metals with nonmetals form ionic substances. Metal oxides form basic ionic solids: Na 2 O(s) + H 2 O(l) 2NaOH(aq) Properties of Five Alkali Metals Vial of K The smooth decrease in melting point and boiling point in Group 1A is not typical. Increased ability to lose electrons going down increased reactivity Nonmetals Nonmetals are more diverse in their behavior than metals. Characteristics: In general, nonmetals are non-lustrous, poor conductors of heat and electricity, and exhibit lower melting points than metals. Seven nonmetallic elements exist as diatomic molecules: H 2, N 2, O 2, F 2, Cl 2, Br 2, and I 2 When nonmetals react with metals, nonmetals tend to gain electrons to form salts. Compounds composed entirely of nonmetals are molecular substances. Most nonmetal oxides are acidic: CO 2 (g) + H 2 O(l) H 2 CO 3 (aq) Metalloids have properties that are intermediate. 13