Chapter 5 Student Notes PHW

Chapter 5 Student Notes PHW - Chapter 5 Objectives 5.1...

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Unformatted text preview: Chapter 5 Objectives 5.1 Introduce the concept of Electromagnetic radiation and important important fundamentals that will be applied to the quantum mechanical model. model. 5.2 Discuss early theories about the nature of matter. 5.3 Present the atomic spectrum for hydrogen and discuss line spectra. spectra. 5.4 Outline Bohr’s Theory and explain its fundamental flaws. Bohr’ 5.5 Introduce the quantum mechanical model. 5.6 Provide a qualitative description of the solutions of the Schrodinger Schrodinger equation including the fundamental descriptions of quantum numbers. numbers. 5.7 Incorporate the use of electron configurations to describe representative locations of electrons within atoms and ions. 5.8 Include a discussion of Aufbau, Pauli, and Hund’s work toward the Hund’ development of quantum models and electron configurations. 9/9/2009 5.9 Discuss Periodic Trends in Zumdahl Chapter 12 Atomic Properties 1 Waves and Light Electromagnetic Radiation – Energy travels through space as electromagnetic radiation – Examples: sunlight, microwave ovens, cell phones, X-rays, radiant Xheat from a fireplace, AM/FM radio, colors from fireworks – All travel as waves – All travel at the speed of light 9/9/2009 Zumdahl Chapter 12 2 1 Light consists of waves of oscillating electric (E) and magnetic fields (H) that are perpendicular to one another and to the direction of propagation of the light λ = wavelength ν = frequency 9/9/2009 Zumdahl Chapter 12 3 The Electromagnetic Spectrum 9/9/2009 Zumdahl Chapter 12 4 2 9/9/2009 Zumdahl Chapter 12 5 Important Equations = 3.00 x 108 m s-1 (speed of light in vacuum) = Energy of a “photon” h = Planck’s constant = 6.62 x 10-34 J s 1 J = 1 Joule = 1 9/9/2009 Zumdahl Chapter 12 6 3 Radio Waves AM 890 kHz FM 99.1 MHz 9/9/2009 Zumdahl Chapter 12 c = λν 7 E = hν Typical (Easy) Problem: Given two values, calculate the third. Problem The laser in an audio compact disc (CD) player uses light with a wavelength of 780 nm. What is the frequency of the light emitted from the laser? 9/9/2009 Zumdahl Chapter 12 8 4 Problem The brilliant red color seen in fireworks displays is due to strontium emission at a frequency (ν) of 4.62 x 1014 s-1. (ν Calculate the wavelength of the light emitted. 9/9/2009 Zumdahl Chapter 12 9 Blackbody Radiation NEW SLIDE E = hν = hc / λ hν 9/9/2009 Zumdahl Chapter 12 10 5 Planck, Einstein, and Bohr Early Observations Demonstrating the Need for Quantum Mechanics In 1901 Max Planck found that the wavelength distribution of blackbody radiation could be explained only if it is assumed that electromagnetic radiation is quantized, i.e., energy can be gained or quantized, lost only in integral multiples of hν: hν n is an integer (1,2,3,…) (1,2,3,… (Avoids the “ultraviolet catastrophe”) 9/9/2009 NEW SLIDE Zumdahl Chapter 12 11 Photoelectric Effect Observations 1. νthreshold is different for each different metal. 2. When ν < νthreshold, radiation is not effective in generating electrons, irrespective of intensity. intensity. 3. When ν > νthreshold, the photoelectron energy depends on ν but not on intensity. A higher intensity produces more electrons, but does not effect intensity. effect the kinetic energy of each electron. Classical theory could notZumdahl Chapter 12above observations explain the 9/9/2009 12 6 In 1905 Albert Einstein, in order to explain the photoelectric effect, suggested that electromagnetic radiation can be viewed as a stream of particles called photons. About the same time, Einstein derived his famous equation The main significance is that photons have mass. 9/9/2009 Zumdahl Chapter 12 13 E = mc2 m= E c2 ⎛c⎞ E = hν = h⎜ ⎟ ⎝ λ⎠ Dual nature of light Mass of a photon: 9/9/2009 Zumdahl Chapter 12 14 7 Atomic Spectrum of Hydrogen 9/9/2009 Zumdahl Chapter 12 15 The Person Behind the Science Niels Bohr (1885-1962 ) Highlights – Worked with J.J. Thomson (1911) who discovered the electron in 1896 – 1913 developed a quantum model for the hydrogen atom – During the Nazi occupation of Denmark in World War II, escaped to England & America – Associated with the Atomic Energy Project – Open Letter to the United Nations in 1950: Peaceful application of atomic physics Moments in a Life 9/9/2009 – Nobel Prize in Physics Zumdahl Chapter 12 1922 16 8 Visible Electronic Transitions (Balmer Series) (Balmer in the Bohr Model for the Hydrogen Atom 9/9/2009 Zumdahl Chapter 12 17 Bohr calculated the angular momentum, radius and energy of the electron orbits in one-electron atoms one- rn = = radius of orbital n a0 is a constant called the Bohr radius n = 1,2,3,…= 1,2,3,… Z= (= 1 for H, 2 for He+, …) The following expression can be derived for the energy of 1-electron 1orbital n: En = 9/9/2009 ε0 = vacuum permittivity = 8.854 x 10-12 J-1 C2 m-1 e = electron charge = 1.602 x 10-19 C Zumdahl Chapter 12 18 Calculated levels match those on the photographic plate shown earlier earlier 9 Quantum Mechanics and Atomic Structure Schrödinger Equation: Ĥψ = Eψ ● Wavefunctions (ψ) of atoms: orbitals ● Heisenberg Uncertainty Principle ● Waves (DeBroglie vs. Bohr model) – Nodes – Quantization – Degeneracy 9/9/2009 Zumdahl Chapter 12 19 Schrödinger Equation: Ĥψ = Eψ Many solutions, i.e.,ψ(n, l, ml) and corresponding E(n, l, ml ), where n, l, ml are quantum numbers. When applied to an electron in an atom, ψ2(x,y,z) describes the probability that the electron is in a certain region of space. 9/9/2009 Zumdahl Chapter 12 20 10 Heisenberg Uncertainty Principle In 1927, Werner Heisenberg established that it is impossible to measure, with arbitrary precision, both the position and the momentum of an object. You cannot measure/observe something without changing that which you are observing/measuring. ∆x ∆p ≥ h/4π imprecision of position It is impossible to know both momentum and position with arbitrary accuracy. Whenever, we analyze the position of a particle, we are altering it enough to disturb the accuracy of readings of its momentum (and vice-versa). vice- imprecision of momentum 9/9/2009 Zumdahl Chapter 12 21 Assume we are able to measure the position of an electron with a precision on the order of 2% of the size of an atom. size of an atom: ~ 10-10 m diameter ∆x = 2 x 10-12 m What is the imprecision in a measurement of the speed, ∆v ? DeBroglie: DeBroglie: particles moving with linear momentum (p) have wave- like waveproperties and a wavelength λ = i.e., ~ 10% of the speed of light! i.e., For an ordinary object, this is not a concern since m is much larger than me andZumdahl Chapter 12 larger than 2 x 10-1222 ! ∆x is much m 9/9/2009 11 The DeBroglie Wavelength A 98 mph fastball (m ~ 150 g) λ = h / mv ~ 1 x 10-34 m An electron accelerated from rest by a 100 volt potential ∆E = (1.6 x 10-19 C) (100 V) = 1.6 x 10-17 J = mev2 / 2 Electron charge λ = h / mev = 0.12 nm λ is the same order of magnitude as the distance between atoms in molecules, and crystals ▬► interference effects should be observable Electron Diffraction: Zumdahl Chapter 12 23 A widely used technique for establishing molecular and crystal structures structures 9/9/2009 The hydrogen electron can be visualized as a standing wave around the nucleus. Not the planetary orbit assumed by Bohr. Bohr. 9/9/2009 Zumdahl Chapter 12 24 12 When it comes to atoms, language can be used only as in poetry. The poet too, is not nearly so concerned with describing facts as with creating images. – Niels Bohr to Werner Heisenberg (German pioneers in quantum theory and chemical bonding 9/9/2009 Zumdahl Chapter 12 25 Skip: The particle in a box 9/9/2009 Zumdahl Chapter 12 26 13 Solutions to the Schrödinger Equation: ψ (n, l, ml) ψ (n, l, ml) 1. n = n = 1, 2, 3, … n is related to the size and energy of the orbital 2. l = ψ (n, l, ml) l = 0, 1, …. (n-1) (nl is related to the shape of the orbital l = 0 is called an orbital l = 1 is called a orbital l = 2 is called a orbital l = 3 is called an orbital 9/9/2009 Zumdahl Chapter 12 27 Solutions to the Schrödinger Equation (con’t) 3. ml = magnetic quantum number ψ (n, l, ml) ml = ml relates to the orientation of the orbital 4. Although not a solution to the Schrödinger Equation, Schrö th quantum number is a4 ms = denoted by ↑↓ ms = electron spin quantum number 9/9/2009 Zumdahl Chapter 12 28 14 9/9/2009 Zumdahl Chapter 12 29 First four energy levels of orbitals in hydrogen ψ (1, 0, 0) 0) ψ (2, 1, -1) n l orbital designation ml # of orbitals ψ (2, 0, 0) 0) ψ(2, 1, 0) ψ (2, 1, +1) 0) +1) 1 0 0 1 0 1 2 0 1 2 3 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 0 0 -1, 0, +1 0 -1, 0, +1 -2, -1, 0, +1, +2 0 -1, 0, +1 -2, -1, 0, +1, +2 -3, -2, -1, 0, +1, +2, +3 1 1 3 1 3 5 1 3 5 7 2 3 Degeneracy n2 = number of degenerate orbitals with the same energy 4 n is related to the size and energy of the orbital l is related to the shape of the orbital ml is related to the orientation of the orbital 9/9/2009 Zumdahl Chapter 12 30 15 l=0 s orbitals ψ (n, l, ml) 9/9/2009 Zumdahl Chapter 12 31 Whenever two or more wavefunctions have the same energy, any linear combination of them also has the same energy and is an equally valid solution of the Schrödinger equation. 9/9/2009 Zumdahl Chapter 12 32 16 l=1 p orbitals n l orbital designation ml 0 0 1 0 1 2 0 1 2 3 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 0 0 -1, 0, +1 0 -1, 0, +1 -2, -1, 0, +1, +2 0 -1, 0, +1 -2, -1, 0, +1, +2 -3, -2, -1, 0, +1, +2, +3 { # of orbitals 1 1 1 3 1 3 5 1 3 5 7 2 3 4 ψ (n, l, ml) n is related to the size and energy of the orbital l is related to the shape of the orbital ml is related to the orientation of the orbital 9/9/2009 Zumdahl Chapter 12 l=2 d orbitals 33 ψ (n, l, ml) n l orbital designation ml # of orbitals 1 0 0 1 0 1 2 0 1 2 3 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 0 0 -1, 0, +1 0 -1, 0, +1 -2, -1, 0, +1, +2 0 -1, 0, +1 -2, -1, 0, +1, +2 -3, -2, -1, 0, +1, +2, +3 1 1 3 1 3 5 1 3 5 7 2 3 4 n is related to the size and energy of the orbital l is related to the shape of the orbital ml is related to the orientation of the orbital 9/9/2009 Zumdahl Chapter 12 34 17 Representation of the boundary surfaces for the 4f orbitals (n = 4, l = 3) 4f 9/9/2009 Zumdahl Chapter 12 35 Introduction to Many Electron Atoms ψ (n, l, ml) called quantum numbers – n is related to the of the orbital – l is related to the of the orbital of the orbital – ml relates to the quantum number – ms is the Pauli Exclusion Principle 9/9/2009 In many electron atoms, the s, p, d, f, …subshells are not degenerate: Es <ChapterEd < Ef (n = const.) degenerate: Zumdahl Ep < 12 36 18 The Periodic Table: Dmitri Ivanovich Mendeleev Mendeleev's Early Periodic Table (1872) Source: Corbis 9/9/2009 Zumdahl Chapter 12 37 Many Electron Atoms: The Aufbau Principle ● Aufbau means “ ” ● ● When several orbitals are equal in energy, the lowest energy configuration is one where as few orbitals as possible are doubly occupied. ● The lowest energy configuration is one with parallel spins in all singly occupied orbitals. orbitals. 9/9/2009 Zumdahl Chapter 12 38 19 Hund’s Rules Applied to Carbon ● When several orbitals are equal in energy, the lowest energy configuration is one where as few orbitals as possible are doubly occupied. ● The lowest energy configuration is one with parallel spins in all singly occupied orbitals. orbitals. 9/9/2009 Zumdahl Chapter 12 39 “Aufbau” from Hydrogen to Neon Aufbau” 9/9/2009 Zumdahl Chapter 12 40 20 The Orbitals Filled for Elements in Various Parts of the Periodic Table 9/9/2009 Zumdahl Chapter 12 41 9/9/2009 Zumdahl Chapter 12 42 21 Valence Electrons ● ● Occupy the outermost (highest energy) shell of an atom, i.e., beyond the immediately preceding noble-gas configuration noble- 9/9/2009 Zumdahl Chapter 12 43 Valence Electrons (con’t) ● Among the s-block and p-block elements, the valence electrons include electrons in s and p subshells only. ● Among d-block and f-block (transition elements), valence electrons usually consist of electrons in (n + 1)s orbitals plus 1)s electrons in unfilled nd and nf subshells. subshells. 9/9/2009 Zumdahl Chapter 12 44 22 Problem Write the valence-electron configuration and state the number of valence electrons in each of the following atoms and ions: (a) Y, (b) Lu, (c) Mg2+ (a) Y (Yttrium): atomic number Z = 39 (b) Lu (Lutetium): Z = 71 (c) Mg2+ (Magnesium (II) ion): Z = 12 9/9/2009 Zumdahl Chapter 12 45 Some Subtleties in Ground State Electron Configurations “Building Up” (Potassium through Gallium) Up” K: 4s1 Ca: 4s2 Sc: 4s23d1 Ti: 4s23d2 V: 4s23d3 Cr: 4s13d5 Mn: 4s23d5 Mn: Fe: 4s23d6 Co: 4s23d7 Ni: 4s23d8 Cu: 4s13d10 Zn: 4s23d10 Ga: Ga: 4s23d104p1 “Tearing Down” (Ground State Ions) Down” Ga : 4s23d104p1 Ga+: 4s23d10 Cr: 4s13d5 Cr+: 3d5 Ga2+: 4s13d10 Ga3+: V: 4s23d3 V+: 4s13d3 V2+: 3d3 3d10 As Z increases, transfer of a 4s electron to a 3d orbital becomes more favorable because the electronbecomes electronelectron repulsions are compensated by attractive interactions between the nucleus and electrons in between the more spatially compact 3d orbital. Hence, all M2+ cations of Sc through Zn have [Ar]4s03dn configurations 9/9/2009 Zumdahl Chapter 12 46 23 NEW SLIDE More Subtleties in Ground State Electron Configurations “Building Up” (Rubidium through Indium) Up” Rb: 5s1 Rb: Mo: 5s14d5 Ag: 5s14d10 Sr: 5s2 Sr: Tc: Tc: 5s24d5 Cd: 5s24d10 Cd: Y: 5s24d1 Ru: Ru: 5s14d7 Ti: 5s24d2 Rh: Rh: 5s14d8 Nb: 5s14d4 Nb: Pd: 4s04d10 In: 4s23d104p1 “Building Up” (Cesium through Thallium not including Lanthanides) Up” Cs: 6s1 Ba: 6s2 Ba: La: 6s25d1 Hf: 6s25d2 Hf: Ta: 6s25d3 W: 6s25d4 Re: 6s25d5 Os: 6s25d6 Ir: 6s25d7 Ir: Pt: 5s14d9 Au: 6s15d10 Hg: 6s25d10 Tl: 5s23d105p1 Tl: Lanthanides: La, Ce, Gd, Lu have 5d1 while all others have only 6s2 and 4f electrons. Ce, Gd, Actinides: Th has 6d2, Ac, Pa, U, Np, Cm, Lr have 6d1, and all others have only 7s2 Np, and 5f electrons. 9/9/2009 Zumdahl Chapter 12 47 Periodic Trends in Atomic Properties • Ionization Energy • Electron Affinity • Atomic Radius 9/9/2009 Zumdahl Chapter 12 48 24 The ionization energy (IE) of an atom is the minimum amount of IE) energy necessary to detach an electron from a ground state atom. 9/9/2009 Zumdahl Chapter 12 49 ↑ 9/9/2009 Zumdahl Chapter 12 50 25 Electron Affinity (EA) Because of stability of closed shell structures, EA tends to parallel IE but is shifted one atomic number lower, e.g., 9/9/2009 Zumdahl Chapter 12 51 Atomic Radius The radius of an atom (r) is defined as 9/9/2009 Zumdahl Chapter 12 52 26 Atomic radii (in picometers) for selected atoms 9/9/2009 Zumdahl Chapter 12 53 Sizes of Atoms Atomic size generally moving down a group Among s-block and p-block elements, atomic size generally moving from left to right 9/9/2009 Zumdahl Chapter 12 54 27 Special Names for Groups in the Periodic Table 9/9/2009 Zumdahl Chapter 12 55 Special Names for Groups in the Periodic Table (con’t) con’ 9/9/2009 Zumdahl Chapter 12 56 28 Chapter 5 Quantum Mechanics and Atomic Theory 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13 5.14 5.15 5.16 Electromagnetic Radiation The Nature of Matter The Atomic Spectrum of Hydrogen The Bohr Model The Quantum Mechanical Description of the Atom The Particle in a Box (skip) The Wave Equation for the Hydrogen Atom The Physical Meaning of a Wave Function The Characteristics of Hydrogen Orbitals Electron Spin and the Pauli Principle Polyelectronic Atoms The History of the Periodic Table The Aufbau Principle and the Periodic Table Further Development of the Polyelectronic Model Periodic Trends in Atomic Properties The Properties of a Group: The Alkali Metals 9/9/2009 Zumdahl Chapter 12 57 29 ...
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