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CHEMISTRY The Molecular Nature of Matter SIXTH EDITION Jespersen • Brady • Hyslop Chapter 8 The Quantum Mechanical Atom Copyright © 2012 by John Wiley & Sons, Inc. The nature of Light Electromagnetic Radiation Light: Energy transferred between atoms/molecules Travels through space at high speed in vacuum c = speed of light = 2.9979 × 108 m/s Light is radiation that carries energy through space by means of waves. Waves or Oscillations Systematic fluctuations in intensities of electrical and magnetic forces Varies regularly with time ExhibitJespersen/Brady/Hyslop wide range of energy Chemistry: The Molecular Nature of Matter, 6E 2 Properties of Waves Wavelength () Distance between two successive peaks or troughs Units are in meters, centimeters, nanometers Frequency () Number of waves per second that pass a given point in space Units are in Hertz (Hz = cycles/sec = 1/sec = s–1) Related by =c Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 3 Properties of Waves Amplitude Maximum and minimum height Intensity of wave, or brightness Varies with time as travels through space Nodes Points of zero amplitude Place where wave goes through axis Distance between nodes is constant nodes Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 4 Learning Check: Converting from Wavelength to Frequency The bright red color in fireworks is due to emission of light when Sr(NO3)2 is heated. If the wavelength is ~650 nm, what is the frequency of this light? 8 c 3.00 ´ 10 m/s n= = l 650 ´ 10-9 m = 4.61 × 1014 s–1 = 4.6 × 1014 Hz Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 5 Your Turn! WCBS broadcasts at a frequency of 880 kHz. What is the wavelength of their signal? A. 341 m B. 293 m C. 293 mm D. 341 km c 3.00 ´ 108 m/s l= = 3 n 880 ´ 10 / s E. 293 mm Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 6 Electromagnetic Spectrum Comprised of all frequencies of light Divided into regions according to wavelengths of radiation high energy, short waves Jespersen/Brady/Hyslop low energy, long waves Chemistry: The Molecular Nature of Matter, 6E 7 Electromagnetic Spectrum Visible light Band of wavelengths that human eyes can see 400 to 700 nm Make up spectrum of colors White light Combination of all these colors Can separate white light into the colors with a prism Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 8 Important Experiments in Atomic Theory Late 1800’s: Matter and energy believed to be distinct Matter: made up of particles Energy: light waves Beginning of 1900’s: Several experiments proved this idea incorrect Experiments showed that electrons acted like: Tiny charged particles in some experiments Waves in other experiments Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 9 Photosynthesis If you irradiate plants with infrared and microwave radiation No photosynthesis Regardless of light intensity If you irradiate plants with visible light Photosynthesis occurs More intense light now means more photosynthesis Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 10 Line Spectrum Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 11 Particle Theory of Light Max Planck and Albert Einstein (1905) Electromagnetic radiation is stream of small packets of energy Quanta of energy or photons Each photon travels with velocity = c Waves with frequency = Energy of photon of electromagnetic radiation is proportional to its frequency Energy of photon E = h h = Planck’s constant = 6.626 × 10–34 J s Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 12 Atomic Spectra Atomic line spectra are rather complicated Line spectrum of hydrogen is simplest Single electron First success in explaining quantized line spectra First studied extensively J.J. Balmer Found empirical equation to fit lines in visible region of spectrum J. Rydberg More general equation explains all emission lines in H atom spectrum (infrared, visible, and UV) Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 13 Rydberg Equation 1 1 1 RH 2 2 n n 2 1 RH = 109,678 cm–1 = Rydberg constant = wavelength of light emitted n1 and n2 = whole numbers (integers) from 1 to where n2 > n1 If n1 = 1, then n2 = 2, 3, 4, … Can be used to calculate all spectral lines of hydrogen The values for n correspond to allowed energy levels for atom Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 14 Learning Check: Using Rydberg Equation Consider n1 = 2 Calculate (in nm) for the transition from n2 = 6 down to n1 = 2. æ1 1ö æ 1ö -1 1 = RH çç 2 - 2 ÷÷ = 109,678 cm çç - ÷÷ = 24,373 cm–1 l è2 6 ø è 4 36 ø 1 l= 1 -5 -1 24,372.9 cm = 410.3 nm = 4.1029 ´ 10 1m 1 nm cm ´ ´ 100 cm 1 ´ 10-9 m Violet line in spectrum Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 15 Learning Check A photon undergoes a transition from nhigher down to n = 2 and the emitted light has a wavelength of 650.5 nm? 1 ´ 10-7 cm -7 l = 650.5 nm ´ = 650.5 ´10 cm 1 nm -1 1 1 1 ) = 109,678 cm ( 650.5 ´ 10-7 cm 22 (n )2 2 1 =(1 - 12 ) 7.13455 4 (n2 ) 1 =11 = 0.110 2 (n2 ) 4 7.13455 (n ) n2 = 3 2 2 1 = = 9.10 0.110 Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 16 Your Turn! What is the wavelength of light (in nm) that is emitted when an excited electron in the hydrogen atom falls from n = 5 to n = 3? A. 1.28 × 103 nm B. 1.462 × 104 nm C. 7.80 × 102 nm D. 7.80 × 10–4 nm E. 3.65 × 10–7 nm Jespersen/Brady/Hyslop 1 1 1 1 109 ,678 cm 2 2 5 3 1 7799 cm1 1 1 ´ 107nm l= ´ -1 1 cm 7799 cm Chemistry: The Molecular Nature of Matter, 6E 17 Significance of Atomic Spectra Atomic line spectra tells us When excited atom loses energy Only fixed amounts of energy can be lost Only certain energy photons are emitted Electron restricted to certain fixed energy levels in atoms Energy of electron is quantized Simple extension of Planck's Theory Any theory of atomic structure must account for Atomic spectra Quantization of energy levels in atom Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 18 What Does Quantized Mean? Potential Energy of Rabbit Energy is quantized if only certain discrete values are allowed Presence of discontinuities makes atomic emission quantized Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 19 Bohr Model of Atom First theoretical model of atom to successfully account for Rydberg equation Quantization of energy in hydrogen atom Correctly explained atomic line spectra Proposed that electrons moved around nucleus like planets move around sun Move in fixed paths or orbits Each orbit has fixed energy Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 20 Energy for Bohr Model of H Equation for energy of electron in H atom 2 4 1 2p me E µ- 2 b= n h2 Ultimately b relates to RH by b = RHhc OR RH hc b E =- 2 =- 2 n n Where b = RHhc = 2.1788 × 10–18 J/atom Allowed values of n = 1, 2, 3, 4, … n = quantum number Used to identify orbit Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 21 Energy Level Diagram for H Atom Absorption of photon Electron raised to higher energy level Emission of photon Electron falls to lower energy level Energy levels are quantized Every time an electron drops from one energy level to a lower energy level Same frequency photon is emitted Yields line spectra Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 22 Bohr Model of Hydrogen Atom n=1 First Bohr orbit Most stable energy state equals the ground state which is the lowest energy state Electron remains in lowest energy state unless disturbed How to change the energy of the atom? Add energy, as light (E = h) or other form. Electron raised to higher n orbit n = 2, 3, 4, … Higher n orbits = excited states = less stable So electron quickly drops to lower energy orbit and emits photon of energy equal to E between levels E = Eh – El Jespersen/Brady/Hyslop h = higher l = lower Chemistry: The Molecular Nature of Matter, 6E 23 Your Turn! In Bohr's atomic theory, when an electron moves from one energy level to another energy level more distant from the nucleus, A. energy is emitted B. energy is absorbed C. no change in energy occurs D. light is emitted E. none of these Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 24 Light Exhibits Interference Constructive interference Waves “in-phase” lead to greater amplitude They add together Destructive interference Waves “out-of-phase” lead to lower amplitude They cancel out Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 25 Diffraction and Electrons Light Exhibits interference Has particle-like nature Electrons Known to be particles Also demonstrate interference Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 26 Standing vs. Traveling Waves Traveling wave Produced by wind on surfaces of lakes and oceans Standing wave Produced when guitar string is plucked Center of string vibrates Ends remain fixed Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 27 Standing Wave on a Wire Integer number (n) of peaks and troughs is required Wavelength is quantized: L is the length of the string Jespersen/Brady/Hyslop l= 2L n Chemistry: The Molecular Nature of Matter, 6E 28 How Do We Describe an Electron? Has both wave-like and particle-like properties Energy of moving electron on a wire is E =½ mv 2 Wavelength is related to the quantum number, n, and the wire length: 2L l= Jespersen/Brady/Hyslop n Chemistry: The Molecular Nature of Matter, 6E 29 Electron Has Quantized Energy Electron energy quantized Depends on integer n Energy level spacing changes when positive charge in nucleus changes Line spectra different for each element Lowest energy allowed is for n =1 Energy cannot be zero, hence atom cannot collapse Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 30 Wave Functions Schrödinger’s equation Solutions give wave functions and energy levels of electrons Wave function Wave that corresponds to electron Called orbitals for electrons in atoms Amplitude of wave function squared Can be related to probability of finding electron at that given point Nodes Regions where electrons will not be found Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 31 Orbitals Characterized by Three Quantum Numbers: Quantum Numbers: Shorthand Describes characteristics of electron’s position Predicts its behavior n = principal quantum number All orbitals with same n are in same shell ℓ = secondary quantum number Divides shells into smaller groups called subshells mℓ = magnetic quantum number Divides subshells into individual orbitals Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 32 n = Principal Quantum Number Allowed values: positive integers from 1 to n = 1, 2, 3, 4, 5, … Determines: E =- Size of orbital Z 2RH hc n2 Total energy of orbital RHhc = 2.18 × 10–18 J/atom For given atom, Lower n = Lower (more negative) E = More stable Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 33 ℓ = Orbital Angular Momentum Quantum Number or Secondary Quantum Number Allowed values: 0, 1, 2, 3, 4, 5…(n – 1) s, p, d, f, g, h Letters: Orbital designation nℓ letter Possible values of ℓ depend on n number n different values of ℓ for given n Determines Shape of orbital Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 34 mℓ = Magnetic Quantum Number Allowed values: from –ℓ to 0 to +ℓ Ex. when ℓ=2 then mℓ can be –2, –1, 0, +1, +2 Possible values of mℓ depend on ℓ There are 2ℓ+1 different values of mℓ for given ℓ Determines orientation of orbital in space To designate specific orbital, you need three quantum numbers n , ℓ , mℓ Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 35 Table 8.1 Summary of Relationships Among the Quantum Numbers n, ℓ, and mℓ Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 36 Orbitals of Many Electrons Orbital Designation Based on first two quantum numbers Number for n and letter for ℓ How many electrons can go in each orbital? Two electrons Need another quantum number Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 37 Spin Quantum Number, ms Arises out of behavior of electron in magnetic field Electron acts like a top Spinning charge is like a magnet S Electron behave like tiny magnets Leads to two possible directions of electron spin Possible Values: Up and down North and south Jespersen/Brady/Hyslop +½ Chemistry: The Molecular Nature of Matter, 6E N ½ 38 Number of Orbitals and Electrons in the Orbitals Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 39 Energy Level Diagram for Multi Electron Atom/Ion 4f 6s 5p 4d 5s 4p 3d 4s Energy 3p 3s 2p 2s How to put electrons into a diagram? Need some rules 1s Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 40 Pauli Exclusion Principle No two electrons in same atom can have same set of all four quantum numbers (n, ℓ, mℓ , ms) Can only have two electrons per orbital Two electrons in same orbital must have opposite spin Electrons are said to be paired Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 41 Hund’s Rule If you have more than one orbital all at the same energy Put one electron into each orbital with spins parallel (all up) until all are half filled After orbitals are half full, pair up electrons Why? Repulsion of electrons in same region of space Empirical observation based on magnetic properties Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 42 Know from Magnetic Properties Two electrons in same orbital have different spins Spins paired—diamagnetic Sample not attracted to magnetic field Magnetic effects tend to cancel each other Two electrons in different orbital with same spin Spins unpaired—paramagnetic Sample attracted to a magnetic field Magnetic effects add Measure extent of attraction Gives number of unpaired spins Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 43 Your Turn! Which of the following is a valid set of four quantum numbers (n, ℓ, mℓ , ms)? A. 3, 2, 3, +½ B. 3, 2, 1, 0 C. 3, 0, 0, –½ D. 3, 3, 0, +½ E. 0, –1, 0, –½ Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 44 Your Turn! What is the maximum number of electrons allowed in a set of 4p orbitals? A. 14 B. 6 C. 0 D. 2 E. 10 Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 45 Ground State Electron Arrangements Electron Configurations Distribution of electrons among orbitals of atom 1. List subshells that contain electrons 2. Indicate their electron population with superscript e.g. N is 1s 2 2s 2 2p 3 Orbital Diagrams Way to represent electrons in orbitals 1. Represent each orbital with circle (or line) 2. Use arrows to indicate spin of each electron e.g. N is 1s Jespersen/Brady/Hyslop 2s 2p Chemistry: The Molecular Nature of Matter, 6E 46 Aufbau Principle 1 1s 2s 3s 4s 5s 6s 7s 8s 2 2p 3p 4p 5p 6p 7p 3 4 5 6 3d 4d 4f 5d 5f 6d Jespersen/Brady/Hyslop 7 8 5g Chemistry: The Molecular Nature of Matter, 6E 47 Aufbau Principle and Periodic Table Divided into regions of 2, 6, 10, and 14 columns This equals maximum number of electrons in s, p, d, and f sublevels Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 48 Sublevels and the Periodic Table Each row (period) represents different energy level Each region of chart represents different type of sublevel Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 49 Orbital Diagram and Electron Configurations: e.g. N, Z = 7 4p 3d 4s Energy 3p 3s 2p Each arrow represents an electron 2s 1s 2 2s 2 2p 3 1s Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 50 Orbital Diagram and Electron Configurations: e.g. V, Z = 23 4p 3d 4s Energy 3p 3s 2p 2s Each arrow represents an electron 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 3 1s Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 51 Learning Check Give electron configurations and orbital diagrams for Na and As 6s 5p 4d 5s 4p 3d 4s Energy 3p 3s 2p 2s Na Z = 11 1s 2 2s 2 2p 6 3s 1 As Z = 33 1s 1s 22s 22p 63s 23p 64s 23d 104p 3 Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 52 Your Turn! What is the correct ground state electron configuration for Si? A. 1s 22s 22p 63s 23p 6 B. 1s 22s 22p 63s 23p 4 C. 1s 22s 22p 62d 4 D. 1s 22s 22p 63s 23p 2 E. 1s 22s 22p 63s 13p 3 Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 53 Where Are The Electrons? Each box represents room for an electron. Read from left to right n= 1 1 H n= 2 3 “ns” orbital being filled “np” orbital being filled “(n – 1)d” orbital being filled “( n – 2)f” orbital being filled 4 Li Be n= 3 11 12 Na Mg n= 4 19 20 21 B C N O F 10 Ne 13 14 15 16 17 Al Si P S Cl Ar 36 53 54 Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe 74 75 76 77 Cs Ba La Hf Ta W Re Os Ir n= 7 87 88 78 79 80 81 82 51 35 52 73 50 34 40 72 49 33 39 57 48 32 n= 5 37 38 n= 6 55 56 47 31 18 Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr 46 30 9 V 45 29 8 K Ca Sc Ti 44 28 7 24 43 27 6 23 42 26 5 He 22 41 25 2 83 84 85 86 Pt Au Hg Tl Pb Bi Po At Rn 89 104 105 106 107 108 109 110 111 Fr Ra Ac Rf Db Sg Bh Hs Mt Ds Rg 58 59 60 61 62 63 64 65 66 67 68 69 70 71 Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu 90 91 Th Pa 92 93 94 95 96 97 98 99 100 101 102 103 U Np Pu Am Cm Bk Cf Es Fm Md No Lr Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 54 Read Periodic Table to Determine Electron Configuration – He Read from left to right First electron goes into period 1 First type of sublevel to fill = “1s ” He has 2 two electrons Electron configuration for He is: 1s 2 Jespersen/Brady/Hyslop n= 1 1 2 “ns” orbital being filled He “np” orbital being filled “(n – 1)d” orbital being filled “( n – 2)f” orbital being filled H n= 2 3 4 Li Be n= 3 11 12 Na Mg n= 4 19 22 23 24 K Ca Sc Ti V Cr Mn Fe Co Ni n= 5 37 20 21 Rb Sr Y Zr Nb Mo Tc Ru Rh Pd 75 76 46 78 Cs Ba La Hf Ta W Re Os Ir Pt 88 74 45 77 n= 7 87 73 44 28 40 72 43 27 39 57 42 26 38 n= 6 55 56 41 25 89 104 105 106 107 108 109 110 Fr Ra Ac Rf Db Sg Bh Hs Mt Ds Chemistry: The Molecular Nature of Matter, 6E 55 Electron Configuration of Boron (B) n= 1 1 2 H n= 2 3 4 Li Be n= 3 11 12 Na Mg n= 4 19 21 N O F Ne 13 14 15 16 17 Al Si P S Cl Ar 36 54 Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe 74 75 76 77 Cs Ba La Hf Ta W Re Os Ir n= 7 87 88 78 79 80 81 82 51 35 53 73 50 34 52 72 49 33 40 57 48 32 39 56 47 31 18 38 n= 6 55 46 30 C Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr 45 29 B 10 V 44 28 9 K Ca Sc Ti 43 27 8 24 42 26 7 23 41 25 6 22 n= 5 37 20 5 He 83 84 85 86 Pt Au Hg Tl Pb Bi Po At Rn 89 104 105 106 107 108 109 110 111 Fr Ra Ac Rf Db Sg Bh Hs Mt Ds Rg B has 5 electrons Fill first shell… Fill two subshells in second shell, in order of increasing energy 22s 22p 1 Electron Configuration B = 1 s Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 56 Learning Check Write the correct ground state electron configuration for each of the following elements. List in order of increasing n and within each shell, increasing ℓ. 1. K Z = 19 = 1 s 2 2s 2 2p 6 3s 2 3p 6 4s 1 2. Ni Z = 28 = 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 8 = 1 s 2 2s 2 2p 6 3s 2 3p 6 3 d 8 4s 2 3. Pb Z = 82 = 1s 2 2s 22p 63s 23p 64s 23d 104p 65s 24d 10 5p 66s 24f 145d 106p 2 = 1s 22s 22p 63s 23p 63d 104s 24p 64d 104f 145s 25p 65d 106s 26p 2 Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 57 Abbreviated Electron Configurations - Noble Gas Notation [noble gas of previous row] and electrons filled in next row Represents core + outer shell electrons Use to emphasize that only outer shell electrons participate in chemical reactions e.g. Ba = [Xe] 6s 2 Ru = [Kr] 4d 6 5s 2 S = [Ne] 3s 2 3p 4 Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 58 Noble Gas Core Notation for Mn Find last noble gas that is filled before Mn Next fill sublevels that follow [Ar] 4s 2 3d 5 n= 1 1 “ns” orbital being filled “np” orbital being filled “(n – 1)d” orbital being filled “( n – 2)f” orbital being filled H n= 2 3 4 Li Be n= 3 11 12 Na Mg n= 4 19 20 21 22 23 n= 5 37 38 39 2 He 5 6 7 8 9 10 B C N O F Ne 13 14 15 16 S 17 18 Cl Ar Al Si P V 24 25 26 27 28 29 30 31 32 33 34 35 36 Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr Y 40 41 42 43 44 45 46 47 48 49 50 51 52 Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te 53 54 n= 6 55 56 57 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 n= 7 87 88 89 104 105 106 107 108 109 110 111 68 69 70 71 K Ca Sc Ti Rb Sr I Xe Cs Ba La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn Fr Ra Ac Rf Db Sg Bh Hs Mt Ds Rg 58 59 60 61 62 63 64 65 66 67 90 91 92 93 94 95 96 97 98 99 100 101 102 103 Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 59 Your Turn! The ground state electron configuration for Ca is: A. [Ar] 3s 1 B. 1s 2 2s 2 2p 6 3s 2 3p 5 4s 2 C. [Ar] 4s 2 D. [Kr] 4s 1 E. [Kr] 4s 2 Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 60 Look at Group 2A Z Electron Configuration 4 1s 22s 2 Abbrev Be Mg 12 1s 22s 22p 63s 2 Ca 20 1s 22s 22p 63s 23p 64s 2 Sr 38 1s 22s 22p 63s 23p 63d 104s 24p 65s 2 [He] 2s 2 [Ne] 3s 2 [Ar] 4s 2 [Kr] 5s 2 Ba 56 1s 22s 22p 63s 23p 63d 104s 24p 64d 105s 25p 66s 2 [Xe] 6s 2 Ra 88 1s 22s 22p 63s 23p 63d 104s 24p 64d 104f 145s 25p 6 [Rn] 7s 2 5d 106s 26p 67s 2 All have ns 2 outer shell electrons Only difference is value of n Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 61 Your Turn! An element with the electron configuration [Xe]6s 24f 145d 7 would belong to which class on the periodic table? A. Transition elements B. Alkaline earth elements C. Halogens D. Lanthanide elements E. Alkali metals Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 62 Shorthand Orbital Diagrams Write out lines for orbital beyond Noble gas Higher energy orbital to right Fill from left to right Abbreviated Orbital Diagrams Ru [Kr] 4d S [Ne] 5s 3s 3p Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 63 Your Turn! Which of the following choices is the correct electron configuration for a cobalt atom? 4s 3d A. [Ar] ↑↓ ↑↓ ↑↓ ↑↓ ↑ B. [Ar] ↑ ↑↓ ↑↓ ↑↓ ↑↓ C. [Ar] ↑ ↑↓ ↑↓ ↑↓ ↑ D. [Ar] E. [Ar] ↑ ↑↓ ↑↓ ↑↓ ↑↓ ↑ ↑↓ Jespersen/Brady/Hyslop ↑↓ ↑↓ ↑ ↑ ↑ Chemistry: The Molecular Nature of Matter, 6E 64 Valence Shell Electron Configurations An even more abbreviated notation for electron configurations Use with representative elements (s and p block elements) – longer columns Electrons in s and p subshells - important for bonding Valence shell = outer shell = occupied shell with highest n Example: Sn = 5s 25p 2 Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 65 Electronic Configurations A few exceptions to rules Element Cr Cu Ag Au Expected [Ar] 3d 44s 2 [Ar] 3d 94s 2 [Kr] 4d 95s 2 [Xe] 5d 96s 2 Experimental [Ar] 3d 54s 1 [Ar] 3d 104s 1 [Kr] 4d 105s 1 [Xe] 5d 106s 1 Exactly filled and exactly half-filled subshells have extra stability Promote one electron into ns orbital to gain this extra stability Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 66 Heisenberg’s Uncertainty Principle Can’t know both exact position and exact speed of subatomic particle simultaneously Such measurements always have certain minimum uncertainty associated with them h Dx Dmv ³ 4p x = particle position mv = particle momentum = mass × velocity of particle h = Planck’s constant = 6.626 × 10–34 J s Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 67 Consequence of Heisenberg’s Uncertainty Principle Can’t talk about absolute position Can only talk about electron probabilities Where is e – likely to be? ψ = wavefunction Amplitude of electron wave ψ2 = probability of finding electron at given location Probability of finding an electron in given region of space equals the square of the amplitude of wave at that point Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 68 1s Orbital Representations a. Dot-density diagram b. Probability of finding electron around given point, ψ2, with respect to distance from nucleus c. Radial probability distribution = probability of finding electron at an “r” distance from nucleus rmax = Bohr radius Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 69 Electron Density Distribution Determined by Shape Size n Orientation m Electron density No sharp boundary Gradually fades away “Shape” Imaginary surface enclosing 90% of electron density of orbital Probability of finding electrons is same everywhere on surface Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 70 Effect of n on s Orbital In any given direction probability of finding electron same All s orbitals are spherically shaped Size increases as n increases Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 71 Spherical Nodes At higher n, now have spherical nodes Spherical regions of zero probability, inside orbital Node for electron wave Imaginary surface where electron density = 0 2s, one spherical node, size larger 3s, two spherical nodes, size larger yet In general: Number of spherical nodes =n–1 Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 72 p Orbitals Possess one nodal plane through nucleus Electron density only on two sides of nucleus Two lobes of electron density All p orbitals have same overall shape Size increases as n increases For 3p have one spherical node Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 73 Representations of p Orbitals Constant probability surface for 2p orbital Simplified p orbital emphasizing directional nature of orbital All 2p orbitals in p sub shell One points along each axis 2px Jespersen/Brady/Hyslop 2py 2pz Chemistry: The Molecular Nature of Matter, 6E 74 There Are Five Different d Orbitals Four with four lobes of electron density One with two lobes and ring of electron density Result of two nodal planes though nucleus Number of nodal planes through nucleus = Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 75 Your Turn! Which sketch represents a pz orbital? A. C. B. D. E. z y x Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 76 Periodic Properties: Consequences of Electron Configuration Chemical and physical properties of elements Vary systematically with position in periodic table i.e. with element's electron configuration To explain, must first consider amount of positive charge felt by outer electrons (valence electrons) Core electrons spend most of their time closer to nucleus than valence (outer shell) electrons Shield or cancel out (screen out, neutralize) some of positive charge of nucleus Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 77 Learning check: Li 1s 22s 1 Three protons in nucleus Two core electrons in close (1s) Net positive charge felt by outer electron: One proton Effective Nuclear Charge (Zeff) Net positive charge outer electron feels Core electrons shield valence electrons from full nuclear charge Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 78 Shielding Electrons in same subshell don't shield each other Same average distance from nucleus Trying to stay away from each other Spend very little time one below another Effective nuclear charge determined primarily by Difference between charge on nucleus (Z ) and charge on core (number of inner electrons) Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 79 Your Turn! What value is the closest estimate of Zeff for a valence electron of the calcium atom? A. 1 B. 2 C. 6 D. 20 E. 40 Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 80 Atomic Size Experiment shows atoms/ions behave as if they have definite size C and H have ~ same distance between nuclei in large number of compounds Atomic Radius (r) Half of distance between two like atoms H—H C—C etc. Usually use units of picometer 1 pm = 1 × 10–12 m Range 37 – 270 pm for atoms Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 81 Trends in Atomic Radius (r) Increases down Column (group) Zeff essentially constant n increases, outer electrons farther away from nucleus and radius increase Decreases across row (period) n constant Zeff decreases, outer electrons feel larger Zeff and radius decreases Transition Metals and Inner Transition Metals Size variations less pronounced as filling core n same (outer electrons) across row Decrease in Zeff and r more gradually Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 82 Atomic and Ionic Radii (in pm) Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 83 Ionic Radii Increases down column (group) Decreases across row (period) Anions larger than parent atom Same Zeff, more electrons Radius expands Cations smaller than parent atom Same Zeff, less electrons, Radius contracts Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 84 Your Turn! Which of the following has the smallest radius? A. Ar B. K+ C. Cl– D. Ca2+ E. S2– Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 85 Ionization Energy Energy required to remove electron from gas phase atom Corresponds to taking electron from n to n = First ionization energy M (g) M +(g) + e– IE = E IE = RHhcZ n 2 eff 2 Trends: Ionization energy decreases down column (group) as n increases Ionization energy increases across row (period) as Zeff increases Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 86 Comparing First Ionization Energies Largest first ionization energies are in upper right Smallest first ionization energies are in lower left Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 87 Table 8.2: Successive Ionization Energies in kJ/mol for H through Mg Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 88 Electron Affinity (EA) Potential energy change associated with addition of one electron to gas phase atom or ion in the ground state X(g) + e– X –(g) O and F very favorable to add electrons First electron affinities usually negative (exothermic) Larger negative value means more favorable to add electron Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 89 Table 8.3 Electron Affinities of Representative Elements Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 90 Trends in Electron Affinity (EA) Electron affinity becomes less exothermic down column (group) as n increases Electron harder to add as orbital farther from nucleus and feels less positive charge Electron affinity becomes more exothermic across row (period) as Zeff increases Easier to attract electrons as positive charge increases Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 91 Successive Electron Affinities Addition of first electron – often exothermic Addition of more than one electron requires energy Consider addition of electrons to oxygen: Change: EA(kJ/mol) O(g) + e – O–(g) –141 O–(g) + e – O2–(g) +844 Net: O(g) + 2e – O2–(g) +703 Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 92 Your Turn! Which of the following has the largest electron affinity? A. O B. F C. As D. Cs E. Ba Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E 93