Lecture outline: Chapter 6 Electronic structure of atoms. Electronic structure of atoms

Transcription

1 Lecture outline: Chapter 6 Electronic structure of atoms 1. Radiant energ 2. Quantum effects 3. The Bohr atom, orbitals 4. Man electron sstems Electronic structure of atoms Understanding the arrangement of electrons in atoms is the ke to understanding the reactivit of atoms and molecules Total number of electrons in atom Locations of electrons in space Energ states of electrons 1 2 The atom is mostl empt space! Nucleus (proton(s) and neutron(s) The superstars of chemical phsics ~10-18 cm electron: orbits the nucleus multielectron atoms have more than one e- orbiting the nucleus Ma Planck Albert Einstein Niels Bohr ~10-13 cm Diameter of atom ~ 10-8 cm (~1-5 Å) 3 Werner Heisenberg Erwin Schrodinger 4

2 Electromagnetic radiation Carries energ Man tpes Moves Wavelike character Properties of waves Regular rise and fall pattern Repeating periodicit Peak maima and peak minima Wavelength (λ, lambda): the distance from one peak maimum to the net Frequenc (ν, nu): the number of peak maima that are passed per unit time Amplitude: the height of the peak maima and minima from the central ais λ Amplitude 5 6 Some waves with different wavelengths and amplitudes λ 1 λ 2 Electromagnetic waves Carr energ Electrical and magnetic components Classified based on wavelength Move at a constant speed (c) No propagating medium needed λ 3 7 8

3 1 7/8 1/8 3/4 1/4 1.0 sec/turn 5/8 3/8 1/2 Frequenc (ν, nu): the number of peak maima that are passed per unit time as the wave propagates ν = 16 maima /second = 16s -1 = 16 h m ν = 8 maima /second = 8s -1 = 8 h Proportionalit Two variables are proportional if a change in the value of one results in a change in the value of the other, and if the two values are related mathematicall b a constant ( k ) Directl proportional: = k Inversel proportional: 1 = k 1 1 = k m ν = 4 maima /second = -1 = 4 h 9 10 What is the difference between AM and FM radio? Electromagnetic Spectrum This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license

4 Author Inductiveload, NASA GNU Free Documentation License, Version 1.2 Unit commonl used for wavelengths Unit Smbol Meaning (10 n ) Radiation tpe meter m 1 TV, radio centimeter cm 10-2 microwave millimeter mm 10-3 infrared micrometer μm 10-6 infrared nanometer nm 10-9 UV, visible Angstrom Å X-ra, gamma ra 13 Author: Victor Blacus, licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license 14 How man peak maima does red light with a wavelength of 649 nm pass in one second? In other words, what is the frequenc of 649 nm light? c = λν What is the wavelength of Q92.1 FM radiowaves? c = λν 15 16

5 Quantum effects: Planck 1900: Ma Planck Energ is released/absorbed onl in discrete units, packets, or quanta A quantum is the smallest quantit or packet of a given form of electromagnetic radiation Energ is quantied E = hν Quantum analogies What is the energ associated with 1 quantum of: (1) 649 nm red light (ν = H) (2) a Q92.1 radiowave (ν = 92.1 MH) (3) a medical -ra (ν = H) E = hν Photons: Einstein An eplanation for a phenomenon known as the photoelectric effect e - Red light e - e - Blue light e - Light energ absorbed e - 19 Sodium metal Sodium metal 20

6 Photons: Einstein An eplanation for a phenomenon known as the photoelectron effect Electromagnetic radiation behaves as if composed of a stream of particles, or photons The energ of one photon = the energ of one quantum The dual nature of electromagnetic radiation Light behaving as a wave: Light behaving as a particle: Light behaving as both a wave and a particle: m in one second 22 The dual nature of light for three wavelengths λ 1 ν = 16 maima /second = 16s -1 = 16 h Both matter and energ are quantied (eist onl in discrete units) Matter: 1 H atom 1.5 H atoms 2 H atoms 2.3 H atoms λ 2 ν = 8 maima /second = 8s -1 = 8 h 3 H atoms 3.7 H atoms λ 3 ν = 4 maima /second = -1 = 4 h Energ: 1 photon 2 photons 1.5 photons 2.3 photons 3 photons 3.7 photons 1 second 23 24

7 What is the energ associated with 1 mol of photons of: (1) 649 nm red light (ν = H) (2) a Q92.1 radiowave (ν = 92.1 MH) E = nhν (3) a medical -ra (ν = H) Niels Bohr: a model for the hdrogen atom Based on a phenomenon of atoms and light known as line spectra Monochromatic vs. polchromatic light Monochromatic light: light (radiation) of a single wavelength (e.: laser light) Visible light: composed of light (radiation) of man different wavelengths Scattering of visible light through a prism commons.wikimedia.org/wiki/file:arcoiris_high_contrasted_and_filtere d.jpg This work has been released into the public domain b its author, I, Alfredo Credit: D-Kuru/Wikimedia Commons, licensed under the Creative Commons Attribution-Share Alike 3.0 Austria license. 28

8 What would happen to the light of a laser if ou shined it through a prism? Attribution: User Kieff, Released into public domain 29 Author Netweb, Creative Commons Attribution-Share Alike 3.0 Unported license. 30 Electron ecitation and relaation gives rise to all of the color that we observe! The heat of the flame ecites an electron to a higher energ state. When the electron relaes back to the ground state, energ is released as visible light. Source light Reflected light How does it work???? 31 Li Na K Cu Pb 32

9 + H 2 - Scattering of the light emitted b an ecited atom through a prism Emitted light Line spectra: Prism E = hν = hc λ Bohr s postulates 1. Onl electron orbits of certain energies are allowed (the energ of an e - is quantied) 2. An electron in a permitted orbit has a specific energ (an allowed energ state ) 3. An electron in an allowed state is stable and will not radiate energ 410 nm 486 nm 656 nm 434 nm Some simple models to illustrate the idea of quantied orbits and electron energies electron absorbs radiant energ nucleus E in is the ground state allowed orbit n > 1 is an ecited state allowed orbit E = hν = electron absorbs radiant energ hc λ 35 Some simple models to illustrate the idea of quantied orbits and electron energies electron emits radiant energ nucleus E out is the ground state allowed orbit n > 1 is an ecited state allowed orbit E = hν = electron emits radiant energ hc λ 36

10 The energ of an orbit is referenced relative to the electrons ero point energ, the point where the electron has been completel removed from the atom An electron can jump (or rela) from an one orbit to another ΔE = E final E initial ΔE = E final E initial ΔE 2 3 Zero point E = 0 ΔE 3 4 n = 5 First ecited state n = 6 n = 7 n = 8 n = ΔE (+) for removing an electron from the atom s ground state orbit ΔE 1 4 Zero point E = 0 n = 5 First ecited state n = 6 n = 7 n = 8 n = ΔE (+) for removing an electron from the atom s ground state orbit ΔE 1 2 Ground state E = (-) Ground state E = (-) The energ of an orbit is referenced relative to the electrons ero point energ, the point where the electron has been completel removed from the atom ΔE = E final E initial ΔE 1 2 ΔE 2 3 Zero point E = 0 ΔE 3 4 n = 5 First ecited state Ground state E = (-) n = 6 n = 7 n = 8 n = ΔE (-) for placing an eternal electron in the atom s ground state orbit 39 Energ levels in the Bohr atom nucleus E = (-R )( 1 n n H 2 R H = J ΔE = E final E initial 1 1 ΔE = (RH )( ) = hν 2 2 n n i f ) 40

11 When an ecited electron in the n=4 orbit relaes directl to the ground state orbit (), what wavelength of energ is released? When an ecited electron in the n=4 orbit relaes directl to the ground state orbit (), what wavelength of energ is released? 1 1 ΔE = (RH )( ) = hν c λ = En = (-RH )( ) 2 n n n i f ν ΔE 1 4 Zero point E = 0 n = 6 n = 5 n = n = 8 n = ΔE = (RH )( ) = hν 2 2 n n i c λ = ν f Ground state E = (-) Electron ecitation and relaation gives rise to all of the color that we observe! Source light Reflected light What is the difference between a normal incandescent lightbulb and a halogen lightbulb? 43 Summar of energ and matter Radiant energ has wavelike properties Radiant energ is quantied (can onl eist in discrete packets) Radiant energ has particle like properties Matter (sp., the e-) has particle like properties The energies/orbits of matter are quantied Does matter have wavelike properties? 44

12 The debroglie wavelength of matter λ = h mv velocit Note: lower case v is velocit The greek letter nu is ν, which is frequenc Don t confuse the two! What is the wavelength of a baseball (120 g) travelling at a speed of 100 mph (44.7 m/s)? λ = h mv Heisenberg The dual nature of matter (a particle and a wave) places limitations on the preciseness with which we can know both the location and the momentum (mass velocit) of an object Know location precisel, then momentum is uncertain Know momentum precisel, then location is uncertain How does this appl to the electron? Compare the sies and wavelengths of the following moving obects: λ = object mass velocit diameter λ ratio λ to diameter baseball 0.12 kg 45 m/s 0.08 m m h mv earth kg m/s m m electron kg m/s m m

13 What does all of this mean for electronic structure??!? Schrodinger: The behavior of the electron is better described b focusing on it s wavelike properties An orbit: a defined, known pathwa The orbital An orbital: a probabilit function; the probabilit that an electron will be found in a given location A description of the distribution of electron densit in space Orbitals have a characteristic shape and energ 49 Each dot represents a position where an electron ma be found at an given moment with respect to the nucleus, which is at the center of the aes 50 An overview of the quantum mechanical model of the atom Electrons reside in areas of space called orbitals Orbitals have defined energies, shapes and sies n = principal quantum number = shell Subshells are energ levels within shells that have defined shapes (s, p, d, f) Orbitals of a given shape (within a subshell) have a specific orientation in space 51 Orbital quantum numbers n (principal) describes the energ of the orbital,2,3,4 shells l (aimuthal) describes the 3-dimensional shape of the orbital (subshells) l values for a given n are integers from 0 to n-1 m l (magnetic) describes the orientation of an orbital in space m l values for a given subshell are integers from -l to +l (2l + 1 possible orbitals for each subshell) A specific orbital is defined b specific and unique values for n, l, and m l 52

14 The orbital Allowed values for l: integers from 0 to n-1 Allowed values for m l : integers from -l to +l The orbitals Allowed values for l: integers from 0 to n-1 Allowed values for m l : integers from -l to +l Shell # (n) Subshell # (l) Orbital # (m l ) Orbital name Orbital shape Orbital orientation spherical smmetric Shell # (n) Subshell # (l) Orbital # (m l ) Orbital name Orbital shape Orbital orientation spherical Smmetric with a wave node Dumbbell/ about node centered on ais elipsoid Dumbbell/ about node centered on ais elipsoid Dumbbell/ elipsoid about node centered on ais s m There is onl one orbital in (1,0,0) 53 There are four orbitals in (2,0,0; 2,1,-1; 2,1,0; 2,1,1 ) 54 The four orbitals The four orbitals spherical Dumbbell (elipsoid) 55 m l = 1 m l = -1 l = 1 m l = 1 S. Ensign electronic m l structure = 1 56

15 l = 1 m l = 1 orbitals l = 1 m n energ shell l shape subshell m l orientation orbital l = 1 m l = -1 Compare the and orbitals node p p p node Shell # (n) Subshell # (l) The orbitals Allowed values for l: integers from 0 to n-1 Allowed values for m l : integers from -l to +l Orbital # (m l ) Orbital name Orbital shape Orbital orientation spherical Smmetric with 2 wave nodes Dumbbell about node centered on ais Dumbbell about node centered on ais Dumbbell about node centered on ais The nine orbitals,,,,,, 2,, 2-2 l = 1 l = pears four quadrants of plane pears four quadrants of plane pears to one torus 2 pears in ais, torus to pears pears Centered about and on and aes pears four quadrants of plane 59 60

16 The nine orbitals,,,,,, 2,, 2-2 The five orbitals l = 1 l = 2 (cutawa view) The,, and orbitals radial probabilit m m m Distance from nucleus 64

17 The orbitals Allowed values for l: integers from 0 to n-1 Allowed values for m l : integers from -l to +l The siteen orbitals,,,, 4d, 4d, 4d 2, 4d, 4d 2-2 4f 7 l = 1 l = 2 l = 3 Shell # (n) Subshell # (l) Orbital # (m l ) Orbital name Orbital shape Orbital orientation spherical Smmetric with 3 wave nodes 4 1-1, 0, 1,, Dumbbell Centered about and on, and aes 4 2-2, -1, 0, 1, 2 4d, 4d, 4d 2, 4d, 4d pears and 2 pears to one torus As for orbitals 4 3-3, -2, - 1, 0, 1, 2, 3 4f 3, 4f 2, 4f, 4f, 4f ( 2 2 ), 4f ( ), 4f (3 2 2 ) Prett complicated! Prett complicated! The seven f orbitals: difficult to draw, rarel encountered in our dail life 0 to n-1 allowed values -l to +l allowed values for each value of l n value l value Subshell name m l value # of orbitals in subshell # of orbitals in shell , 0, , 0, , -1, 0, 1, , 0, d -2, -1, 0, 1, f -3, -2, -1, 0, 1, 2,

18 Principal quantum number n (shell) Number of subshells (l) 1 1 s 2 2 s, p 3 3 s, p, d 4 4 s, p, d, f 5 5 s, p, d, f, g Tpe of subshell Number of orbitals in that subshell s 1 p 3 d 5 f 7 Subshell name (tpe of orbital) m l Atomic orbitals summar : One orbital : Four orbitals:,, : nine orbitals:,,,, 2,, 2-2 : Siteen orbitals:,, 4 p 69 4d, 4d, 4d 2, 4d, 4d 2-2 4f 7 70 Energies of the orbitals in n=1 to 4 for the H atom Orbitals for the 1 st four energ levels of the H atom Zero point E = 0 n = n = 4d 4f 4d 4f Ground state E = (-) 71 72

19 Energies of the orbitals in n=1 to 4 for the H atom n = Shells (energies) 4d 4f Specific orbitals: defined orientations in space subshells (orbital shapes) subshells (orbital shapes) Multielectron atoms All of the considerations to now were developed for the H atom with a single electron How does the quantum mechanical model appl to multielectron atoms? Same quantum numbers, shapes, orbitals Maimum of 2 electrons can occup each orbital Energies of orbitals are affected b presence of other electrons in other orbitals Principle energies are lower in multielectron atom Energies of subshells are split in multielectron atoms Some crossover of energ levels in multielectron atoms results in certain subshells having lower energies than subshells with lower n values Electrostatic interactions are responsible for the differences in energies for the single- and multielectron atoms n = 4d 4f ΔE 1 2 6s 5s 5p 4d 4f Z p+ ΔE 1 2 Energ levels of the single electron atom Energ levels of the multielectron atom, where additional electrons occup higher energ orbitals in succession 75 76

20 The spin quantum number, m s N S S N m s = +1/2 m s = -1/2 How do electrons populate orbitals in a multielectron atom? The Pauli eclusion principle: No two electrons in an atom can have the same set of four quantum numbers n energ shell l shape subshell m l orientation orbital m s electron spin clockwise (CW) or CCW Populating orbitals in a multielectron atom 6s 5s 5p 4d 4f The Pauli eclusion principle: No two electrons in an atom can have the same set of four quantum numbers Electrons want to occup the lowest energ orbital available The Pauli eclusion principle: No two electrons in an atom can have the same set of four quantum numbers n energ shell l shape subshell m l orientation orbital m s electron spin clockwise (CW) or CCW Electrons want to occup the lowest energ orbital available Represent an electron b a single sided arrow: and 80

21 n l Subshell m l value value value name # of orbitals # of orbitals in subshell in shell , 0, , 0, , -1, 0, 1, The Pauli eclusion principle: No two electrons in an atom can have the same set of four quantum numbers n energ shell l shape subshell m l orientation orbital m s electron spin clockwise (CW) or CCW Electrons want to occup the lowest energ orbital available The H atom: one e- m m s = +1/2 81 m m s = +1/2 m m s = -1/ , 0, d -2, -1, 0, 1, f -3, -2, -1, 0, 1, 7 2, 3 The Pauli eclusion principle: No two electrons in an atom can have the same set of four quantum numbers n energ shell l shape subshell m l orientation orbital m s electron spin clockwise (CW) or CCW Electrons want to occup the lowest energ orbital available The He atom: two e- 82 m m s = +1/2 m m s = +1/2 m m s = -1/2 The Pauli eclusion principle: No two electrons in an atom can have the same set of four quantum numbers n energ shell l shape subshell m l orientation orbital m s electron spin clockwise (CW) or CCW Electrons want to occup the lowest energ orbital available The Li atom: 3 e- 83 m m s = +1/2 m m s = +1/2 m m s = -1/2 m m s = -1/2 The Pauli eclusion principle: No two electrons in an atom can have the same set of four quantum numbers n energ shell l shape subshell m l orientation orbital m s electron spin clockwise (CW) or CCW Electrons want to occup the lowest energ orbital available The Be atom: 4 e- 84

22 m m s = +1/2 m m s = -1/2 The Pauli eclusion principle: No two electrons in an atom can have the same set of four quantum numbers l = 1 m l = 1 m s = +1/2 Electrons want to occup the lowest energ orbital available The gist of all this: An electron will occup the lowest energ orbital that is available A maimum of two electrons can occup an given orbital (Pauli eclusion principle) m m s = +1/2 m m s = -1/2 The B atom: 5 e The B atom: 5 e- The C atom: 6 e- An electron will occup the lowest energ orbital that is available A maimum of two electrons can occup an given orbital (Pauli eclusion principle) An electron will occup the lowest energ orbital that is available A maimum of two electrons can occup an given orbital (Pauli eclusion principle) Where do we put the 6 th electron? 87 88

23 Hund s rule For degenerate orbitals (orbitals of the same energ), the lowest energ is attained when the number of electrons with the same spin is maimied Two e- with different spins Two e- with same spins The C atom: 6 e- An electron will occup the lowest energ orbital that is available A maimum of two electrons can occup an given orbital (Pauli eclusion principle) For degenerate orbitals (orbitals of the same energ), the lowest energ is attained when the number of electrons with the same spin is maimied The N atom: 7 e- The O atom: 8 e- An electron will occup the lowest energ orbital that is available A maimum of two electrons can occup an given orbital (Pauli eclusion principle) For degenerate orbitals (orbitals of the same energ), the lowest energ is attained when the number of electrons with the same spin is maimied 91 An electron will occup the lowest energ orbital that is available A maimum of two electrons can occup an given orbital (Pauli eclusion principle) For degenerate orbitals (orbitals of the same energ), the lowest energ is attained when the number of electrons with the same spin is maimied 92

24 The O atom: 8 e- Electron configuration for the O atom A faster wa to draw orbital filling: Electron configuration: Write electron configurations for and elements Write electron configurations for elements 95 96

25 Rules for adding electrons to orbitals Electrons go into the lowest energ orbital available For a given n shell, s orbitals are lower in energ than p which are lower in energ than d which are lower than f Onl two electrons can occup a given orbital For orbitals of the same energ, one electron will occup each orbital before the start pairing up Some energ level crossovers occur due to electrostatic effects Two eas was to keep track of the order of orbital filling in multielectron atoms Use the periodic table to guide ou The principle quantum number of d block elements is one less than that of the adjacent s and p block elements The principle quantum number of f block elements is two less than that of the adjacent s and p block elements, and one less than the adjacent d block Even easier: use the Auf-Bau principle The periodic table color coded b the tpe of subshell being filled The periodic table color coded b principle quantum number of the orbital being filled 5s 6s 7s 4d 5d 6d 5p 6p 7p 4f 5f 99 5s 4d 5p 6s 4f 5d 6p 100

26 The periodic table color coded b principle quantum number of the orbital being filled The Auf-Bau Rule : The Order in which the Orbitals Fill in Polelectronic Atoms d 10 4f 14 5s 2 5p 6 5d 10 5f 14 6s 2 6p 6 6d 10 6f 14 7s 2 7p 6 Follow this rule and ou can t go wrong!! 5s 4d 5p 6s 4f 5d 6p s 4d 5p 6s 4f 5d 6p 102 Write electron configurations for n = 5 elements 6s 5p 5s 4d 4f Write electron configurations for n = 6 elements 6s 5p 5s 4d 4f d 10 4f d 10 4f 14 5s 2 5p 6 5d 10 5f 14 5s 2 5p 6 5d 10 5f 14 6s 2 6p 6 6d 10 6f 14 6s 2 6p 6 6d 10 6f 14 7s 2 7p 6 7s 2 7p 6 5s 4d 5p 103 5s 4d 5p 6s 4f 5d 6p 104

27 Electron configurations of the elements Electron configurations of the elements, color coded b subshell tpe d 10 4f 14 5s 2 5p 6 5d 10 5f 14 Anomolous electron configurations are in red 6s 2 6p 6 6d 10 6f 14 7s 2 7p 6 Anomolous electron configurations are in red