Chapter 7.! Atomic Structure and Periodicity

Transcription

1 Chapter 7! Atomic Structure and Periodicity

2 From Classical Physics to Quantum Theory Quantum Mechanics: the physics of the very small

3 The Players Erwin Schrodinger Werner Heisenberg Louis Victor De Broglie Neils Bohr Albert Einstein Max Planck James Clerk Maxwell

4 James Clerk Maxwell Proposed that visible light consists of electromagnetic waves. waves A vibrating disturbance by which energy is transmitted.

5 Waves!! Electromagnetic waves have 3 primary characteristics: 1.! Wavelength,!: distance (m, nm, etc.) between two peaks in a wave. 2.! Frequency, ": number of waves per second that pass a given point in space. Units = Hertz, Hz, cycles/second, s -1, 1 /s. Use 1 /s in calcs! 3.! Speed: speed of light is # 10 8 m/s in a vacuum.

6 As wavelength! decreases, frequency, ", increases. Inverse relationship

7 Wavelength and frequency can be interconverted.! " = c " = frequency (s $ 1 )! = wavelength (m) c = speed of light (m/s)

8 Figure 7.2: Classification of electromagnetic radiation. You must know this order! high frequency low frequency

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10 The Players Erwin Schrodinger Werner Heisenberg Louis Victor De Broglie Neils Bohr Albert Einstein Max Planck James Clerk Maxwell

11 An Observable Fact hot objects radiate electromagnetic energy classical physics assumed that radiating energy was continuous, due to its wavelike nature.

12 iron bar

13 Red Hot

14 White Hot

15 Blue Hot Classical physics predicts a continuous radiating energy, due to wavelike nature. The Ultraviolet Catastrophe: classical physics predicts an infinite amount of energy could be released in a radiation process!

16 Max Planck the energy of the emitted electromagnetic radiation is proportional to frequency E = h" = hc/! where h = x J s Planck s constant

17 %E = n h" Max Planck n is a whole number (integer) Planck tried a what-if scenario: there is a smallest change in energy possible for black body radiation. Light energy is always emitted in multiples of h". This assumption turns what was an integral over all wave energies into a sum over allowed energies. Fixes the theoretical catastrophe!

18 Blue Hot h" Max Planck %E = n h" Black body radiation is emitted in multiples of h", where n = integer. h" h" Energy emitted as electromagnetic radiation by an object (such as a hot iron bar) can have only certain discrete values. Its energies are QUANTIZED Max Planck = father of the quantum concept

19 Energy and the EM spectrum high frequency high energy low frequency low energy

20 The Players Erwin Schrodinger Werner Heisenberg Louis Victor De Broglie Neils Bohr Albert Einstein Max Planck James Clerk Maxwell

21 Another Mystery in Physics: The Photoelectric Effect Shine light on a metal surface and you can only eject electrons out of it when the light s energy is above a certain threshold. Very bright/intense light below that energy threshold does nothing. Very bright/intense light above that energy threshold ejects electrons but not any faster than dim light at same energy.

22 Photoelectric Effect

23 Albert Einstein 1905 Accounted for the photoelectric effect by treating light as though it were a stream of particles -- photons. quantization of electromagnetic radiation

24 Albert Einstein 1905 Energy of incident light = h" = minimum energy to remove electron (binding energy) + extra speed/kinetic energy h" = binding energy + kinetic energy e - Binding energy = h" 0 where " 0 = threshold freq. kinetic energy of e - = 1/2 m e- v 2 = h" h" 0

25 Depending on the experiment, electromagnetic radiation exhibits wave or particulate properties. wave /particle duality

26 Example Calculate the energy(in joules)of a photon with a wavelength 5.00 x 10 4 nm (infrared region). E = hc! E = h " c " =! E = (6.63 x J. s )(3.00 x 10 8 m/s) 1 x 10-9 m 5.00 x 10 4 nm x 1 nm = 3.98 x J

27 The Players Erwin Schrodinger Werner Heisenberg Louis Victor De Broglie Neils Bohr Albert Einstein Max Planck James Clerk Maxwell

28 Figure 7.6: (a) A continuous spectrum containing all wavelengths of visible light. (b) The hydrogen line spectrum contains only a few discrete wavelengths.!

29 Bohr Solution the electron circles nucleus in a circular orbit He imposed quantum condition on electron energy: only certain orbits and energies allowed energy is emitted when electron moves from higher energy state (excited state) to lower energy state the lowest electron energy state is ground state

30 Bohr Solution An electron in the n th orbit away from the nucleus in an atom with atomic number Z (Z protons) has this energy: E = Ê J Z 2 ˆ n Á Ë n 2 Only works for the H atom and for weird ions that have 1 e- like He +, Li 2+, etc.

31 Stable, lowest energy state of hydrogen atom ( ground state ) Ê E n = J Z 2 ˆ Á Ë n 2 Ê E 1 = JÁ 12 Ë 1 2 ˆ = J

32 Excited state of hydrogen atom Ê E n = J Z 2 ˆ Á Ë n 2 Ê E 4 = JÁ 12 Ë 4 2 ˆ = J

33 An electron that falls from n=4 to n=2 produces one of the lines in the Balmer series h" Ê 1 DE = E f - E i = -( J)Z 2 2 n - 1 ˆ Á 2 Ë f n i Ê 1 = -( J) ˆ Á = J Ë 2 4 2

34 Example What is the wavelength of the photon emitted during its transition from the n i = 4 state to the n f = 2 state in the hydrogen atom? %E = J = hn = hc l l = hc DE = ( Js)( m ) s J = m = 486nm = turquoise what part of spectrum?

35 486nm = what part of spectrum?

36 Two ways of looking at electron transitions - energy and orbit

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38 The Players Erwin Schrodinger Werner Heisenberg Louis Victor De Broglie Neils Bohr Albert Einstein Max Planck James Clerk Maxwell

39 Wave /Particle Duality If a light wave has a particular nature might not a particle have wave properties?

40 Figure 7.5: (a) Diffraction occurs when electromagnetic radiation is scattered from a regular array of objects, such as the ions in a crystal of sodium chloride. The large spot in the center is from the main incident beam of X rays. (b) Bright spots in the diffraction pattern result from constructive interference of waves. The waves are in phase; that is, their peaks match. (c) Dark areas result from destructive interference of waves. The waves are out of phase; the peaks of one wave coincide with the troughs of another wave. Electrons do the same kind of thing!

41 Albert Einstein Theory of special relativity leads to realization of the equivalence of mass and energy energy E = m c 2 mass speed of light 3.00 x 10 8 m/s

42 Louis Victor De Broglie showed that electrons have wave properties wave-particle duality mc 2 = h c! h! = mc E (photon) = h" E (photon) = mc 2 watch units! 1 J = 1 kgm 2 /s 2 = h c!! = h mv for moving matter (not light)! baseball! 1.9 x m Waaaay too small to see!! e-! 7.3 x m About size of an atom!

43 Figure 7.9: The standing waves caused by the vibration of a guitar string fastened at both ends. Each dot represents a node (a point of zero displacement).

44 Connection between debroglie electron waves and Bohr orbits

45 The Players Erwin Schrodinger Werner Heisenberg Louis Victor De Broglie Neils Bohr Albert Einstein Max Planck James Clerk Maxwell

46 Werner Heisenberg Uncertainty principle position and momentum of an electron cannot be simultaneously determined if position is measured accurately, uncertainty in measuring momentum (speed) is large, vice versa %x %p = h/4p uncertainty in position uncertainty in momentum

47 The Players Erwin Schrodinger Werner Heisenberg Louis Victor De Broglie Neils Bohr Albert Einstein Max Planck James Clerk Maxwell

48 Erwin Schrodinger wave (quantum) mechanics Schrodinger Equation Emphasis on the wave properties of the electron Started with formulas that describe any wave s motion Energy ^ HY = EY Hamiltonian differential operator wavefunction

49 Solutions of the Schrodinger Wave Equation for a One-Electron Atom

50 Quantum Numbers

51 Quantum Numbers each orbital is characterized by a unique set of quantum numbers principal quantum number: n angular momentum quantum number: l (azimuthal) magnetic quantum number: m l

52 Principal quantum number: n related to size and energy of orbital shells: integral values: 1, 2, 3,... higher n the electron, on average, is farther from nucleus the electron less strongly bound by nucleus (higher energy potential)

53 Angular momentum quantum number: l related to shape of orbital subshells: integral values: 0, 1, 2,, n - 1 l = 0: s orbital l = 1: p orbital l = 2: d orbital l = 3: f orbital

54 Relation of n and l n = 1 n = 2 l = 0 l = 0, 1 1s 2s, 2p n = 3 n = 4 l = 0, 1, 2 l = 0, 1, 2, 3 3s, 3p, 3d 4s, 4p, 4d, 4f

55 Magnetic quantum number: m l related to orientation of orbital in space integral values between l and -l

56 Charge-Cloud Model Bohr s orbits were WRONG, but are still useful as a model. It turns out, the best we can know is the probability of finding an electron somewhere. To find the probability of finding an electron somewhere in a particular atomic orbital, take its wavefunction (the function that defines its orbital) and square it. Atomic Theory Polka!

57 Figure 7.12: (a) Cross section of the hydrogen 1s orbital probability distribution divided into successive thin spherical shells. (b) The radial probability distribution. Most probable distance (equals Bohr radius!)

58 Odyssey demo: d-orbitals

59 Figure 7.13: Two representations of the hydrogen 1s, 2s, and 3s orbitals.!

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61 Figure 7.14: Representation of the 2p orbitals. (a) The electron probability distributed for a 2p orbital. (b) The boundary surface representations of all three 2p orbitals.!"#$%&'()&*$+,$($-$./$0$$-$1 m l = -1 m l = 0 m l = +1

62 Figure 7.16: Representation of the 3d orbitals. m l = -2 m l = -1 m l = 0 m l = +1 m l = +2

63 Figure 7.17: Representation of the 4f orbitals in terms of their boundary surface.

64 Atomic Orbitals

65 Relation of l and m l s: l = 0 m l = 0 p: l = 1 m l = -1, 0, 1 d: l = 2 m l = -2, -1, 0, 1, 2 f: l = 3 m l = -3, -2, -1, 0, 1, 2, 3

66 energies of hydrogen orbitals for the hydrogen atom (only 1 electron), all orbitals with the same principal quantum number ( n value) have the same energy i.e., they are degenerate

67 4s 4p 4d 4f 3s 3p 3d 2s 2p E 1s Orbital energy levels in the hydrogen atom

68 energies of multi-electron orbitals for a many-electron atom, the energy depends on both the principal quantum number (n) and the angular momentum quantum number (l) i.e., each subshell represents a different energy in a multi-electron system

69 5s 4s 4p 4d 3d E 3s 3p 2s 2p 1s Orbital energy levels in a many-electron atom

70 Why do subshells (eg. 3s vs. 3p vs. 3d) in multielectron atoms have different energies?

71 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 7s 6p 7p 6d Order in which subshells are filled in a many-electron atom

72 Electron Configuration The electron configuration of an atom tells us how the electrons are distributed among the various atomic orbitals.

73 Figure 7.19: A picture of the spinning electron. Spin Quantum Numbers: m s = +1/2 m s = -1/2

74 The Pauli Exclusion Principle Tried to explain the lengths (8, 18, 32) of rows/periods in the periodic table Said no two electrons can have all the same quantum numbers, so two electrons can occupy the same orbital only when they have opposite spins 2 s company, 3 s a crowd!

75 Orbital Filling Rules (1) electrons are added to orbitals beginning with the orbital of the lowest energy (aufbau principle) (2) maximum of two electrons per orbital (Pauli exclusion principle)

76 First Period principal quantum number (n) = 1 Hydrogen Helium Z = 1 Z = 2 1s 1 1s 2 Quantum Number Rag! 1s 2s 2p H He

77 Diamagnetism and Paramagnetism Diamagnetic substances are mostly unaffected by a magnetic field. all electron spins are paired He Paramagnetic substances are attracted by a magnet. contain at least one electron with an unpaired spin H

78 Second Period principal quantum number (n) = 2 Z 1s 2s 2p Li 3 Be 4 B 5 C 6

79 Hund s Rule (3) when two or more orbitals are of equal energy, each one is singly occupied before any are doubly occupied the most stable arrangement of the electrons in the sub-shells is the one with the greatest number of parallel spins

80 Second Period principal quantum number (n) = 2 Z 1s 2s 2p Li 3 Be 4 B 5 C 6

81 Second Period cont... Z 1s 2s 2p N 7 O 8 F 9 Ne 10

82 Short-hand Notation of Electron Configurations

83 [Ne] = 1s 2 2s 2 2p 6 Third Period Na Mg Al Si P S Cl Ar [Ne] 3s 1 [Ne] 3s 2 [Ne] 3s 2 3p 1 [Ne] 3s 2 3p 2 [Ne] 3s 2 3p 3 [Ne] 3s 2 3p 4 [Ne] 3s 2 3p 5 [Ne] 3s 2 3p 6 [Ne] core

84 [Ar] = 1s 2 2s 2 2p 6 3s 2 3p 6 K Ca Sc [Ar] 4s 1 [Ar] 4s 2 [Ar] 4s 2 3d 1 Fourth Period [Ar] core Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn first series of transition elements

85 Transition Metals have incompletely filled d subshells or readily give rise to cations that have incompletely filled d subshells

86 First Transition Series Sc 21 [Ar] 4s 2 3d 1 Ti 22 [Ar] 4s 2 3d 2 V 23 [Ar] 4s 2 3d 3 Cr 24 [Ar] 4s 1 3d 5 Mn 25 [Ar] Fe 26 [Ar] Co 27 [Ar] Ni 28 [Ar] Cu 29 [Ar] Zn 30 [Ar]

87 Periodic Anomalies 4s 3d Cr expected [Ar] Cr actual [Ar]

88 First Transition Series Sc 21 [Ar] 4s 2 3d 1 Ti 22 [Ar] 4s 2 3d 2 V 23 [Ar] 4s 2 3d 3 Cr 24 [Ar] 4s 1 3d 5 Mn 25 [Ar] 4s 2 3d 5 Fe 26 [Ar] 4s 2 3d 6 Co 27 [Ar] 4s 2 3d 7 Ni 28 [Ar] 4s 2 3d 8 Cu 29 [Ar] 4s 1 3d 10 Zn 30 [Ar] 4s 2 3d 10

89 Periodic Anomalies 4s 3d Cr expected [Ar] Cr actual [Ar] Cu expected [Ar] Cu actual [Ar]

90 Notice any e- configuration patterns in the periodic table?

91 Notice any e - configuration patterns in the periodic table? 6d Electron Configuration Polka!

92 Development of the Periodic Table

93 John Newlands - Law of Octaves 1864 When arranged in order of atomic mass, every eighth element had similar properties.

94 Dimitri Mendeleev / Lothar Meyer 1869 organized elements arranged according to atomic mass. Mendeleev showed how useful the table could be in predicting the existence and properties of yet unknown elements

95 Mendeleev s predicted element properties vs. observed Mendeleev song!

96 Modern Periodic Table - Henry Mosley 20th Century Organized according to atomic number.

97 The Periodic Table

98 For each of the upcoming parts, which orbitals are being filled?

99 Main groups group numbers indentified by suffix A

100 Main group metals Alkali metals Alkaline earth metals

101 Nonmetals Halogens Noble gases

102 transition metals Lanthanides

103 Actinides transition metals Lanthanides

104 Periodic Classification of the Elements

105 Valence Electrons The outer e- s of an atom, which are important to chemists because they are involved in chemical bonding. Elements in the same group of the periodic table generally have the same # of valence e- s.

106 Group 8A noble gases He Ne Ar Kr Xe Rn 1s 2 [He]2s 2 2p 6 [Ne]3s 2 3p 6 [Ar]3d 10 4s 2 4p 6 [Kr]4d 10 5s 2 5p 6 [Xe]5d 10 4f 14 6s 2 6p 6

107 Group 1A alkali metals H Li Na K Rb Cs Fr 1s 1 [He]2s 1 [Ne]3s 1 [Ar]4s 1 [Kr]5s 1 [Xe]6s 1 [Rn]7s 1

108 Group 2A Alkaline earth metals Be Mg Ca Sr Ba Ra [He]2s 2 [Ne]3s 2 [Ar]4s 2 [Kr]5s 2 [Xe]6s 2 [Rn]7s 2

109 Group 7A halogens F Cl Br I At 2s 2 2p 5 3s 2 3p 5 4s 2 4p 5 5s 2 5p 5 6s 2 6p 5

110 Electron Configurations of Cations Element Atom Ion Sodium Na [Ne]3s 1 Magnesium Mg [Ne]3s 2 Aluminum Al [Ne]3s 2 3p 1 Na + [Ne] Mg 2+ [Ne] Al 3+ [Ne] Isoelectronic species have the same number of electrons.

111 Electron Configurations of Anions Element Atom Ion Hydrogen H 1s 1 H Fluorine F 1s 2 2s 2 2p 5 F Oxygen O 1s 2 2s 2 2p 4 O 2 Nitrogen N 1s 2 2s 2 2p 3 N 3 1s 2 1s 2 2s 2 2p 6 1s 2 2s 2 2p 6 1s 2 2s 2 2p 6 Isoelectronic species have the same number of electrons.

112 Ions most commonly encountered ions have noble gas electron configuration Li + O 2 F Na + Mg 2+ Al 3+ S 2 Cl K + Ca 2+ Br Sr 2+ I - Ba 2+ isoelectronic ions

113 Periodic Variation in Physical Properties

114 Shielding - a way towards understanding trends in element properties shielding - when inner/core e - s repel e - s in outer orbits, pushing out on them and effectively canceling out (shielding) the pull in of some of the p + s in the nucleus. Ex. Li 1s 2 2s 1 n=2 n=1 3p + # of p + s = 3 # of shielding e - s = 2 So outer e - effectively feels the pull of 3-2 = 1 p + s

115 Shielding - periodic trends How many p + s are unshielded and are left pulling on the outermost electron of the following?: # unshielded p + pulling on outer e - s = total # of p + - # of inner/shielding e - s Element # unshielded p + pulling on outer e - s Li 3-2 = 1 Na = 1 F 9-2 = 7 Cl = 7 any alkali metal 1Mark these on your any halogen 7Bohr orbit diagram!

116 Atomic Radius Br 2 measure distance between centers of 228pm bonded atoms therefore atomic radius of Br is 114pm Trends down and across periodic table? atomic radius decreases from left to right across periodic table. increases going down a column.

117 Atomic radius decreases Atomic radius increases

118 Atomic radius decreases Atomic radius increases

119 Ionic Radius the size of a cation or an anion

120 + Li F Li + F Size changes when Li reacts with F to give ions in LiF

121 Li + Be 2+ O 2 F Na + Mg 2+ Al S Cl K + Ca 2+ Ga 3+ Se 2 Br Rb + Sr 2+ In 3+ Sn 4+ Sb 5+ Te 2 I

122 Ionization Energy

123 Ionization Energy (I) energy required to remove an electron from an atom (or ion) in the gas phase %H! for reaction: X(g) X + (g) + e %H! : the change in heat energy (kj/mol)

124 Ionization Energy Decreases Going Down a Group I 1, kj/mol H 1312 Li 520 Na 495 K 419 Rb 409 Cs 382 1s 2s 3s 4s 5s 6s Why? Same pull of 1 p + on outer e - but outer e- is farther away from p + s

125 Ionization Energy Decreases Going Down a Group I 1, kj/mol He 2377 Ne 2088 Ar 1527 Kr 1356 Xe 1176 Rn s 2p 3p 4p 5p 6p Why? Same pull of 8 p + s on outer e - s but outer e- s are farther away from p + s

126 Al: [Ne]3s 2 3p 1 Ionization Energies First ionization energy: Al(g) Æ Al + (g) + e I 1 = 580 kj/mol Second ionization energy: Al + (g) Æ Al 2+ (g) + e I 2 = 1815 kj/mol Third and fourth ionization energies: Al 2+ (g) Æ Al 3+ (g) + e I 3 = 2740 kj/mol Al 3+ (g) Æ Al 4+ (g) + e I 4 = 11,600 kj/mol!?! Why so much harder to pull off 4th e-?

127 Ionization Energies Third and fourth ionization energies: Al 2+ (g) Æ Al 3+ (g) + e Al 3+ (g) Æ Al 4+ (g) + e I 3 = 2740 kj/mol I 4 = 11,600 kj/mol Why so much harder to pull off 4th e-? Compare shielding for 3rd vs. 4th electron removed = 3 p + pulling 13-2 = 11 p + pulling!!! The large jump in I.E. is the result of removing core electrons which feel the pull of more p + s than valence e - s.

128 Ionization Energy Tends to Increase Across a Period

129 Ionization Energy Tends to Increase Across a Period

130 Ionization Energy Tends to Increase Across a Period

131 Ionization Energy Tends to Increase Across a Period

132 anomalies in I.E. trend

133 Be B N O 1s 2s 2p 1s 2s 2p The drop in E.I. is due to : the 2s electrons shielding the 2p a little repulsion in O between e- s in the same orbital

134 Electron affinity

135 Electron affinity is the energy change that occurs when an electron is accepted by an atom in the gaseous state (kj/mol). X(g) + e - X - (g) The more negative the electron affinity, the greater the tendency of the atom to accept an electron.

136 X(g) + e - Electron affinity X - (g) (-) kj/mol The sign of the electron affinity represents the energy released when an electron is accepted. X(g) Æ X + (g) + e (+) kj/mol A positive ionization energy means that energy must be supplied to remove an electron (endothermic)

137 Electron affinity increases Electron affinity decreases