Electronic Structure of Atoms. Chapter 6
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1 Electronic Structure of Atoms Chapter 6
2 Electronic Structure of Atoms 1. The Wave Nature of Light All waves have: a) characteristic wavelength, λ b) amplitude, A
3 Electronic Structure of Atoms 1. The Wave Nature of Light Maxwell (1873) proposed: visible light consists of electromagnetic waves. Electromagnetic radiation: the emission and transmission of energy in the form of electromagnetic waves. All electromagnetic radiation λ x ν = c Speed of light (c) in vacuum = 3.00 x 10 8 m/s
4
5 Electronic Structure of Atoms Planck: energy can only be absorbed or released from atoms in certain amounts called quanta Energy E E frequency ν = h ν h: Planck s constant ( J.s)
6 Electronic Structure of Atoms The photoelectric effect : provides evidence for the particle nature of light -- quantization. Light has both: 1. wave nature 2. particle nature Photon is a particle of light A Photocell
7 White light can be separated into a continuous spectrum of colors
8 Bohr noticed the line spectra of certain elements
9 Bohr s Model of the Hydrogen Atom Bohr s s Model Na: H: The energy states --- orbits --- quantized
10 7.3
11 Bohr s Model of the Hydrogen Atom Bohr s s Model The energy states --- orbits --- quantized The light emitted from excited atoms must be quantized and appear as line spectra. E n 1 = RH n 2 n: the principal quantum number (where n = 1, 2, 3,. and nothing else) R H : the Rydberg constant ( J)
12 E = hν E = hν 7.3
13 Bohr s Model of the Hydrogen Atom Bohr s s Model * The first orbit has n = 1, is closest to the nucleus, and has negative energy by convention. * The furthest orbit has n close to infinity and corresponds to zero energy. E n 1 = RH n 2
14 Bohr s Model of the Hydrogen Atom Bohr s s Model * Electrons in the Bohr model can only move between orbits by absorbing and emitting energy in quanta (hv). * The amount of energy absorbed or emitted: E = = E E f i h ν
15 Bohr s Model of the Hydrogen Atom Bohr s s Model E = = E E f i h ν ν = E h When n i > n f, energy is emitted. = When n f > n i, energy is absorbed. R h H 1 n 2 i n 1 2 f
16 Bohr s Model of the Hydrogen Atom The line spectrum of hydrogen : The visible line spectrum of hydrogen : transitions of electrons in H atoms from n = 5 to n = 2, n = 4 to n = 2, and n = 3 to n = 2
17 Bohr s Model of the Hydrogen Atom For the transition from n = 5 to n = 2 E RH 1 1 ν = = 2 2 h h ni n f E J ν = = = s h J s λ = c ν = m/ s s = m= 433nm
18 The Wave Behavior of Matter Light Matter Using Einstein s and Planck s equations, de Broglie supposed: h λ = mv mv (momentum): a particle property λ: a wave property The particle nature The wave nature The particle nature The wave nature???
19 The Wave Behavior of Matter de Broglie s work λ = h mv Matter The particle nature (m, υ) The wave nature ( λ) To study small objects: a) X-ray diffraction b) Electron microscopy
20 Heisenberg s s Uncertainty Principle On the mass scale of atomic particles, we cannot determine the exactly the position, direction of motion, and speed simultaneously. For electrons: we cannot determine their momentum and position simultaneously. x p 2 h π
21 Heisenberg s Uncertainty Principle Example: A macroscopic object, a bullet, with mass 10 g, how about the uncertainty of its velocity if the uncertainty of its position is x 0.01cm? x p h 2 π -34 h υ 2π m x = υ m s
22 Heisenberg s Uncertainty Principle For a microscopic particle, an electron: m= kg diameter of an atom: m x--- at least m υ? υ 34 h = 2π m x υ m s 1 The uncertainty of velocity is obvious. m: very small The uncertainty of both the location and momentum is important.
23 Heisenberg s Uncertainty Principle It is impossible for an electron to move in well-defined orbits about the nucleus.
24 Quantum Mechanics and Atomic Orbits Schrödinger Wave Equation(1926): (Incorporate both the wave-like and particlelike behavior of electrons) ψ Wave terns particle terms A new way of dealing with subatomic particles
25 Quantum Mechanics and Atomic Orbits Schrödinger Wave Equation: θ ϕ θ ϕ θ cos sin sin cos sin r z r y r x = = = z y x r + + = ( ) 0 8 sin 1 sin sin = ϕ π ϕ ϕ θ θ ϕ θ θ θ ϕ V E h m r r r r r r
26 Quantum Mechanics and Atomic Orbits is the function of n, l, m i.e.: the electrons in a Hydrogen atom n=1, l=0,m=0 n=2, l=0, m= , 1, 1 a Z e a Z = π ϕ ,0, a Z e a Z a Z = π ϕ
27 Quantum Mechanics and Atomic Orbits is the function of n, l, m n=2, l=1, m=0 ϕ 2,1,0 1 Z = 4 2π a re Z a 0 cos θ
28 Quantum Mechanics and Atomic Orbits Wave function : to describe the state of electrons in an atom--- atomic orbit ψ 1,0, s orbit ( 1s ) 2,0, s orbit, ( 2s ) 2,1, p z orbit, ( 2pz )
29 Quantum Mechanics and Atomic Orbits ψ2
30 Quantum Mechanics and Atomic Orbits Orbits and Quantum Numbers Schrödinger s equation requires 3 quantum numbers 1. Principal Quantum Number, n ( ) 2. Azimuthal Quantum Number, l ( ) 3. Magnetic Quantum Number, m l ( )
31 Quantum Mechanics and Atomic Orbits 1.Principal Quantum Number,n : As n becomes larger, the atom becomes larger and the electron is further from the nucleus. N: 1, 2, 3, 4, 5, 6, 7 K L M N O P
32 Quantum Mechanics and Atomic Orbits 2. Azimuthal Quantum Number, l ( ): a) This quantum number l depends on n b) It has integral values between 0 and n-1 i.e.:the principal quantum number n=3 l =0 l =1 l=2
33 Quantum Mechanics and Atomic Orbits 2. Azimuthal Quantum Number, l ( ): l: 0, 1, 2, 3 Letter used: s, p, d, f Orbital: s, p, d, f (The shape of orbitals: p204,-206)
34 l = 0 (s orbits)
35 l = 1 (p orbits) m l = -1 m l = 0 m l = 1 l = 2 (d orbits) m l = -2 m l = -1 m l = 0 m l = 1 m l = 2
36 The f Orbitals m l: -3, -2, -1, 0, +1, +2, +3
37 The s Orbitals
38 Quantum Mechanics and Atomic Orbitals Orbitals and Quantum Numbers 3. Magnetic Quantum Number, m l ( ) a) This quantum number depends on l. b) It has integral values between -l and +l. c) It gives the 3D orientation of each orbital
39 Quantum Mechanics and Atomic Orbitals Orbitals and Quantum Numbers
40 Quantum Mechanics and Atomic Orbitals Energy of orbits in a single electron atom only depends on principal quantum number n n=3 n=2 1 E n = -R H ( ) n 2 n=1
41 Energy of orbits in a multi-electron atom depends on n and l n=3 l = 2 n=3 l = 0 n=2 l = 0 n=3 l = 1 n=2 l = 1 n=1 l = 0
42 Orbitals in Many Electron Atoms A qualitative energy-level diagram For a many-electron atom
43 Orbitals in Many Electron Atoms Electron Spin and the Pauli Exclusion Principle
44 Orbitals in Many Electron Atoms Electron Spin and the Pauli Exclusion Principle 4. Spin quantum number m s: m =± s 1 2 Pauli s s Exclusion Principle: No two electrons can have the same set of 4 quantum numbers.
45 Orbitals in Many Electron Atoms Electron Spin and the Pauli Exclusion Principle
46 Orbitals in Many Electron Atoms Electron Spin and the Pauli Exclusion Principle
47 Review ψ: wave function ( ψ 1,0,0) Quantum numbers: n, l, m, m s n: Principal quantum number l: Angular quantum quantum number m l :Magnetic Quantum Number m s: Spin quantum number
48 Electron Configurations Three rules: 1. Electrons fill orbitals starting with lowest energy and moving upwards; 2. No two electrons can fill one orbital with the same spin (Pauli). 3. For degenerate orbitals ( ), electrons fill each orbital singly before any orbital gets a second electron (Hund s rule);
49 Electron Configurations
50 Electron Configurations and the Periodic Table
51
52 Electron Configurations and the Periodic Table Shorthand way of writing electron configurations: Example: P: 1s 2 2s 2 2p 6 3s 2 3p 3 Ne : 1s 2 2s 2 2p 6 P: [Ne]3s 2 3p 3
53 Electron Configurations The special cases for Hund s rule: the more stable configurations: S 2, p 6, d 10, f 14 S 1, p 3, d 5, f 7 S 0, p 0, d 0, f 0
54 Electron Configurations 29 Cu s 2s 2p 3s 3p 4s 3 d ( ) 24 Cr s 2s 2p 3s 3p 4s 3 d ( )
55
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