Electronic Structure of Atoms. Chapter 6

Electronic Structure of Atoms Chapter 6

Electronic Structure of Atoms 1. The Wave Nature of Light All waves have: a) characteristic wavelength, λ b) amplitude, A

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

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 (6.626 10-34 J.s)

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

White light can be separated into a continuous spectrum of colors

Bohr noticed the line spectra of certain elements

Bohr s Model of the Hydrogen Atom Bohr s s Model Na: H: The energy states --- orbits --- quantized

7.3

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 ( 2.18 10 18 J)

E = hν E = hν 7.3

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

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

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

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

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 18 2.18 10 J 1 1 34 2 2 ν = = = 6.90 10 s h 6.63 10 J s 5 2 14 1 λ 7 8 14 1 = c ν = 2.99 10 m/ s 6.9 10 s = 4.33 10 m= 433nm

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???

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

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

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 6.626 10 υ 2π m x = 2 3.14 10 10 0.01 10 υ 1.054 10 28 m s 1-3 -2

Heisenberg s Uncertainty Principle For a microscopic particle, an electron: m=9.11 10 31 kg diameter of an atom:---10 10 m x--- at least 10 11 m υ? υ 34 h 6.626 10 = 2π m x 2 3.14 9.11 10 10 31 11 υ 1.157 10 7 m s 1 The uncertainty of velocity is obvious. m: very small The uncertainty of both the location and momentum is important.

Heisenberg s Uncertainty Principle It is impossible for an electron to move in well-defined orbits about the nucleus.

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

Quantum Mechanics and Atomic Orbits Schrödinger Wave Equation: θ ϕ θ ϕ θ cos sin sin cos sin r z r y r x = = = 2 2 2 z y x r + + = ( ) 0 8 sin 1 sin sin 1 1 2 2 2 2 2 2 2 2 2 = + + + ϕ π ϕ ϕ θ θ ϕ θ θ θ ϕ V E h m r r r r r r

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=0 0 2 2 3 0 0 0, 1, 1 a Z e a Z = π ϕ 0 2 0 2 3 0,0,0 2 2 2 4 1 a Z e a Z a Z = π ϕ

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 0 5 2 re Z a 0 cos θ

Quantum Mechanics and Atomic Orbits Wave function : to describe the state of electrons in an atom--- atomic orbit ψ 1,0,0 --- 1s orbit ( 1s ) 2,0,0 --- 2s orbit, ( 2s ) 2,1,0 --- 2p z orbit, ( 2pz )

Quantum Mechanics and Atomic Orbits ψ2

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 ( )

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

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

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)

l = 0 (s orbits)

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

The f Orbitals m l: -3, -2, -1, 0, +1, +2, +3

The s Orbitals

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

Quantum Mechanics and Atomic Orbitals Orbitals and Quantum Numbers

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

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

Orbitals in Many Electron Atoms A qualitative energy-level diagram For a many-electron atom

Orbitals in Many Electron Atoms Electron Spin and the Pauli Exclusion Principle

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.

Orbitals in Many Electron Atoms Electron Spin and the Pauli Exclusion Principle

Orbitals in Many Electron Atoms Electron Spin and the Pauli Exclusion Principle

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

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);

Electron Configurations

Electron Configurations and the Periodic Table

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

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

Electron Configurations 29 Cu 2 2 6 2 6 2 9 1s 2s 2p 3s 3p 4s 3 d ( ) 24 Cr 2 2 6 2 6 2 4 1s 2s 2p 3s 3p 4s 3 d ( )