Quantum Chemistry Chapter 6

Copyright © Houghton Mifflin Company. All rights reserved.6 | 2 Electromagnetic Radiation

Copyright © Houghton Mifflin Company. All rights reserved.6 | 3 Electromagnetic Waves

Copyright © Houghton Mifflin Company. All rights reserved.6 | 4 Electromagnetic Radiation = frequency of the wave c = speed of light = wavelength

Copyright © Houghton Mifflin Company. All rights reserved.6 | 5 Electromagnetic Spectrum

Copyright © Houghton Mifflin Company. All rights reserved.6 | 6 Electromagnetic Spectrum

Copyright © Houghton Mifflin Company. All rights reserved.6 | 7 Visible Spectrum

Copyright © Houghton Mifflin Company. All rights reserved.6 | 8 Energy, Wavelength & Frequency The energy of a photon is given by – h = 6.626× J. s, Plank’s constant c = 3.00×10 8 m/s

Copyright © Houghton Mifflin Company. All rights reserved.6 | 9 Sample Problem What is the energy of a photon of infrared light that has a wavelength of 850. nm?

Copyright © Houghton Mifflin Company. All rights reserved.6 | 10 Hydrogen Spectra

Copyright © Houghton Mifflin Company. All rights reserved.6 | 11 Emission Spectrum When hydrogen atoms are excited, they emit radiation. The wavelengths of this radiation can be calculated from -

Copyright © Houghton Mifflin Company. All rights reserved.6 | 12 Hydrogen Spectra

Copyright © Houghton Mifflin Company. All rights reserved.6 | 13 Emission Spectra

Copyright © Houghton Mifflin Company. All rights reserved.6 | 14 Bohr Model Bohr postulated that the energy an electron has when it occupies an orbit around the nucleus in a hydrogen atom is: n = 1, 2, 3, 4, …….. Ground state is the lowest energy level, n = 1. Excited state is a higher energy level. Bohr model of the hydrogen atom

Copyright © Houghton Mifflin Company. All rights reserved.6 | 15 If an electron moves from a lower energy level to a higher energy level, it absorbs energy. If an electron moves from a higher energy level to a lower energy level, it emits energy. The change in energy is –  E = E f - E i Bohr Model

Copyright © Houghton Mifflin Company. All rights reserved.6 | 16 Bohr Model

Copyright © Houghton Mifflin Company. All rights reserved.6 | 17 Bohr Model For the hydrogen electron –

Copyright © Houghton Mifflin Company. All rights reserved.6 | 18 Electronic Transitions

Copyright © Houghton Mifflin Company. All rights reserved.6 | 19 Sample Problem Calculate the wavelength of light emitted by the transition of a hydrogen electron from n=4 to n=1.

Copyright © Houghton Mifflin Company. All rights reserved.6 | 20 Wave - Particle Duality Very small, light weight particles, such as electrons can behave like waves. de Broglie’s equation allows us to calculate the wavelength of an electron. h = Planck’s constant m = mass v = velocity

Copyright © Houghton Mifflin Company. All rights reserved.6 | 21 De Broglie Wavelength

Copyright © Houghton Mifflin Company. All rights reserved.6 | 22 Sample Problem What is the wavelength of an electron traveling 5.31×106 m/s?

Copyright © Houghton Mifflin Company. All rights reserved.6 | 23 The Wave Equation If an electron can behave like a wave, it should be possible to write an equation that describes its behavior. Schrödinger equation allows us to calculate the energy available to the electrons in an atom. Ψ is a wave function that describes the position and paths of the electron in its energy level.

Copyright © Houghton Mifflin Company. All rights reserved.6 | 24 The Wave Equation Ψ*Ψ, the square of the wave function, is the probability of finding the electron in some region of space.

Copyright © Houghton Mifflin Company. All rights reserved.6 | 25 Quantum Numbers There are four quantum numbers used to describe the electron in the hydrogen atom n, principle quantum number, describes the size and energy of the orbital n = 1, 2, 3, 4, ………(only integers) l – angular momentum quantum number, describes the shape of the orbital. l = 0 to n-1 (only integers)

Copyright © Houghton Mifflin Company. All rights reserved.6 | 26 Quantum Numbers m l – magnetic quantum number, describes the spatial orientation of the orbital. m l = -l to 0 to +l (only integers) m s – spin quantum number, describes the direction and spin of the electron. m s = +1/2 or -1/2 (only two values)

Copyright © Houghton Mifflin Company. All rights reserved.6 | 27 Quantum Numbers

Copyright © Houghton Mifflin Company. All rights reserved.6 | 28 Quantum Numbers

Copyright © Houghton Mifflin Company. All rights reserved.6 | 29 Quantum Numbers

Copyright © Houghton Mifflin Company. All rights reserved.6 | 30 Pauli Exclusion Principle No two electrons can have the same four quantum numbers. Spins of electrons in an orbital must be opposite.

Copyright © Houghton Mifflin Company. All rights reserved.6 | 31 Quantum Numbers

Copyright © Houghton Mifflin Company. All rights reserved.6 | 32 Orbital Shapes: s orbital

Copyright © Houghton Mifflin Company. All rights reserved.6 | 33 s Orbitals

Copyright © Houghton Mifflin Company. All rights reserved.6 | 34 Orbital Shapes: s orbital

Copyright © Houghton Mifflin Company. All rights reserved.6 | 35 p Orbitals

Copyright © Houghton Mifflin Company. All rights reserved.6 | 36 Orbital Shapes: 2p x orbitals

Copyright © Houghton Mifflin Company. All rights reserved.6 | 37 Orbital Shapes: 2p y orbital

Copyright © Houghton Mifflin Company. All rights reserved.6 | 38 Orbital Shapes: 2p z orbital

Copyright © Houghton Mifflin Company. All rights reserved.6 | 39 d Orbitals

Copyright © Houghton Mifflin Company. All rights reserved.6 | 40 Orbital Shapes: 3d x 2 -y 2 orbital

Copyright © Houghton Mifflin Company. All rights reserved.6 | 41 Orbital Shapes: 3d z 2 orbital

Copyright © Houghton Mifflin Company. All rights reserved.6 | 42 Orbital Shapes: 3d xy orbital

Copyright © Houghton Mifflin Company. All rights reserved.6 | 43 Orbital Shapes: 3d yz orbital

Copyright © Houghton Mifflin Company. All rights reserved.6 | 44 Orbital Shapes: 3d xz orbital

Copyright © Houghton Mifflin Company. All rights reserved.6 | 45 f Orbitals

Copyright © Houghton Mifflin Company. All rights reserved.6 | 46 Orbital Energies

Copyright © Houghton Mifflin Company. All rights reserved.6 | 47 Electron spin Spin upSpin down

Copyright © Houghton Mifflin Company. All rights reserved.6 | 48 Electron shielding

Copyright © Houghton Mifflin Company. All rights reserved.6 | 49 Orbital Energy Levels in Multi-electron Atoms

Copyright © Houghton Mifflin Company. All rights reserved.6 | 50 Electron Configurations Aufbau principle gives the order of the orbitals

Copyright © Houghton Mifflin Company. All rights reserved.6 | 51 Sample Problem Write the electron configuration for Ca using the Aufbau principle. 1s22s22p63s23p64s21s22s22p63s23p64s2

Copyright © Houghton Mifflin Company. All rights reserved.6 | 52 Hund’s Rule Hund’s rule - maximize the number of unpaired electrons in orbitals. Orbital diagram for C (z = 6) would be: (  ) (  ) (  ) (  ) ( ) 1s 2s 2p not (  ) (  ) (  ) ( ) ( ) 1s 2s 2p

Copyright © Houghton Mifflin Company. All rights reserved.6 | 53 Electron configuration Three possible electron configurations for carbon electron configurations

Copyright © Houghton Mifflin Company. All rights reserved.6 | 54 Periodic Table

Copyright © Houghton Mifflin Company. All rights reserved.6 | 55 Electron Configurations Representative Elements are s orbital and p orbital fillers. Transition metals fill the d orbitals. Lanthanides are 4f fillers. Actinides are 5f fillers

Copyright © Houghton Mifflin Company. All rights reserved.6 | 56 Periodic Table Blocks

Copyright © Houghton Mifflin Company. All rights reserved.6 | 57 Sample Problem Write the electron configuration for Br & Fe using the periodic table. Br: [Ar]4s 2 3d 10 4p 5 Fe: [Ar]4s 2 3d 6

Copyright © Houghton Mifflin Company. All rights reserved.6 | 58 Homework 26, 34, 38, 46, 52, 64, 76, 82, 92, 98, 106,