Lecture Presentation Chapter 6 Electronic Structure of Atoms 2012 Pearson Education Inc John D Bookstaver St Charles Community College Cottleville MO Waves To understand the electronic structure of atoms one must understand the nature of electromagnetic radiation The distance between corresponding points on adjacent waves is the wavelength 2012 Pearson Education Inc Electronic Structure of Atoms Waves The number of waves passing a given point per unit of time is the frequency For waves traveling at the same velocity the longer the wavelength the smaller the frequency 2012 Pearson Education Inc Electronic Structure of Atoms Electromagnetic Radiation All electromagnetic radiation travels at the same velocity the speed of light c 3 00 108 m s Therefore c 2012 Pearson Education Inc Electronic Structure of Atoms The Nature of Energy The wave nature of light does not explain how an object can glow when its temperature increases 2012 Pearson Education Inc Electronic Structure of Atoms The Nature of Energy Max Planck explained it by assuming that energy comes in packets called quanta 2012 Pearson Education Inc Electronic Structure of Atoms The Nature of Energy Einstein used this assumption to explain the photoelectric effect He concluded that energy is proportional to frequency E h where h is Planck s constant 6 626 10 34 J s 2012 Pearson Education Inc Electronic Structure of Atoms The Nature of Energy Therefore if one knows the wavelength of light one can calculate the energy in one photon or packet of that light c E h 2012 Pearson Education Inc Electronic Structure of Atoms The Nature of Energy Another mystery in the early twentieth century involved the emission spectra observed from energy emitted by atoms and molecules 2012 Pearson Education Inc Electronic Structure of Atoms The Nature of Energy For atoms and molecules one does not observe a continuous spectrum as one gets from a white light source Only a line spectrum of discrete wavelengths is observed 2012 Pearson Education Inc Electronic Structure of Atoms The Nature of Energy Niels Bohr adopted Planck s assumption and explained these phenomena in this way 1 Electrons in an atom can only occupy certain orbits corresponding to certain energies 2012 Pearson Education Inc Electronic Structure of Atoms The Nature of Energy Niels Bohr adopted Planck s assumption and explained these phenomena in this way 2 Electrons in permitted orbits have specific allowed energies these energies will not be radiated from the atom 2012 Pearson Education Inc Electronic Structure of Atoms The Nature of Energy Niels Bohr adopted Planck s assumption and explained these phenomena in this way 3 Energy is only absorbed or emitted in such a way as to move an electron from one allowed energy state to another the energy is defined by E h Electronic Structure of Atoms 2012 Pearson Education Inc The Nature of Energy The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation 1 E hcRH ni 2 where RH is the Rydberg constant 1 097 107 m 1 and ni and nf are the initial and final energy levels of the electron 1 nf 2 Electronic Structure of Atoms 2012 Pearson Education Inc The Wave Nature of Matter Louis de Broglie posited that if light can have material properties matter should exhibit wave properties He demonstrated that the relationship between mass and wavelength was h mv Electronic Structure of Atoms 2012 Pearson Education Inc The Uncertainty Principle Heisenberg showed that the more precisely the momentum of a particle is known the less precisely is its position is known x mv h 4 2012 Pearson Education Inc Electronic Structure of Atoms The Uncertainty Principle In many cases our uncertainty of the whereabouts of an electron is greater than the size of the atom itself 2012 Pearson Education Inc Electronic Structure of Atoms Quantum Mechanics Erwin Schr dinger developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated This is known as quantum mechanics 2012 Pearson Education Inc Electronic Structure of Atoms Quantum Mechanics The wave equation is designated with a lowercase Greek psi The square of the wave equation 2 gives a probability density map of where an electron has a certain statistical likelihood of being at any given instant in time 2012 Pearson Education Inc Electronic Structure of Atoms Quantum Numbers Solving the wave equation gives a set of wave functions or orbitals and their corresponding energies Each orbital describes a spatial distribution of electron density An orbital is described by a set of three quantum numbers 2012 Pearson Education Inc Electronic Structure of Atoms Principal Quantum Number n The principal quantum number n describes the energy level on which the orbital resides The values of n are integers 1 2012 Pearson Education Inc Electronic Structure of Atoms Angular Momentum Quantum Number l This quantum number defines the shape of the orbital Allowed values of l are integers ranging from 0 to n 1 We use letter designations to communicate the different values of l and therefore the shapes and types of orbitals 2012 Pearson Education Inc Electronic Structure of Atoms Angular Momentum Quantum Number l Value of l Type of orbital 0 s 1 p 2 d 3 f 2012 Pearson Education Inc Electronic Structure of Atoms Magnetic Quantum Number ml The magnetic quantum number describes the three dimensional orientation of the orbital Allowed values of ml are integers ranging from l to l l ml l Therefore on any given energy level there can be up to 1 s orbital 3 p orbitals 5 d orbitals 7 f orbitals and so forth 2012 Pearson Education Inc Electronic Structure of Atoms Magnetic Quantum Number ml Orbitals with the same value of n form a shell Different orbital types within a shell are subshells 2012 Pearson Education Inc Electronic Structure of Atoms s Orbitals The value of l for s orbitals is 0 They are spherical in shape The radius of the sphere increases with the value of n 2012 Pearson Education Inc Electronic Structure of Atoms s Orbitals Observing a graph of probabilities of finding an electron versus distance from the nucleus we see that s orbitals possess n 1 nodes or regions where there is 0 probability of finding an electron Electronic Structure of Atoms 2012 Pearson Education Inc p Orbitals The value of l for p orbitals is 1 They have two lobes with a node between them 2012 Pearson Education Inc Electronic Structure of Atoms d Orbitals The