1Atomic Theory:The Quantum Modelof the Atom Chapter 11Review: the planetary model of the atom(1911)• Every atom contains an extremely small, extremely densenucleus.• All of the positive charge and nearly all of the mass of anatom are concentrated in the nucleus.• The nucleus is surrounded by a much larger volume ofnearly empty space that makes up the rest of the atom.• In the vast open space that comprises most of the volumeof an atom, electrons travel in circular orbits around thenucleus2Limitations of the planetary model• First ionization Energy:Energy required toremove one electron froma gaseous atom of anelement• The properties of theelements do not changesmoothly as the atomicnumber increases!Limitations of the planetary model• Does not explain the different properties ofatoms in different groups (or chemical families)• Why are the noble gases so unreactive?– Why are they gases?• Why do metals conduct electricity?3Limitations of the planetary model• Does not allow us to understand or predict the way thatatoms will bond to create molecules• Why do the atoms of some elements tend to form anions,while others form cations?• Why do the atoms of the element oxygen tend to bond totwo others atoms (H2O), while carbon atoms make 4bonds (CH4)?• And why don’t the electrons spiral down into the nucleus?Na+Ca2+Cl-Fe3+Fe2+Br-“Quantization” of light• White light shone through a prism produces a continuousspectrum4The “Quantization” of light• When an element is heated until it emits light and thatlight passes through a prism, a line spectrum forms• The light only contains a few wavelengths - only waveswith specific energiesEach element has a unique linespectrum• The line spectra of hydrogen, mercury, and neon• Each type of atom emits specific, but different, wavelengthsof light5Absorption and emission of light• Energy is absorbed as an electron is promoted from oneorbit to another• Energy (light) is emitted as the electron returns to it’s groundstate - an exact amount of energy corresponding to aspecific wavelength of light• The emission lines happen when heat excites the electrons,which emit photons when they return to the ground stateWhat have we learned?• Only specific colors (wavelengths) of light are observed inemission spectra• Energy is being emitted in specific amounts (quanta)• The electron orbitals have very specific energies• But so far we haven’t explained anything!– what about the pattern of ionization energies?– why do the elements have different chemical properties?– why don’t electrons fall into the nucleus?• Max Planck made the math work by only allowing certainspecific energies to exist– the energies needed for electrons to traverse “the last spiral” intothe nucleus are not available to those electrons!6The Quantum conceptThe Bohr model of the hydrogen atom• Proposed by Niels Bohr, a Danish scientist, in 1913.• Bohr took Planck’s “mathematical cheat” and assumed itwas real• Electrons can only be in certain orbits7The Bohr model• Ground State: Lowest-energy orbit available• Excited States: Orbits with higher energy than the groundstate• Orbits in the Bohr model are called Principal Energy Levels or Principal Quantum Numbers (n) Explains the line spectra and keeps the electrons awayfrom the nucleus, but leaves us with some questions• Why do the electrons only occupy certain orbits?• Why do elements have the properties we observe?• de Broglie (1924): Matter in motion, such as electrons, hasproperties that are normally associated with waves• mv = h/λ– m = mass– v = velocity– h = Planck constant– λ = wavelength• An electron traveling at one twentieth light speed has awavelength of 5 x 10-11 m - the radius of a hydrogen atom• A 50 kg person running at 10 m/sec has a wavelength of1.3 x 10-36 m - which is not meaningful• Schrödinger (1925-28): Applied the principles of wavemechanics to atomsThe quantum mechanical model ofthe atom8Wave mechanics• The vibration of a constrained string (a guitar string is attachedat the bridge and the nut) has certain natural frequencies(harmonics) that are integer multiples of the fundamental• The same is true for an electron behaving as a wave,constrained by the potential well of the nucleusSuggests that electrons are particles,in specific locations.Heisenberg (1925-1927) showed thatthis was not a meaningful model dueto uncertainty in the speeds andpositions of the electrons.Suggests that electrons are waves.Orbitals are interpreted asprobability densities.Electrons are fuzzy clouds ofcharge.9Solutions to the Schrodinger equationfor the hydrogen atom• Orbitals• Region in spacearound a nucleus inwhich there is ahigh probability offinding an electron• Each orbital can beoccupied by 0, 1 or2 electronsspdThe quantum mechanical description of each electron inin a multi-electron atom can be described using fourquantum numbersFor each electron there is a unique set of quantumnumbersThe quantum numbers describe the energy level andprobable location of the electronQuantum numbers10(Remember the Bohr “orbits”)Principal Energy Levels, n• n = 1,2,3,4,5,6,7• Generally, energy increases with increasing n• Distance of the electron from the nucleus increaseswith increasing nSublevels and Orbitals• For each principal energy level there are one or moresublevels (s, p, d, f) associated with different types of orbital• The total number of sublevels is equal to n, the principalquantum numberPrincipal quantum number = 1The lowest energy level• Just one solution to theSchrodinger equation,• One sublevel, s• One orbital, which cancontain a maximum of twoelectrons• If your atom only containstwo electrons they are likelyto be in this region of space11Sublevels and Orbitals• For each principal energy level there are one or moresublevels (s, p, d, f) associated with different types of orbital• The total number of sublevels is equal to n, the principalquantum number Principal quantum number(principal energy level) = 2• Two sublevels, s and p• One orbital in the s subleveland three in the p sublevel• Each orbital can contain amaximum of two electrons• Maximum electrons at thisprinciple energy level = 8spSublevels and Orbitals• For each principal energy level there are one or moresublevels (s, p, d, f) associated with different types of orbital• The total number of sublevels is equal to n, the