Problem Solving hints Use white AP constant sheet hc = 1.99  J  m = 1.24  10 3 eV  nm h = 6.63  J  s = 4.14  eV  s 1 eV = 1.6  J 1 amu = 1 u = 1.66  kg = 931 MeV/c 2

Davisson-Germer Experiment scattering electrons off of poly- crystalline nickel targets explosion in lab data changed - nickel had formed large crystals diffraction pattern seen -- electron waves diffracting electrons with momentums comparable to X-rays diffract the same

Heisenberg’s Uncertainty Principle  p  x  h/(2  )  E  t  h/(2  )

Experiments to determine structure of atoms Rutherford  -particle scattering experiment Characteristic line spectra (Lyman, Balmer, Paschen series of lines in hydrogen)  1/ = R(1/ /n 2 )n = 2, 3, 4, …  1/ = R(1/ /n 2 )n = 3, 4, 5, …  1/ = R(1/ /n 2 )n = 4, 5, 6, …

Rutherford experiment There must be a dense central part surrounded by a lot of empty space

Line Spectra

Bohr model Electrons move in specific orbits with quantized angular momenta of L n = nh/(2  ) Leads to wavelength formula 1/ = K(1/n f 2 - 1/n i 2 ) which agrees with observed lines from the Lyman, Balmer, Paschen, etc. series

Bohr: Electrons exist in “stationary states.” Only specific orbits are allowed -- electron does not move between states, it “jumps.” For hydrogen and hydrogen-like ions, E n = (-13.6eV)Z 2 /n 2 where Z is atomic number and n is energy level

deBroglie: Electron waves around the nucleus can only exist in certain orbits (“standing waves”)

Current view Electrons around nucleus exist in “orbitals” Orbitals are probability clouds No two electrons in the same atom can have all of the same quantum numbers (waves interfere)

Energy levels Energy levels in an atom are not evenly spaced. The difference between the n = 1 and n = 2 level is greatest. The energy levels get closer and closer together for higher n. Using Bohr’s formula, can you determine the energy of a photon released when an electron drops from n = 2 to n = 1 in a H-atom?

Can you determine the minimum energy needed to free an electron from the hydrogen atom if it starts in the ground state? That would be the same as moving it from n = 1 to n = infinity… This energy is called the ionization energy ionization energy. What about the energy needed to free an electron from an O 7+ ion? Why can’t we use Bohr’s formula for a normal oxygen atom?