September 22, 1998 Models of the Atom - Orbits to Clouds Bohr:1. Newton’s 2nd Law… electric force causes electron to move at velocity v at radius r. k e2/r2 = m v2/r 2. Energy is kinetic and electric. E = 1/2 m v2 - k e2/r 3. Angular motion is “quantized”. L = m v r = n h/ 2 p 4. Photon equals energy difference Ef - Ei = h f

September 22, 1998 2 DeBroglie (1914) But what if the electron is wave of wavelength l such that m v = h / l. Shroedinger Wave Equation (1926): Energy = Kinetic + Electric When solved, the results gave conditions

September 22, 1998 3 Each electron has 4 “Quantum Numbers”: n = 1, 2, 3, 4,… gives orbit like Bohr l = 0, 1, 2,… n-1… gives L ml = - l…0... l … gives vertical part of L ms = +1/2, -1/2 And: No two electrons can have same set.

September 22, 1998 4 Application: n = 1 1 0 0 +1/2 1 0 0 -1/2 Only two electrons allowed in first orbit. n = 2 2 0 0 +1/2 2 0 0 -1/2 2 1 -1 +1/2 2 1 -1 -1/2 2 1 0 +1/2 2 1 0 -1/2 2 1 1 +1/2 2 1 1 -1/2 Eight electrons allowed in second orbit

September 22, 1998 5 Clouds of the Hydrogen Atom…(film/computer) Atom in a Box www.physics.ucla.edu/~dauger Spectrum of Hydrogen Atom… transitions from higher levels to lower levels… Applying the Hydrogen quantum levels to other atoms… the periodic table (film)

September 22, 1998 6 Applications Atoms and Isotopes (Stable vs Unstable) Fission, Fusion, Radioactivity Molecules: H2 CH4 H2O Sharing electrons Chemical Reactions Conservation of Atoms, Energy Solids Crystal Structure and Uses