Bohr Model of the Atom Objective: Discuss the Bohr model of the atom and calculate the energy of the photon emitted or absorbed by an electron as it transitions from one energy level to another energy level.

Emission spectrum of H We can use the emission spectrum to determine the energy levels for the hydrogen atom.

The Bohr Model Niels Bohr uses the emission spectrum of hydrogen to develop a quantum model for H. Central idea: electron circles the “nucleus” in only certain allowed circular orbitals. Bohr postulates that there is Coulombic attraction between e- and nucleus. However, classical physics is unable to explain why an H atom doesn’t simply collapse.

The Bohr Model (cont.) • Energy levels get closer together     • Energy levels get closer together as n increases • at n = infinity, E = 0

The Bohr Model (cont.)  

Radius of the electron orbit  

Ionization energy The amount of energy needed to remove an electron from the atom. Equal to the negative of the energy of the electron. Eionization = - En

Kinetic energy of the electron that is removed from the atom  

Extension to Higher Z • The Bohr model can be extended to any single electron system….must keep track of Z (atomic number). Z = atomic number n = integer (1, 2, ….) • Examples: He+ (Z = 2), Li+2 (Z = 3), etc.

Where does this go wrong? The Bohr model’s successes are limited: • Doesn’t work for multi-electron atoms. • The “electron racetrack” picture is incorrect. That said, the Bohr model was a pioneering, “quantized” picture of atomic energy levels.

The Wave Mechanical Model of the Atom (de Broglie and Schroedinger – mid-1920’s) Orbitals Nothing like orbits Probability of finding the electron within a certain space

Continuum, emission and absorption spectrum

Continuum, emission and absorption spectrum Emission spectra are produced by thin gases in which the atoms do not experience many collisions (because of the low density). The emission lines correspond to photons of discrete energies that are emitted when excited atomic states in the gas make transitions back to lower-lying levels. A continuum spectrum results when the gas pressures are higher. Generally, solids, liquids, or dense gases emit light at all wavelengths when heated. An absorption spectrum occurs when light passes through a cold, dilute gas and atoms in the gas absorb at characteristic frequencies; since the re-emitted light is unlikely to be emitted in the same direction as the absorbed photon, this gives rise to dark lines (absence of light) in the spectrum.