The Bohr Model Glenn V. Lo, Ph.D. Department of Physical Sciences Nicholls State University

Brief History Dalton: atom = structureless spheres J.J. Thomson: CRT experiments led to discovery of electrons; proposed “plum pudding” model Rutherford: alpha-scattering experiments led to the nuclear model: Most of mass in tiny, positively charged nucleus Negatively-charged electrons found in mostly empty space around nucleus

Problem with Nuclear Model Knowledge at the time suggests that nuclear model cannot be stable. Electrons moving around nucleus will continually emit light (lose energy) and eventually crash into nucleus.

Line Spectra White light can be separated into a continuous band of colors (“continuous spectrum”), but light from atoms only have certain colors (“line spectrum” or “discrete spectrum”). Why? Each element has a characteristic line spectrum Hydrogen

Bohr’s model Niels Bohr proposed the existence of stable circular orbits for electrons. radius of nth orbit = 52.9 n2 pm. (1 pm = 10-12 m) Energy of electron is quantized “quantized” = cannot just have any value Energy in nth orbit = (-13.6 eV) / n2 = (-2.18x10 x 10-18 J) / n2 eV = “electron volt”; J = Joule; 1 eV = 1.6x10-19 J By convention: when electron is at infinite distance from the nucleus (n=infinity), Energy = 0 Negative energy in nth orbit means electron must gain energy in order to “escape” from the atom. Ionization energy = energy needed to remove electron from first orbit.

Explaining Line Spectra Energy of particles are quantized When particle undergoes an energy change, the photon energy of light emitted or absorbed is equal to the change in energy of particle: Ephoton = E Since not every value of energy is allowed, only some photon energies (colors) are observed. Recall: Ephoton = h c /  The aforementioned are still currently accepted, even though Bohr’s method for calculating the allowed energies is no longer acceptable.

Failures of Bohr model Bohr’s model only works for H atom and ions with one electron (such as He+, Li2+). E = -(13.6 eV) Z2 / n2 where Z = atomic number (for He, Z=2)

Failures of Bohr model Other experiments towards the end of the 19th century led to the Heisenberg Uncertainty Principle: “it is impossible to precisely locate electron and know its velocity at the same time.” The well-defined circular orbit in Bohr’s model is not consistent with this principle.