Emission Spectra and Bohr-Rydberg http://chemwiki.ucdavis.edu/Physical_Chemistry/Quantum_Mechanics/09._The_Hydrogen_Atom/Bohr's_Hydrogen_Atom Limitations of the Bohr Model The Bohr Model was an important step in the development of atomic theory. However, it has several limitations. It is in violation of the Heisenberg Uncertainty Principle.  The Bohr Model considers electrons to have both a known radius and orbit, which is impossible according to Heisenberg. The Bohr Model is very limited in terms of size.  Poor spectral predictions are obtained when larger atoms are in question. It cannot predict the relative intensities of spectral lines. It does not explain the Zeeman Effect, when the spectral line is split into several components in the presence of a magnetic field.  The Bohr Model does not account for the fact that accelerating electrons do not emit electromagnetic radiation. Hydrogen gas when viewed through a spectroscope gives off four discrete lines. We are going to use the Rydberg equation based off the Bohr model to calculate the wavelength of these lines.

Show Work N= 6 N= 4 N= 4 N= 3 N= 2 N= 1 Calculate the wavelength of light emitted by a hydrogen atom for the cases below where an electron is dropping down to lower energy levels emitting a photon. Convert all wavelengths into nanometers. Indicate where it falls on the electromagnetic spectrum and its color (if visible)! Draw a visual depiction of the cases mirroring the pattern of the image on the right. Use Plank’s formula to calculate the energy of the photon after finding lambda in J and eV. An electron jumps from n = 3 to n=2. An electron jumps from n = 4 to n=2 An electron jumps from n = 5 to n=2 An electron jumps from n = 6 to n=2 An electron jumps from n = 2 to n=1 Show Work N= 6 N= 4 N= 4 .25-91/90 N= 3 λ = wavelength of light in meters r = Rydberg constant = 1.097 x 107m-1 nf = final energy level ni = initial energy level E = energy in joules c= speed of light = 3.00 x 108m/s h = Plank’s Constant = 6.62607004 × 10-34 m2 kg / s 1 Joule = 6.242x1018eV N= 2 N= 1

nf = 2 ni =3 r = constant An electron jumps from n = 3 to n=2. N= 6 λ = wavelength of light in meters r = Rydberg constant = 1.097 x 107m-1 nf = final energy level ni = initial energy level E = energy in joules c= speed of light = 3.00 x 108m/s h = Plank’s Constant = 6.62607004 × 10-34 m2 kg / s 1 Joule = 6.242x1018eV N= 2 N= 1

nf = 2 ni =3 r = constant An electron jumps from n = 3 to n=2. A nanometer is x10-9 so we move the decimal right two places Red light

An electron jumps from n = 3 to n=2. Red light A nanometer is x10-9 so we move the decimal right two places N= 6 N= 4 N= 4 N= 3 Photon: Red Light N= 2 λ = wavelength of light in meters E = energy in joules c= speed of light = 3.00 x 108m/s h = Plank’s Constant = 6.62607004 × 10-34 m2 kg / s 1 Joule = 6.242x1018eV N= 1