Fall 2003 Emission Spectra of Elements Purpose: To compare and contrast the emission spectra of various gases. Investigate quantitatively the emission spectrum of hydrogen and relate it to Bohr's theory of atomic structure. Calculate the Rydberg constant Discussion: Emission Spectra When gases or vapors of elements are heated or exposed to high voltage they emit light. The emitted light can be split into its component wavelengths by passing it through a diffraction grating or prism. The emission spectrum is unique and characteristic to each element. Emission spectra of elements are line spectra, which reveals that the electronic energy levels are quantized. An electron within an atom may be excited to a higher energy level by absorbing e nergy from an electric discharge. When the electron relaxes back to its ground state, the energy is emitted as a photon of light. The lines arise because only a particular number of transitions are possible. These transitions are represented in the following diagram.
The emission spectrum of hydrogen consists of three series of lines: Lyman (ultraviolet), Balmer (visible), and Paschen (infrared). The Balmer series corresponds to transitions from excited states to the n=2 energy level. Balmer found that the wavelengths of the lines in the emission spectrum follow the rule: Rydberg constant R = 1.09737 x 10 7 m -1 Because wavelength,, is related to frequency,, and frequency is in turn related to energy, the energy of the emitted photon that corresponds to a transition from an initial state of higher energy E i to a final state of lower energy E f, is given by:, c = E = h E = hc/ Planck s constant h = 6.63 x 10-34 (Js), Speed of light c = 2.998 x 10 8 (m/s).. The Balmer series produce lines in the visible region, they have transitions between n f = 2 and n i = 3, 4, 5, or 6. You will use this series to calculate a value for the Rydberg constant.
Procedure Go to http://home.achilles.net/~jtalbot/data/elements/ Observe the emission spectra for the elements listed on this page. Pay attention to the difference in complexity of the line spectra of hydrogen compared to the larger elements. Scroll down to the table of Most common elements in solar spectrum. Click on hydrogen.txt in the DataFile column. This will display a list of wavelengths of emission lines and their relative intensity. The first column states wavelengths in Angstroms (Å) (1 Angstrom = 1x10-10 m) Use the wavelength values to calculate a value of R for each transition (n=3 to n=2, n=4 to n=2, etc.) using, Tabulate your data in the space provided in page 4 Calculate the energy associated with each of the transitions. Calculate the value of the Rydberg constant Convert wavelength from Angstroms to meters Plot reciprocal wavelength (1/ ) vs 1/n 2 This should yield a linear relationship with slope R, and intercept R/4 Compare your results with the known value R = 1.09737 x 10 7 m -1. Repeat the above calculation of the Rydberg constant using selected data from any of the other emission spectra. Attach your plots to the lab report
Name Hydrogen Emission Spectrum Wavelength (Å) Transition n i to n f 1/ (m -1 ) 1/n 2 Energy (J) Value of R found from slope Value of R found from intercept Emission Spectrum for Wavelength (Å) Transition n i to n f 1/ (m -1 ) 1/n 2 Energy (J) Value of R found from slope Value of R found from intercept
Name Questions 1. The colors of the four lines of the hydrogen spectrum are: red, blue-green, and two shades of violet. Which initial states n i = 3, 4, 5, or 6 correspond to these colors? (Hint: The colors of the visible spectrum, from longest to shortest wavelengths, are: red, orange, yellow, green, blue, violet.) Wavelength[nanometers] 400 450 500 550 600 650 700 750 Frequency[terahertz] 749 666 600 545 500 461 428 400 2. Transitions to the n=1 (ground state) level from higher levels in the hydrogen atom never produce visible wavelength photons. Are the wavelengths produced by transitions to the n=1 level longer or shorter than visible wavelengths? Explain.
Name 3. Scroll down to the bottom of http://home.achilles.net/~jtalbot/data/elements/ Click on the link to Color spectra of emission lines in planetary nebula [Java] Is there any evidence to suggest that iron is present in the NGC2440 planetary nebula? 4. Compare your values of R with the quoted value of R = 1.09737 x 10 7 m -1 Material sourced from: http://home.achilles.net/~jtalbot/data/elements/ http://www.efg2.com/lab/scienceandengineering/spectra.htm http://www.astro.washington.edu/covey/teaching/spectralab.html http://www.colorado.edu/physics/phys2020/phys2020_f98/lab_manual/lab6/lab6.html http://chemweb.calpoly.edu/chem/124/124experiments/emissionspec/emissionspectab.html http://www.emporia.edu/physics/keithron/collegelab2/spectra.htm