CHEM 1103 - Atomic Spectrum of Hydrogen

Note: You will not need to formall come to lab to complete this experiment. The report for this experiment will be due at your next lab session. Be sure that you indicate the name of your TA and your lab section on the front of the report. The report for the previous week's experiment will still be due to your teaching assistant's mailbox in the Chemistry office by the normal starting time for your lab section. YOU STILL HAVE A LAB REPORT DUE THIS WEEK. Follow the instructions for completing this assignment carefully.

You can find a discussion of line spectra and the spectrum of hydrogen on pages 237-243 of the lecture text. You should probably read most of chapter 7 (at least pp 224-244) before beginning this experiment to provide some context.

It is advised that you make use of the computer facilities and perform your calculations using a spreadsheet (Quattro Pro or Excel). Bonus points will be given for the most creative use of the computer facilities, including spreadsheets, word processors, etc.

Procedure Notes and Modifications:

Generally follow the format given in the lab manual for your calculations.

When a gas, such as hydrogen or helium is bombarded with sufficient energy, such as an electrical discharge, it emits radiation in the form of photons of visible and non-visible electromagnetic radiation (light). In the early 1900s, Bohr modeled the hydrogen atom (one proton and one electron) as a small, dense sphere (the nucleus, the proton), with the much lighter electron in orbit, much the way the planets are known to orbit the sun. It was also known at the time that the spectra emitted by gases within discharge tubes contained light of very specific wavelengths (colors) rather than a broad spectrum, as is obtained from a black body source, such as an electric stove. In this experiment, we will attempt to explain the origin of the line spectrum of hydrogen.

Line spectra, such as those shown on pages 230-233 of the lecture text, may be obtained using a spectroscope or a prism. A prism is shown on page 230 of the lecture text. A spectroscope is shown below:

Click here for a picture of a spectroscope

Each serves the purpose of spreading out the incident light into a spectrum that can be projected onto a scale. The scale can be calibrated so that the wavelength of each of the emission lines can be read. Figure 7.24 of your lecture text describes the sodium emission spectrum. Note that many street lamps contain sodium vapor - that is why they have the yellow color.

As you might suspect, there is more than one possible orbit that the hydrogen electron can occupy as it circles the nucleus. Also, one might suspect that each different path has a different, discrete energy level associated with it. First, we will use Bohr's theory to predict the values of the energies associated with many of the hydrogen electron's possible orbits. Next, we will calculate the wavelengths of the energy (light) associated with these energy levels. Finally, we will use the calculations to assign specific energies and orbits to the observed wavelengths in the line spectrum of hydrogen.

Our goal will be to fill in and discuss Table 10.1 in the lab manual.

The Calculations:

A. Calculations of the energy Levels of the Hydrogen Atom

First, we will determine the energies of the ten lowest energy "orbits" of the hydrogen atom. These are numbered using integers, with "1" representing the lowest energy or "ground" state. Use table 10.2 in the Lab Manual as a guide and Equation 6 to perform the calculations. You are on the right track if the energies increase as the integer, or "quantum number" increases. Note that Equation 6 calculates energies in kJ/mol - be sure to include the units in your table. Be sure also to reproduce and fill-in the energy level diagram as an additional figure in your report.

B. Calculation of the Wavelengths of the Lines in the Hydrogen Spectrum

The lines in the hydrogen spectrum occur because, when energy is added to the hydrogen atom, the electron "jumps" from a lower energy level to a higher energy level. After awhile (a few picoseconds), the electron relaxes back to the lower state. When it relaxes, since energy must be conserved, the energy is released in the form of a photon. So, table 10.3 is set up to help us calculate and keep track of the wavelengths for many of the jumps, called "transitions."

The lower energy levels are listed on the left side; the higher levels are listed across the top. For each transition shown in the table, calculate the change in energy, using the data you generated in part A. For example, in the top half of the top left square, subtract the energy associated with n=1 from the energy associated with n=6. This is the energy change associated with the transition from the higher level ("excited state") n=6 to the lower level n=1. Note: N=1 is also called the "ground state." Repeat this calculation for each of the transitions indicated in the table.

Next, in the bottom half of each square, use Equation 4 and the energy change you just calculated and wrote in the top half of the square, to calculate the wavelength of light associated with that energy change. Note how Equation 4 is derived from Planck's Law. You might want to work through the Lab Manual's algebra to be sure that it is correct.

C. Assignment of Observed Lines in the Hydrogen Spectrum

The instructions given in the first paragraph of this section in the Lab Manual are pretty straightforward. Complete Tables 10.1 and 10.4 and the energy level diagram according to the instructions given.

For Your Report:

You report should have the usual sections, except that no procedure or data sections are necessary. Be sure to indicate the name of your TA and your lab section on the front of your report. You may exceed the two page limit for this report. You must make your own tables and charts - do NOT just fill in those in the lab manual and tear them out. You are given extra time for this report both in keeping with the class schedule and to allow you time to make use of the computer facilities. Bonus points will be given for especially creative uses of the word processing, spreadsheet and graphics software that is available on the SHU networks. For your discussion, address the questions given in the Data and Calculations section in the Lab Manual. You might also discuss in detail the derivation of the equations that you used in the calculations from Planck's Law. Also, complete and attach the advance study assignment for THIS experiment to your report.

These pages are maintained by Dr. Nicholas H. Snow. For more information or to make a comment, please send email.

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