Spectrum of the Hydrogen Atom

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Prelab Problems
1. a. Use the Bohr equation (2) to calculate the energy, in J, of the lowest six energy levels of the hydrogen atom.
b. Calculate the energy difference, in J, between levels 1 and 2, levels 2 and 3, and levels 3 and 4. Label each transition by the name of the series it falls in (Balmer, Lyman, etc.)
c. Convert the energy differences in part b to light frequencies, in s-1, and light wavelengths in both m and nm units. Identify the region of the electromagnetic spectrum of each transition.

2. Use the Atomic Spectra Applet on the ChemLab website to find the wavelengths of the four visible lines in the Balmer series of the hydrogen spectrum. Include the initial and final energy levels and color of each line you expect to observe. Sodium emits light in the yellow part of the visible spectrum in an apparently single intense line called the D line. Look up the spectral emission lines of sodium and record the wavelength of the two lines of highest intensity. Confirm that this closely-spaced pair of emission lines corresponds to the D line by checking that the wavelength corresponds to yellow light. Be sure to include a reference.

3. Define the effective nuclear charge, Zeff, for an electron in a multielectron atom in qualitative terms. How would you expect Zeff to compare for the 3s and 3p electrons in a sodium atom and why?

4. Suppose the following values for a given emission line were obtained with a meterstick spectroscope:

a = 17.00 cm rulings /mm of grating = 600
b = 40.00 cm

Calculate the value of θ, tan θ, sin θ, and λ (in both m and nm units). Assume that a first order spectrum was observed. Note that the lines per mm of grating value must be converted to mm per ruling. Your result should be in the visible portion of the electromagnetic spectrum. If it is not, check your units. If you set up an Excel spreadsheet to calculate these values, you will be able to use it to analyze your data from the experiment.

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