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The Hydrogen Spectrum And Energy Levels

INTRODUCTION

    In this experiment you will use a diffraction grating to measure the wavelength of four visible colored lines emitted by hydrogen, and from those results determine the allowed energy levels of the hydrogen electron.

EXPERIMENT

1. Measuring the diffraction angle for Hydrogen and Sodium lines:

  1. Your instructor will explain the operation and initial setup of the spectroscope, as shown below.

    Spectroscope

  2. Create a data table in your report as follows:

    Line Color Angle (left),
    θleft     		Angle (right),
    θright     		Average Angle, θ Wavelength, λ
    (nm)
    Faint-Violet        
    Violet        
    Blue-Green        
    Red        
    .
    Yellow
    Sodium     		      589.3

  3. Swing the telescope left of center until the crosshair is lined up with the first hydrogen line you see. When the hydrogen line is centered, write down the angle θ indicated by the pointer (you should estimate to 0.1º). Repeat for the other hydrogen lines that are visible.

  4. Swing the telescope right of center, and repeat the measurements of θ for the four hydrogen lines. Average θ for each hydrogen line observed.

  5. To calibrate the spectroscope, carry your spectroscope to the sodium lamp and measure the angle θ for the yellow line.

2. Calculating wavelengths:

  1. The wavelength of the yellow line of sodium, λNa, is 589.3 nm. Find the wavelengths of the four hydrogen lines using the expression below, and record those wavelengths in your table. Be sure to use 4 significant figures!

    eqn

3. Calculating theoretical energy levels and wavelengths:

  1. Construct a large (at least half the page) energy level diagram (as shown below) and calculate the theoretical energy levels for n = 1 to n = 6 using: En = –13.61 / n2. The units are electron volts (1 eV = 1.602x10–19 J). Write these energy levels on the diagram.

    Energy level diagram

  2. Calculate the wavelengths for all eight transitions shown, using:

    lambda

    (if ΔE is in eV, then λ has units of nm). Write these wavelengths next to each transition.

4. Calculating the energy levels from your measured colors:

  1. Identify the series and the individual transitions for each line observed by comparing your measured wavelengths with those found in step 3b above.

  2. Calculate the percent difference between your measured and calculated values of the wavelength of each line.

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© St. Lawrence University Department of Physics
Revised: 25 Jun 2003 Canton, NY 13617