The Grating Spectrometer (Lab 19)

The Grating Spectrometer (Lab 19)

Aim: To determine, using the grating spectrometer, the wavelength of lines in the discrete emission spectrum of mercury.

Materials/Apparatus: Spectrometer, diffraction, grating, mercury.

Procedure:

1. Clamp the grating so that it is perpendicular to the collimator. Clamp the spectrometer table and do not move it during the experiment.

2. Place the telescope so that it is perpendicular to the grating. You will see a bright image of the collimator slit in the cross hairs. Then swing the telescope to the left and to the right until you observe the separated colors of the spectrum.

3. Set the telescope cross hairs to the first mercury line to the right. Read the angle from your apparatus. Always take your angular readings from the same window of apparatus. Swing the telescope to find the same yellow line to the left. Record that setting. This is the n = 1 data for the first mercury line.

4. Repeat the procedure for the other colors. Take care that you are observing the first line of each color.

5. Now measure the angles (left and right) for the second appearance of just the green and yellow lines. Record this data for the n = 2 lines.

Calculations and Conclusions:

Color n Left angle reading (in degrees) Right angle reading (in degrees) α (in degrees) / 2

Violet n = 1 45 18.5 13.25

Blue-Violet 46.5 17.5 14.5

Blue 48.5 15.5 16.5

Green 50 13.5 18.25

Yellow 51.5 12.5 24.5

Green n = 2 70.5 353 ((72.5-0) + (360-353))/2 = 38.75

Yellow 73 350 ((75-0) + (360-350))/2 = 41.5

From the laboratory manual:

d = 1.69 * 10^(-6) m = 16900 A D = n (λ) = d*sin(α) => λ = d*sin(α) / n

• n = 1: λ = 16900 * sin(α) / 1

o Violet: 16900sin(13.25) = 3873.5 => %Error = (3873.5-4046) *100% / 4046 = 4.3%

o Blue-Violet: 16900sin(14.5) = 4231.4 => %Error = (4231.4-4358) *100% / 4358 = 2.9%

o Blue: 16900sin(16.5) = 4799.9 => %Error = (4799.9-4750) *100% / 4750 = 1.1%

o Green: 16900sin(18.25) = 5292.5 => %Error = (5292.5-5461) *100% / 5461 = 3.1%

o Yellow: 16900sin(24.5) = 7008.3 => %Error = (7008.3-5770) *100% / 5770 = 21.5%

• n = 2: λ = 16900 * sin(α) / 2

o Green: 16900sin(38.75) / 2 = 5289.1 => %Error = (5289.1-5461) *100% / 5461 = 3.15%

o Yellow: 16900sin(41.5) = 5599.1 => %Error = (5599.1-5770) *100% / 5770 = 2.9%

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