Experiment 14: Color and Spectra

PURPOSE: In this experiment, the spectrum of colors were viewed in white light and the light from colored filters that contains hydrogen gas.

FORMULAS & DERIVATIONS:

Illustration of the experiment. An observer will see through the double slit which has a grating of about 500 lines per mm. 

Using similar triangle technique, the following derivations can take place.

PROCEDURE:

SETUP OF EXPERIMENT

Top View

The distance of the color spectrum was measured from the light source.

The color spectrum of white light

Spectra of a Hydrogen gas

Setup with Hydrogen Gas as the "light source"

Spectra of Hydrogen gas. 

DATA & ANALYSIS

Measurement of the white light spectra:

Calculation to determine wavelength for both ends of the spectrum. Note d is given by the double slit (there are 500 lines per mm). The slit was 1.89 meters away (L). The distance of the light, D was a measured value with uncertainty.

Uncertainty was measured through standard deviation. The Theoretical values for the visible spectrum was given and the uncertainty lies within the true values of the wavelength.

Calibration of the wavelength was determined on the right side of the board using both the experimental and theoretical values of the wavelength.

Measurement of Hydrogen Gas

Calculations for the different colors presented in the spectrum. The yellowish-green color was not calculated since it is not in the spectrum of hydrogen gas, and perhaps it was light interfered from another source. 

Calculation of the theoretical wavelengths of  hydrogen gas using the Bohr Model. 

ERROR ANALYSIS

The uncertainty does not lie within the actual values based on the standard deviation model of uncertainty, and the wavelength between the 1st and 3rd line was not visible to the naked eye

CONCLUSION:

The spectra of visible light from the white light was verified and based on the uncertainty the values were also verified by the theoretical values. The white light helped find a means of calibration for the next portion of the experiment in order to verify the spectra of hydrogen. There were only three of the four lines that were seen that would indicate hydrogen in the spectra. The reason for the λ₂₄   to not be seen is that it was too close to the other lines which made it harder to see with the naked eye. The values of the wavelengths from the experimental side however could not verify the the theoretical values of hydrogen based on the uncertainty which was determined by standard deviation. Consistently, the experimental wavelengths all fell shortly under the true values of the wavelength. When calculating percent error the values all fall under 8% error which shows both precision and accuracy in the experiment. Therefore, the spectra of hydrogen can be verified in this experiment. Although, the second line could not be seen, based on the theoretical calculations there seems to be a hole where the value should be indicating that this spectra does indeed belong to hydrogen.