Experiment 14: Color and Spectra

Introduction

The purpose of this experiment was to understand how different elements only emit certain wavelengths and to identify an unknown element based on the wavelengths the element emits. This experiment hired the concept of the light ray diffraction. When a light source is shone through a slit, different colors with distinct wavelengths interfere constructively with each other, creating different colors at different positions. By knowing the distance between the light source and the color of interest, the wavelength of the interested color can be computed by using λ = Dd/L when the distance between the light source and the colored filter is very small compared to the slit. Alternatively, λ = Dd/√(L²+D²) can be used. The following image shows the derivation.  

Derivation of λ = Dd/√(L²+D²)

This experiment was conducted using a light source, colored filter, and two 1-meter sticks. The light source was shone to the colored filter which located 1 meter from the light source. Another 1 meter stick was located beside the colored filter in order to measure the distance of each color spectrum from the light source. The color spectrum was seen through the colored filter, and the distance between the light source and each type of color was recorded. A plot between the experimental and actual wavelength was constructed in order to made adjustment in further experimentation. A hydrogen light source was obtained, and the distance of each color from the light source was measured in same manner. Lastly, an unknown element light source was obtained to find the wavelength the element emits. The unknown element was identified based on the wavelengths.

Figure 1: The light spectrum from a white light source

Figure 2: The unknown light source (left) and the light spectrum from the unknown light source (right)

Figure 3: The light spectrum from a neon light source

Data and Analysis

Table 1: Wavelengths of visible light spectrum from a white light

Color	Range of the distance between the light source and the light spectra(cm)	Average distance(cm)	Average experimental wavelength(nm)	Average actual wavelength(nm)
Violet	18.00-22.50 ± 0.50	20.25 ± 0.50	405 ± 10	415
Blue	22.50-24.20 ± 0.50	23.35 ± 0.50	467 ± 10	463
Green	24.20-27.50 ± 0.50	25.85 ± 0.50	517 ± 10	533
Yellow	27.50-30.00 ± 0.50	28.75 ± 0.50	575 ± 10	580
Red	30.00-38.50 ± 0.50	34.25 ± 0.50	685 ± 10	685

Table 2: Wavelengths of visible light spectrum from a H­₂ light source

Color	Distance between the light source and the light spectra(cm)	Experimental wavelength(nm)	Adjusted experimental wavelength(nm)	Actual wavelength(nm)
Violet	19.90 ± 0.50	398 ± 10	405 ± 23	410
Green	22.10 ± 0.50	442 ± 10	449 ± 23	434
Yellow	27.00 ± 0.50	540 ± 10	545 ± 23	486
Red	31.60 ± 0.50	632 ± 10	636 ± 23	656

Table 3: Wavelengths of visible light source from unknown #4 light source

Color	Distance between the light source and the light spectra(cm)	Experimental wavelength(nm)	Adjusted experimental wavelength(nm)
Violet	23.40 ± 0.50	468 ± 10	474 ± 23
Green	27.20 ± 0.50	544 ± 10	549 ± 23
Yellow	29.90 ± 0.50	598 ± 10	602 ± 23
Orange	31.10 ± 0.50	622 ± 10	626 ± 23
Red	33.00 ± 0.50	660 ± 10	663 ± 23

Graph 1: Experimental vs. Actual wavelength

Conclusion

                According to table 1, the experimental wavelengths were within the uncertainty of experimental errors, except the green spectrum. When the experimental vs. the actual wavelength was constructed as in graph 1, the relationship between the experimental and actual wavelength was obtained. This was used to obtain wavelengths that would be within visible range when spectrum from hydrogen and unknown light source were computed. As shown in table 2, the violet spectrum from the hydrogen gas was not within the range of visible light. After computing using the equation between the experimental and actual relationship, all of the wavelengths became within the visible range. Additionally, the adjusted wavelengths became within the uncertainty, except the yellow spectrum. This error was possibly contributed because the range of distinct color of light did not appear clearly. Hence, there were uncertainty in measurement of the distance between the light source and the color spectrum.          

                 Based on the wavelengths obtained from unknown light source as shown in table 3, the unknown gas #4 was identified to be neon gas since the peak wavelengths matched the neon spectrum most among the different elements in the periodic table. the neon light spectrum is shown in figure 3.