Atomic Spectroscopy Lab

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Montana State University *

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141

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Chemistry

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Feb 20, 2024

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Atomic Spectroscopy Lab Ella Raisley Chemistry 141-13 TA: Dalton Compton 02/09/2020 Introduction : The purpose of the atomic spectroscopy lab was to find the Rydberg constant based on the spectral lines of light observed. The properties that were measured were the color within the diffraction of the light and the distance from the center point. The light diffraction was displayed on a whiteboard from an overhead projector. In order to measure the distances in millimeters, a meter stick was used. Light diffraction happens every day in the real world. For example, sunlight shining through clouds causes the light rays to be spread out, also known as diffraction. Procedure and Observations : In this lab all that was used was a spectroscope, a meter stick, an overhead projector, and light sources. The first light source that was observed through a spectroscope was white light. White light gave off a very continuous diffraction of colors. The white light included all of the colors of the rainbow (red, orange, yellow, green, blue, indigo, and violet) and displayed them very clearly. On the other hand, the florescent light gave off a very broken up diffraction of colors. It only had four visible colors of the rainbow, though it included all of them. Florescent light had red, orange, blue, and violet visible when it was observed through a spectroscope. In the next section of the lab helium and hydrogen spectrums were displayed on an overhead projector. First, the measurements from the center line for the helium spectrum were taken for the six colors observed. The colors observed were red, yellow, teal, blue, blue, and

violet. The colors were not spread out evenly amongst each other. Both the distance and wavelengths decreased as the colors went from red to violet. This was expected because longer wavelengths appear more red and shorter wave lengths appear bluer or violet. The next spectrum that was observed was the hydrogen spectrum. It was also projected on to the whiteboard and the center point was found. After, the measurements were found from the center line with a meter stick. There were only four colors observed in the hydrogen spectrum versus the six observed in the helium spectrum. The colors observed in the hydrogen spectrum were red, light blue, blue, and blue. Like the helium spectrum, the colors were not evenly spread out amongst each other. The wavelengths and distance both decreased from red to blue. There were many similarities between the helium and hydrogen spectrums, but they were also very different. The helium spectrum had more colors compared to the hydrogen spectrum. Data : The data shown below is from the helium spectrum that was observed earlier in the lab. Helium: Wavelength (nm) 667.8 nm 587.5 nm 501.5 nm 492.3 nm 471.3 nm 447.1 nm Color Red Yellow Teal Blue Blue Violet Distance (mm) 612 mm 529 mm 445 mm 418 mm 397 mm 344 mm (Table 1: Helium data that was observed. Wavelength (nanometers), color, and distance from the center point (millimeters) were all measured and recorded.)

The data shown below is the figure of the helium spectrum which was recorded above. 300 350 400 450 500 550 600 650 0 100 200 300 400 500 600 700 800 f(x) = 0.85 x + 138.48 Helium Distance (mm) Wavelength (nm) (Figure 1: Helium data. X-axis: distance from center point (mm). Y-axis: wavelength (nm).) The data below is from the hydrogen spectrum that was observed earlier in the experiment. Hydrogen: Wavelength (nm) 444.9 nm 461.0 nm 501.1 nm 640.6 nm Color Red Light Blue Blue Blue Distance (mm) 590 mm 426 mm 379 mm 360 mm (Table 2: Hydrogen data that was observed. Wavelength (nanometers), color, and distance from the center point (millimeters) were all measured and recorded.)

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The hydrogen figure that corresponds to the data in the table 2 is shown below. 300 350 400 450 500 550 600 650 0 100 200 300 400 500 600 700 f(x) = 0.85 x + 138.52 Hydrogen Distance (mm) Wavelength (nm) (Figure 2: Hydrogen data. X-axis: distance from center point (mm). Y-axis: wavelength (nm).) The Rydberg’s Constants were also found based off of the delta energy and the n values from the hydrogen data. ∆ Energy (Joules) N initial N final Rydberg Value (Joules) 4.47E-19 J 6 2 2.01E-18 J 4.31E-19 J 5 2 2.05E-18 J 3.97E-19 J 4 2 2.12E-18 J 3.10E-19 J 3 2 2.32E-18 J (Table 3: Shows the delta energy (joules), the initial/final n values, and the Rydberg values found from the delta energy and n values.)

The figure below displays the Rydberg constants that were found. The average Rydberg constant was 1.655x10 -18 ,when it was calculated by the line of best fit. 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.00E+00 5.00E-20 1.00E-19 1.50E-19 2.00E-19 2.50E-19 3.00E-19 3.50E-19 4.00E-19 4.50E-19 5.00E-19 f(x) = 0 x + 0 Rydberg's Constants Found (1/n-final^2)-(1/n-initial^2) Delta Energy (joules) (Figure 3: Rydberg’s Constants. X-Axis: (1/n Final 2 )-(1/n Initial 2 ). Y-axis: Delta Energy of the hydrogen data (joules).) Data Analysis & Calculations : In the first section of the experiment where white and fluorescent light were observed, there were no calculations used. The colors were only observed. In the second section of the experiment when the helium and hydrogen spectrums were observed there were many calculations used. •Rydberg constant value for each line: Rydberg constant= ∆E ( 1 nfinal 2 ) − ( 1 ninitial 2 ) (1a) Red: 4.47E-19 J ( 1 36 ) − ( 1 4 ) = 2.01E-18 Joules Light Blue: 4.31E-19 J ( 1 25 ) − ( 1 4 ) = 2.05E-18 Joules

Blue: 4.31E-19 J ( 1 16 ) − ( 1 4 ) = 2.12E-18 Joules Blue: 3.10E-19 J ( 1 9 ) − ( 1 4 ) = 2.32E-18 Joules The constants found were predicted because of the color spectrum and the color red’s intensity versus the color blue’s intensity. • ∆ E = hc / λ (1b) Red: 4.47E-19 J oules= ( 6.626 ∙ 10 − 34 )( 3.00 ∙ 10 8 ) 444.9 nm Light Blue: 4.31E-19 Joules= ( 6.626 ∙ 10 − 34 )( 3.00 ∙ 10 8 ) 461.0 nm Blue: 3.97E-19 Joules= ( 6.626 ∙ 10 − 34 )( 3.00 ∙ 10 8 ) 501.1 nm Blue: 3.10E-19 Joules= ( 6.626 ∙ 10 − 34 )( 3.00 ∙ 10 8 ) 640.6 nm This was expected because the color red has the most amount of energy in it. The amount of energy in joules decreases as the color spectrum moves from red to violet. • Percent error for Rydberg constant: known value − experimental value known value ∗ 100 (2a) % error for the hydrogen table: ( 2.18 ∙ 10 − 18 )−( 2.13 ∙ 10 − 18 ) 2.18 ∙ 10 − 18 ∗ 100 = -2.5% % error for the Rydberg constants found figure: ( 2.18 ∙ 10 − 18 )−( 1.656 ∙ 10 − 18 ) 2.18 ∙ 10 − 18 ∗ 100 = -24% This shows by using the table, the experimenter received a more accurate Rydberg constant compared to using a figure to find the Rydberg constant.

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• y=0.8512x+138.48 (Finding the wavelength of hydrogen) (2b) Red: y=0.8512(360 mm)+138.48= 444.9 nm Light Blue: y=0.8512(379 mm)+138.48= 461.0 nm Blue: y=0.8512(426 mm)+138.48= 501.1 nm Blue: y=0.8512(590 mm)+138.8= 640.6 nm These calculations were all expected because red has the shortest wavelength and the wavelengths increase as the color spectrum moves from red to violet. This means that the colors become less intense. •Average Rydberg value in Table 3: 2.13 ∙ 10 − 18 Joules (3a) •Average Rydberg value in figure 3: 1.66 ∙ 10 − 18 Joules (3b) The chemical formula for helium is Z while the chemical formula for hydrogen is H. They are both elements on the periodic table. There was more percent error when the Rydberg constant was found with the figure instead of finding it by calculating the average of the Rydberg constants found. Conclusion : The purpose of this experiment was to find the Rydberg constant based on the spectral lines of light observed. In part one of the lab, the experimenter observed the difference between white and fluorescent light when viewed through a spectroscope. The differences between the two were recorded. White light had a more continuous spectrum and contained all of the colors of the rainbow. Fluorescent light was very broken up in the spectrum and only had a few colors out of the rainbow. In part two, it was important for the experimenter to know to use Balmer Series because the final value of n was always 2. The Rydberg constant was found in two ways in this

experiment: by putting the data into a figure and finding the line of best fit and calculating it based on the average of the other Rydberg constants found. This experiment successfully found the Rydberg constant. The results that came from the figure were way less accurate than the results found when the average of the Rydberg constants were calculated. The percent error when the Rydberg constant was found using figure 3 was - 24.0% versus when it was found with table 3 it was only -2.5%. This big difference of -21.5% could possibly be from an outlier on the graph. Another possible reason why the percent error was off in both could be because the hydrogen gas was old or mixed with another substance when it was put into the light. Another reason why the percent error could be so off for the figure is from the Excel software. It could have not looked at all of the values, but just at their positions on the figure. Citations : Chemistry 141 Laboratory Manual . Christina Bahn and Hayden-McNeil, 2020.