In this experiment we were provided a cereal box spectrometer to observe the emission lines of noble gases and hydrogen. Based on the scale readings on the spectrometer and the Balmer-Rydberg formula, their wavelengths and percent error were able to be extrapolated. Based on the literature values, the cereal box spectrometer proved its value as a decently accurate spectrometer. Introduction: Every element and subsequent atom associated emits light; also know as electromagnetic radiation, when in an excited state.
Analyzing this emitted light can give insight to the makeup and characteristics of them. The light given off by an energetically excited atom is not a continuous distribution of all possible wavelengths, but rather consists of a few wavelengths giving a series of discrete lines. Spectroscopy is the analysis of that emitted light and its dispersion into to it’s component wavelengths and colors. Niels Bohr explained the discrete spectrum of hydrogen? by relating it to the electron. Normally the electron in the hydrogen atom is located in the first energy-level.
When a hydrogen atom atoms gains energy, the electron moves from a lower energy-level to one of higher energy. The energy gained by the atom is exactly the amount of energy needed to move the electron from the lower energy-level to the higher energy-level. With its electron in a higher energy-level, the atom is now in an unstable, higher energy, excited state. The tendency is for electrons to occupy the lowest level available. So shortly after gaining the energy, the electron returns to a lower energy-level. Energy must be given up when this occurs, and the energy is lost as light.
Each line in the emitted light of hydrogen represents the movement of an electron from a specific outer level to a specific inner one. We judge this emitted light against the electromagnetic spectrum with a spectrometer. A spectrometer is an instrument that gathers light particles (photons) and is able to determine the chemical make-up of the source. A spectrometer breaks up a beam of light into its component colors. Usually it uses a prism or a diffraction grating. Light goes in as a beam of white light and is split into a rainbow. Particular atoms generate light at particular frequencies (colors) and so can be identified in the lab.
The electromagnetic spectrum is the range of all possible wavelengths of electromagnetic radiation. This range extends from sub-radio waves to gamma rays. Visible light falls within this spectrum. The light emitted by each element is independently different and has different “colors” that can be seen on the spectrum. The Balmer-Rydberg formula is used to describe the emission lines of hydrogen across the entire spectrum and not just visible light. The purpose of this laboratory experiment is to see the emitted wavelengths of elements through a spectroscope and calculate the wavelengths with the Balmer-Rydberg formula.
Then with the calculations, relate them to the atom. I believe that with the correct calculations and comparisons the wavelengths, each emission line will be able to be determined. Experimental The procedures as per the lab manual page 258 (Grossie, Underwood, 2012) were to first calibrate our spectroscope with helium. Looking at helium through the spectroscope, the emission lines where seen and recorded. That data was then put into Microsoft Excel and put into a graph. From the graph a formula was extrapolated. The spectroscope was used to observe and record the fours spectral lines of hydrogen.
The calibration plot from helium determine the wavelengths of each of the lines by extrapolation. Comparing the calculated wavelengths to those determined from the calibration plot, and then calculate the percent error for the values. Then the spectroscope was used to view the spectral lines of argon, krypton, neon and Xenon. These noble gasses are then calculated in the same manner as hydrogen. Data Results The wavelengths (? ) for helium for the calibration were given to us in our lab manual on page 261 (Grossie, D. , et al. 2012). With the spectroscope, the helium in the discharge tube was observed. The emission line scale eading and colors were then recorded on table 1. 1 which can be found below. These values where then put into an excel spreadsheet and graph was formed (table 1. 2). An equation was then extrapolated from the data that would give the experimental wavelength (expt ? ) values that will be used for later values. The trend line for table 1. 2 was established to see the relationship between wavelength and scale readings. Expt ? =a ? +b Expt ? =7. 1541 ? + 343. 12
The measuring and calculating of the emission lines in the Neon, Argon, Krypton and Xenon line spectrums yielded the data on tables 1. 4-1. 7. The calculated wavelength (Calc ? ) was determined by the Balmer-Rydberg formula. 1? =R(1m2-1n2) R=Rydberg Constant=1. 0968x107m-1 The percent error was then calculated by the following equation. error %=(calc ? -expt ? )calc ?
The helium trend line in table 1. 2 shows that as the longer the wavelength gets, higher the scale rating becomes. This is because the longer the wavelength is, the less energy it has. The emission lines of hydrogen were then observed and recorded on table 1. 3 with the scale readings. The m and n levels were already given to us on the table prior to the beginning of the lab.
Using the Balmer-Rydberg formula, the wavelength could be calculated. Using the calibration of helium, the experimental calculation was able to be determined with the equation extrapolated from excel. The two results gave rise to the error calculations. Comparing the hydrogen results with tables 1. 4 – 1. 7, its can be seen that there is a trend of the longer the wavelength is, the more percent error there is. Through our cereal box spectrometers, the emission lines of the low energy waves viewed a the color red are more broad than that of the high energy waves because theirs are much longer respectively.
This makes it more difficult to determine the exact scale reading. With the correct calculations as proposed, each emission line was able to be determined. Conclusion The ability to observe emission lines then decipher the element is a useful application in the fields of astronomy. Astronomers are able to view the emissions and determine the chemical make up of a specific object billions of miles away. The data collected indicated that as the lower the energy of the waves, there was a error percentage. This error is also from a cereal box spectrometer.
It can be inferred that there is an inherent amount of decreased precision in assessing the scale readings. Future experiments could still make use of the cereal box but also have a laboratory quality spectrometer to compare accuracy too. There could be significant human error in the construction of the cereal box versions. The results of this experiment, bar any inaccuracy, where still in line of the calibrated helium.
Grossie, D. & Underwood K. (2011). Laboratory Guide for Chemistry. “Atomic Spectrometry”, Wright State University. Dayton, OH.
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