Objectives Emission Spectroscopy Observe spectral lines from a hydrogen gas discharge tube Determine the initial and final energy levels for the electronic transitions associated with the visible portion of the hydrogen atomic emission spectrum. Use the results of the Bohr model of the hydrogen atom for your calculations. Observe the atomic emission spectra of several other elements using the gas discharge tubes Discuss the unsuitability of the Bohr model for atoms beyond hydrogen. Introduction Electrons in atoms can exist only in certain discrete (quantized) energy levels. Electrons may transition from one energy level to another via the absorption (or emission) of certain packets of energy. When an electron goes from a higher energy level to a lower energy level, the atom loses energy and emits a photon of light. Energy may be lost in the form of electromagnetic radiation with a frequency,, and an energy per photon of the radiation is proportional to The proportionality constant, h, is Planck s constant (h = 6.626 x 10-34 J-s). The absolute value of the change in the atom s energy, ΔE, is: ΔE = h We have to use the absolute value of ΔE because when the atom loses energy, ΔE is negative. Not using the absolute value would give a negative frequency which is, of course, non-sense. Niels Bohr developed the first theoretical model of the atom which could successfully explain the observed atomic emission spectrum of hydrogen. His approach was to assume that electrons moved in fixed circular orbits around the nucleus. He set the centripetal acceleration of the fixed orbits equal to the centrifugal force and found that electrons in a hydrogen atom was restricted to quantized energy levels described by E x J ( 1 n 2 ) where n is an integer. For the emission of light, Energy is released and, by convention, E<0. If we designate the initial energy level for an electronic transition as n i and the final energy level as n f, then the change in the atom s energy as a result of the transition is 1
ΔE x J ( 1 n f 2 1 n i 2 ) The frequency of the transition may be calculated using the equation ΔE = h. Naturally, these same equations can be used to calculate the frequency of the radiation absorbed when n f > n i. For an emission, n f < n i and ΔE < 0 while for an absorption, n f > n i and ΔE > 0. Once we have the frequency, we can also find the wavelength using c = λ, or we can combine the equations as: ΔE hc λ Figure 1 below schematically shows the spacing of the energy levels of the hydrogen atom. The figure also shows various series of transitions which are named for the scientists who characterized the series. Each emission in a given series has the same n f. The only series that you are able to see in this lab is the Balmer series. Using your eyes as the detector in this lab, you ll never see these transitions (they are outside of the wavelengths visible to the human eye). On the other hand, the energy changes associated with the Balmer series yield visible light. Thus, you ve already met part of one of the objectives of this lab. You know that the final energy level for all the electronic transitions you ll observe in this lab will be in the n f = 2 level. Other frequencies of light are emitted continuously, but are not visible to the human eye. The frequencies of light emitted in the Paschen series are in the infrared region of the spectrum. The energy changes associated with the Lyman series are so large that the frequencies of the emitted light are in the ultraviolet region of the electromagnetic spectrum (and not visible to the naked eye). They will be occurring, but you won t be able to see them. The Bohr model works well for the hydrogen atom. It gives the same results as the exact quantum mechanical solution. However, the Bohr model fails for any atom beyond hydrogen because it doesn t take into account the inter-electron repulsion present when there is more than one electron. You ll get a chance in this lab to observe the atomic emission spectra of several elements. The spectra are more complex than that of hydrogen because they have more electrons, thus making their energy level structures more complex. Remember, however, that you can t use the equation of the Bohr model to determine anything about the initial and final energy levels for these other elements. You ll also observe the characteristic flame spectra of sodium, potassium, and lithium.
Spectroscopes In order to see the individual colors (wavelengths) emitted by the hydrogen gas, you need to separate the emitted light into its components just as sunlight is separated into its components in a rainbow or by passing through a prism. A spectroscope essentially consists of something to separate the light into its components (the dispersive medium), a detector, and a way to measure wavelength or frequency. The
spectroscope you ll be using is pictured in Figure 2. Your spectroscope is a plastic box with a diffraction grating on one end to act as the dispersive medium and a scale on the other end to measure wavelength. The detector is your eye. You ll look through the spectroscope box at the emitting sample and read the wavelengths of the individual lines in the spectrum directly off the scale in the spectroscope. To ensure that you properly read the scale and that your spectroscope is calibrated, you ll first observe the emission spectrum of mercury using a modified fluorescent lamp. The wavelengths of the visible lines in the mercury spectrum are: Violet 405 nm (very faint to some people) Blue 436 nm Green 546 nm Orange/Yellow 578 nm Safety Precautions The gas discharge tubes use a high voltage power supply. DO NOT TOUCH the power supply or the discharge tubes when power is on. Your instructor will give you more information on how to safely operate the apparatus. Be careful when observing the flame spectra. It is easy to get too close, especially when looking through the spectroscope. Pre Lab Problems (answer on separate paper) 1. Determine the wavelength of light emitted when the electron in a hydrogen atom makes a Balmer series transition with each of the following values of n i: (a) n i = 3 (b) n i = 4 (c) n i = 5 (d) n i = 6 2. Determine the frequency of light emitted when the electron in a hydrogen atom makes a Paschen series transition with n i=6. In what region of the electromagnetic spectrum does this radiation lie? Equipment Spectroscope Gas discharge tubes containing various elements
Procedure 1. Your instructor will lead you through the viewing of spectra. Record your observations and try to describe the appearance of the spectra. 2. Observe and record the range of the spectroscope. What is the scale range of the spectroscope? What does this (in simplistic terms) correlate with? 3. View the mercury spectrum and make a calibration curve by plotting the observed scale reading vs. actual wavelengths of the mercury spectral lines, i.e., actual wavelength is the x-axis. Using the graphical analysis program, and draw a smooth curve through the points by using the linear regression routine. This will allow you to find the wavelengths of unknown spectral lines in a variety of emission spectra. 4. Observe the hydrogen gas discharge tube using your spectroscope. Record the general appearance of the spectrum and the wavelengths of each line. Use the calibration curve you generated from the mercury spectrum to determine the actual wavelengths for the hydrogen atom. Finally, using the Bohr model of the atom, determine the initial and final energy levels for the electronic transitions associated with each line of hydrogen spectrum. 5. Observe several other gas discharge tubes. Record your observations and try to describe the appearance of the spectra; your descriptions should be detailed enough to enable you to recall which element gave rise to the spectrum. 6. As a last viewing, a mystery gas will be shown; make an assessment of the identity of the gas {you may use whatever knowledge from everyday life, to 'researching' to assist you in this determination}. Cleanup Clean your lab area and return your spectroscope to its proper location before being signed out by your lab assistant. Completion (You will need to show the appropriate calculations for each of the below). Determine the actual wavelengths for the Hydrogen spectrum, using your calibration curve. Determine which transitions these wavelengths correspond to (from which energy level down to which energy level?).. Determine the energy required to completely remove an electron from hydrogen (you may assume that removal has occurred when the electron reaches the n=100 level).
Report: Emission Spectroscopy Name Lab Partner(s) Section Date performed Data Mercury Spectrum Range of the Spectroscope From: To: Observed Actual Color Wavelength Wavelength Hydrogen Spectrum Observed Actual Color Wavelength Wavelength n i n f Other Spectra Element Appearance of Spectrum 7