Spectroscopy of the Hydrogen Atom

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1 CHEM 121L General Chemistry Laboratory Revision 1.0 Spectroscopy of the Hydrogen Atom Learn about the Interaction of Photons with Atoms and Molecules. Learn about the Electronic Structure of Atoms. Learn about Spectroscopy. In this laboratory exercise, we will probe the behavior of the electron within the Hydrogen atom via Emission Spectroscopy. We will observe the line spectrum of excited Hydrogen atoms and measure the wavelength of each spectral line. This will allow us to generate a diagram of the energy states for the electron of the Hydrogen atom. Probing the behavior of electrons within atoms is problematic; atoms themselves are far too small to be seen and their presence must be inferred, and the electron itself is a quantum mechanical object. However, understanding the behavior of these electrons is important because this behavior determines an atom s chemistry. Thus, we must find an indirect probe of the electronic behavior of an atom. It is found that useful probes of this behavior are the photons of light which interact with an atom. If an interacting photon s energy matches that of an electronic transition within the atom, the photon can be absorbed. Conversely, an electronically excited atom can relax and emit a photon whose energy matches the atom s electronic transition. These photons are directly observable; therefore they provide us with a window on the behavior of electrons within an atom. Photons are quantum mechanical objects that exhibit a Wave-Particle Duality. The wavelength ( ) of a photon is related to its speed (c) via: c = (Eq. 1) where is its frequency. In a vacuum the speed of a photon is c = x 10 8 m/sec. Its energy (E) is then related to its frequency via: E = h (Eq. 2) where h represents Planck s constant; h = x Jsec. Photons can cover a wide range of energies, from very low energy Radio Waves to high energy Gamma Radiation. This Electromagnetic Spectrum of photon wavelengths is represented below:

2 P a g e 2 Typical electronic transitions within atoms and molecules are such that the corresponding photons have energies in the Visible and Ultraviolet regions of the spectrum. If a photon of the correct Energy impinges on an atom, such that this energy matches the energy required for an atomic quantum state transition, the photon can be absorbed: This phenomenon will result in a dark line in the rainbow of colors emerging from a sample radiated with White Light. Conversely, if an atom that has previously been excited into a higher quantum state relaxes, a photon who's Energy matches the difference in state energies can be emitted:

3 P a g e 3 This will appear as distinctly colored light emitted from the excited sample. In these cases, the Energy difference between the participating quantum states is related to the Energy of the photons via: E = E photon = hc / (Eq. 3) Thus, the photons absorbed or emitted by a sample of the atom in question are a direct probe of the energy difference between quantum states of that atom. In the case of emissions from excited atoms, observing emitted photons of multiple wavelengths implies many quantum states may be involved in producing the spectrum. For example, three quantum states can produce emitted photons of three different wavelengths: Visually we see these photons as a characteristic color emitted by the sample. For instance, excited Sodium (Na) atoms emit visible photons of wavelengths nm, nm, and nm; with the latter two, called the Sodium D-Lines, being much more intense than the first one. Thus, the yellow color we see emitted by Na atoms is dominated by these two intense D-Lines, which occur in the Yellow region of the spectrum. (This is why sodium vapor lamps have a yellow hue to them.)

4 P a g e 4 Sodium Vapor Lamp "Sodium-glow" by Jurii - The photons emitted by an atom can be separated according to wavelength by passing the emitted light through a dispersing element, such as a prism or diffraction grating, to produce a series of spectral lines; each line corresponding to photons of a given wavelength. Identifying which quantum states are involved in the emission of photons of a particular wavelength is usually difficult and will not, in general, be considered here. For our purposes, we will excite our atoms in a gas discharge tube; a glass tube which contains a gaseous sample and is fitted with metal electrodes at either end. The tube is placed in a power supply, which impresses a high voltage across the tube, sending an electrical discharge through the tube, and thereby creating a plasma of excited atoms within the tube.

5 P a g e 5 In the resulting plasma, the H 2 molecules dissociate and leave the resulting H atoms in an excited state (H*). H 2 2 H* (Eq. 4) H* H + photon (Eq. 5) These excited atoms will subsequently relax, giving off photons corresponding to the energy differences between associated quantum states. We will examine the resulting glow by passing this light through a dispersing element, such as a prism or diffraction grating, to disperse the photons according to their wavelength. A diffraction grating is a glass element ruled with a very large number of equally spaced slits. Reflection off the various slits results in an interference pattern which diffracts the light. Diffraction Gratings The wavelength of the diffracted light is related to the angle of diffraction according to: = a sin / n (Eq. 6) where a is a constant associated with the number of lines per unit length of the grating and n is the order of the diffraction spectrum; usually n=1 for our spectra. We will view the resulting spectral lines thru a spectroscope that includes a slit for focusing the light from the discharge tube, a diffraction grating and a rotatable viewer to find the spectral lines.

6 P a g e 6 The basic procedure for measuring the wavelength of a spectral line is to align the grating perpendicular to the spectroscope's collimator, place the discharge tube in front of the entrance slit, adjust the slit width to a minimum and then observe the undispersed light source and make a reading of this "zero diffraction" angle; o. The rotating telescope arm is then rotated into line with the desired spectral line. The resulting diffraction angle ' is then measured. The angle of diffraction for this spectral line is then obtained by difference. = ' - o (Eq. 7) The first model of the Hydrogen atom to explain these spectral lines was put forth by Neils Bohr in In this model, the electron orbits the nucleus in quantized orbits. In its most relaxed or Ground State, the electron orbits very close to the nucleus. When excited, the electron moves into a higher energy orbit farther from the nucleus. When it relaxes, the electron moves back to an orbit closer to the nucleus, emitting a photon in the process. Unfortunately this model, although predictive for the Hydrogen atom, has some physically unappealing features and is not extendable to the electronic behavior of atoms of other elements. Even Helium, which has only one additional electron, has a much more complex electronic spectrum than that of Hydrogen. To illustrate this, we will also observe the visible lines in Helium s discharge spectrum.

7 P a g e 7 Pre-Lab Safety Questions 1. What kind of damage can occur to your eyes due to exposure to Ultraviolet (UV) Radiation? Below what wavelength radiation should you be concerned about UV exposure? Above what intensity radiation should you be concerned about UV exposure? 2. What kind of eye protection must be worn to prevent eye damage due to UV radiation? 3. Other than the present lab, in which lab were we concerned about eye damage due to UV radiation exposure?

8 P a g e 8 Procedure Directions for how to make diffraction angle measurements using a diffraction grating in the spectroscope are provided in the appendix. You should review these directions and follow them in making your measurements. 1. The spectroscope should already be leveled, focused and aligned. If you suspect that this is not the case, consult with your laboratory TA. 2. Place the Hydrogen discharge tube into the power supply and align it with the spectroscope's entrance slit. Adjust the position of the tube such that you can view a bright undiffracted source line in the eyepiece of the telescopic arm. Adjust the slit width so as to obtain a bright but narrow source line. 3. Align the telescope arm such that the undiffracted light source line is in the vertical crosshair. Make an initial angle reading; o. 4. Now rotate the telescope so as to sight in on one of the spectral lines. Again, make sure the spectral line is in the vertical cross-hair and make an angle reading; '. 5. Repeat this procedure for all four of Hydrogen's spectral lines; Red, Blue/Green, Violet and faint Violet. 6. Replace the Hydrogen discharge tube with that of Helium. Repeat the alignment procedure and merely observe the spectrum of Helium. Record your observations.

9 P a g e 9 Data Analysis 1. Examine the complete emission spectrum for Hydrogen provided in the Appendix. (We are only able to observe the "visible" spectral lines of Hydrogen's spectrum; the so-called Balmer spectral lines. Spectral lines occurring in the UV and IR regions of the spectrum are not observable by the naked eye. The lines which occur in the UV region of the spectrum, Lyman Lines, are given in the spectrum of the Appendix; as are the Paschen IR lines.) Determine the wavelengths of the emission lines you observed. For our diffraction grating, a = 3.3 x 10-3 mm. Use the wavelengths of the lines reported in the Appendix to determine the percentage error in your wavelength measurements. 2. Calculate the photon energies for each spectral line you observed. 3. Prepare an Energy Level Diagram of quantum states which are responsible for the emission lines you observed. For this diagram, assume all the Balmer Lines terminate in the same quantum state. (This state is designated with quantum number n = 2.) Provide quantum number designations (n = 3, 4, 5,...) for your quantum states in the Energy Level Diagram. 4. Identify the orbits in the Bohr Model of the Hydrogen atom responsible for each quantum state. The Bohr Model provides that the radius of the electron s orbit is given by: r = x n 2 [Angstroms] (Eq. 8) where n is the state s quantum number. Calculate the radius of each of these orbits. 5. Wavelengths for all the visible spectral lines for Helium can be found at: Assign wavelengths to all the spectral lines you observed for Helium. 6. The following spectral lines are due to the indicated transitions: Line Transition nm 3d 2p nm 4d 2p What is the wavelength of the spectral line corresponding to a 4d 3d transition? In what region of the spectrum does this spectral line occur?

10 P a g e 10 Post Lab Questions 1. What is the Ritz Combination Principle? 2. Examine the emission spectrum of the Hydrogen atom provided in the Appendix. The first two Lyman Lines are due to n = 2 to 1 and n = 3 to 1 quantum state transitions. Use the photon wavelengths of these lines to calculate the energy differences for the associated states. Do the same for the first Balmer Line, which is due to a n = 3 to 2 quantum state transition. Are the results internally consistent? Explain. A simple energy Level Diagram may be useful. 3. Determine the circumference of the second Bohr orbit of the Hydrogen atom. Use this to determine the wavelength of the electron in this orbit; the electron's wave must consist of an integral number of wavelengths about its orbit's circumference (Why?). orbit circumference = n (Eq. 9) Finally, determine the velocity v of the electron in this orbit using de Broglie's prescription for the wavelength of matter waves. = h / mv (Eq. 10) What percentage of the speed of light is this velocity? 4. What is the Correspondence Principle?

11 Appendix - Complete Emission Spectrum of Hydrogen P a g e 11

12 Appendix - Pasco Scientific Student Spectrometer Manual (partial) P a g e 12

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